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Spectroscopic characterization of novel cluster ions

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Title:
Spectroscopic characterization of novel cluster ions
Creator:
Lessen, Daniel E., 1962-
Publication Date:
Language:
English
Physical Description:
xi, 310 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Atoms ( jstor )
Binding energy ( jstor )
Electronics ( jstor )
Energy ( jstor )
Ground state ( jstor )
Ions ( jstor )
Lasers ( jstor )
Molecules ( jstor )
Photolysis ( jstor )
Vibrational frequencies ( jstor )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Dissociation ( lcsh )
Transition metals ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Summary:
Diatomic molecules, Photodissociation, Electronic spectroscopy.
Thesis:
Thesis (Ph. D.)--University of Florida, 1992.
Bibliography:
Includes bibliographical references (leaves 303-309).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Daniel E. Lessen.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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29233126 ( OCLC )
AJN6897 ( NOTIS )
AA00004743_00001 ( sobekcm )

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a'


SPECTROSCOPIC CHARACTERIZATION OF NOVEL CLUSTER IONS


















By

DANIEL E. LESSEN


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1992














ACKNOWLEDGEMENTS


The completion of this work would not have been possible

without the help of the other members of the research group:

Dr. Philip Brucat, my principal advisor, and fellow graduate

student Robert Asher. Dr. Brucat, served as scientific

mentor, motivator and friend. His enthusiasm in the quest for

scientific knowledge was infectious. In the beginning years

of my graduate career, it was Phil who taught me the art of

many different occupations besides chemist: namely,

electrician, machinist, plumber, and computer programmer.

I would like to thank Robert Asher, not only for his

friendship, but for sharing the physical and mental burden of

operating the experimental apparatus. Much of the research

presented in this Dissertation is a consequence of effective

teamwork between Robert and myself.

Special thanks go to my wife, Christine, for her patience

and support in all those trying moments.

I dedicate this Dissertation to my parents. Without

their support throughout my educational career I would not

have succeeded in this accomplishment.



















TABLE OF CONTENTS


ACKNOWLEDGEMENTS .

LIST OF TABLES .

LIST OF FIGURES .

ABSTRACT .

INTRODUCTION .

EXPERIMENT .
Overview ....
Beam Generation .
Mass Selection .
Optical Spectroscopy .
Computer Control .

INDUCTIVELY BOUND DIATOMICS


Threshold to Photodissociation .
Resonant Photodissociation of VAr*


. ii

. V

. vii

. x

. 1

. 7

. 10
. 19
. 27
. 36


Sand
. .
and


Photodissociation of CoAr and CoKr .
Resonant Photodissociation of ZrAr+
Photodissociation of CaKr .
Discussion .

DIATOMIC POTENTIAL ENERGY SURFACES .
Analytic Potentials .
Vibrational Eigenvalues from
Approximation .


VKr*
. .
* .
. .
. .

. .
. .
the
. .


. .
. .
WKB
. .

. .


METAL RARE-GAS CLUSTERS .


METAL CATIONS WITH PHYSISORBED POLYATOMICS .
Predissociation of V(OCO)* .
Vibration Structure of Electrostatically Bound V+-
(H20) .. .. .
Resonant Photodissociation of V(NH) .
Resonant Photodissociation of Cr(N2) .
Resonant Photodissociation of Ca(N2). .


42
42
54
74
91
105
108

116
116

119

133

143
143

154
162
165
167


iii


. .









METAL-METAL SYSTEMS . 171
Threshold Photodissociation of Cr2 186
Photodissociation of Ca2 .. 194

CONCLUSIONS . 199

APPENDIX A ELECTRICAL CIRCUITS .. 203

APPENDIX B COMPUTER CODE ... .205
WKB Grid Program .. 205
CAMAC Low Level Routines .. 213
CAMAC Header File .... 220
Control Program ... 220
Supporting Assembly Language Routines .. .258

APPENDIX C ANALYTIC PAIR POTENTIALS .. 284
Lennard-Jones Potentials ... 284
Born-Meyer Potential .. 291

APPENDIX D UNASSIGNED PHOTODISSOCIATION SPECTRA 295

REFERENCES ... 303

BIOGRAPHICAL SKETCH . .. .310















LIST OF TABLES


Table 1. Optogalvanic Positions for Neon. ... 31

Table 2. Ground State Spectroscopic Parameters for
NiAr+ and CrAr.. .. 52

Table 3. Line positions for "V40Ar* and "VIKr* in
wavenumbers. . ... 58

Table 4. Spectroscopic Parameter for VAr+ and VKr+. 71

Table 5. Line positions of assigned 59Co40Ar+
transitions in wavenumbers. .. 80

Table 6. Line positions of assigned 5Co'Kr' vibronic
transitions in wavenumbers. .. 81

Table 7. Experimental Molecular Constants for 59Co4Ar+
and 5CoMKr+ in cm'.. 88

Table 8. Line Positions for assigned vibronic
transitions of 9Zr40Ar+ in wavenumbers. ... 94

Table 9. Unassigned line positions (cm-') for "Zr40Ar+
grouped by progression. 94

Table 10. Spectroscopic Parameters of Excited State in
ZrAr+. . ... 98

Table 11. Dissociation Energy for ZrAr+ Excited
States. . ... 101

Table 12. Ground State Adiabatic Bond Strength. 109

Table 13. Spectroscopic Parameters for Excited
States. . ... 109

Table 14. WKB Parameterization of Born-Meyer Potential
with Experimental Eigenvalues. .. 125

Table 15. Line Positions for R2PD of Ni,+ (cm'). 181









Table 16.

Table 17.

Table 18.

Table 20.

Table 22.


Excited State Parameters for Metal-Ligands.

Ground State Adiabatic Bond Strength. .

Lennard-Jones [8,4] Relations. .

Lennard-Jones [6,4] Relations. .

Lennard-Jones [12,4] Relations. .


200

201

288

289

290














LIST OF FIGURES


Figure 1. Experimental Apparatus. 9

Figure 2. Cross Section of Source Block. .. 12

Figure 3. Mass Spectrum of Cobalt Helide Cations. 22

Figure 4. Mass Spectrum of Aluminum Anions. 24

Figure 5. Photofragmentation of Co 26

Figure 6. Laser Dye Curve for Rhodamine R6G. ... 28

Figure 7. Optogalvanic Transitions for Neon. 30

Figure 8. Error in Quantel Dye Laser. .. 33

Figure 9. Doppler Shift for Coaxial versus Cross beam
Photoexcitation of V(OCO)*. ... 35

Figure 10. Sweet Spot of Solenoid Pulse Valve. 41

Figure 11. Photodissociation Threshold for NiAr*. 44

Figure 12. Laser Fluence Dependence for
Photodissociation of NiAr*. .. 46

Figure 13. Isotopic Shift for Photodissociation of
NiAr ... .... .. 48

Figure 14. Photodissociation Threshold for CrAr+. 51

Figure 15. Resonant Photodissociation of VAr. 55

Figure 16. Vibrational Fit for VAr* and VKr 61

Figure 17. Residuals to the Vibrational Fit of VAr*. 63

Figure 18. LeRoy-Bernstein Fit for VAr+ and VKr. 69

Figure 19. Vibrational Binding Energy for VAr* and
VKr . 73


vii










Figure 20. Resonant Photodissociation of CoAr....

Figure 21. Photodissociation Spectrum of CoKr*
Isotopes. . .


Figure 22.

Figure 23.

Figure 24.
CoKr+ S

Figure 25.

Figure 26.

Figure 27.

Figure 28.

Figure 29.

Figure 30.

Figure 31.
States

Figure 32.

Figure 33.

Figure 34.

Figure 35.
CoAr6+.

Figure 36.

Figure 37.

Figure 38.

Figure 39.

Figure 40.

Figure 41.

Figure 42.


V(H20) . .


Vibration Fit to Band Origins for CoKr States83

Dissociation Limits of CoAr.. 87

Vibrational Binding Energy for CoAr and


states.


. 90


92

97

99

103

107

123


127

129

131

132


. .












ted
. .

* .

. .

* .


. . 135


Relative Abundance of VAr,+ and CoAr..

Collision Induced Dissociation of CoArn,'.

Stick Plot of V(OCO) Photodissociation.

Photoexcitation Spectrum of V(OCO). .

[VO+]/[V] Branching Ratio ....

Energetics for Photodissociation of VCO2.

Resonant Photofragmentation Spectrum of


138

140

145

148

150

153


156


viii


I


Resonant Photodissociation of ZrAr+.

Isotopic Shifts for ZrAr. .

Vibrational Fit of ZrAr. .

ZrAr C State Dissociation Limit .

Photodissociation of CaKr+. .

RMS Contour Plot of CoKr* C state.

Potential Energy Curves of CoKr Exci


WKB Error for Morse Potential. .

Residuals to WKB. .

Potential Energy Surfaces for VKr. .

Mass Spectra for the Uniquely Stable










Figure 43. Isotope Shifts of V+(8OH2) minus V+('6OH). 159

Figure 44. Photodissociation Spectra of Deuterated
Isotopes of V(Water)+ ... 161

Figure 45. Resonant Photodissociation of V(NH3)+. 163

Figure 46. Photodissociation Threshold for Cr(N,)+ -
Cr + N . .. 166

Figure 47. Vibrationally Excited Photofragments of
Ca(N2)+. . 168

Figure 48. Mass Spectrum of Argon Seeded Nickel Beam. 173

Figure 49. Photofragmentation of NizAr. ... 177

Figure 50. Resonant Two-Photon Dissociation of Ni2. 180

Figure 51. Photodissociation Threshold of Cr2 Cr + Cr187

Figure 52. Cr2 Photodissociation Mechanisms. 189

Figure 53. R2PD of Cr2,. .. 191

Figure 54. Resonant Photodissociation of Ca+. 195

Figure 55. Valve Driver Circuit. 203

Figure 56. Bias Conditions for Microchannel Plate
Detector. .. 204

Figure 57. Photodissociation Spectrum of Fe. 296

Figure 58. Photodissociation of NiO -* Ni + 0. 297

Figure 59. Photodissociation Spectrum of ZrOAr+ ZrO+
+ Ar. . 298

Figure 60. Photodissociation Spectrum for Zr(OCO)+ -
Zr+ + OCO. .... .299

Figure 61. Photodissociation of Co(HOH) Co+ + H20. 300

Figure 62. Photodissociation of Co(OCO)+ Co+ + CO2. 301

Figure 63. Photodissociation of Co(NN)+ Co+ + N. 302














Abstract of Dissertation Presented to the Graduate
School of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy

SPECTROSCOPIC CHARACTERIZATION OF NOVEL CLUSTER IONS


By

Daniel E. Lessen

December 1992

Chairman: Philip J. Brucat
Major Department: Chemistry

A variety of molecular ions, many without conventional

covalent bonds, have been generated by adiabatic supersonic

expansion of a laser driven plasma and spectroscopically

probed in the visible region. Photofragmentation of these

mass selected ions with a tunable visible laser reveals

spectroscopic parameters of both excited and ground states.

Specifically, the spectra of the systems of Cr(N2)*, CrAr, and

NiAr, exhibit a sharp change in photodissociation cross

section corresponding to a diabetic threshold from which the

ground state binding energy is determined. Resonant

photodissociation spectra display sharp vibronic features of

bound quasi-bound transitions corresponding to excited state

vibrational progressions for the inductively bound diatomic

systems of VAr+, VKr+, CoAr+, CoKr+, CaKr+, and ZrAr+.

Often, analysis of the vibronic transitions for a given system








will accurately determine the excited state vibrational

frequency, anharmonicities, and electronic origin besides the

ground and excited state binding energy. Additionally,

vibrational structure for many of these diatomic systems is

used to parameterize a variety of analytic potentials that

incorporate a charge-induced dipole attractive term via the

semiclassical Wentzel-Kramers-Brillouin method.

Transition metal cations with physisorbed polyatomic

adducts are spectroscopically probed in the visible region.

Resonant photodissociation spectra of V(H2O)+, V(CO2)+, and

V(NH3)+ are discussed. The photodissociation spectrum of

V(H2O)+ reveals an electrostatically bound system. The

resonant photodissociation of the system V(CO2)+ displays two

distinct dissociation pathways that arise from the same

photoexcited state: V(OCO) V+ + CO2 and V(OCO) -* VO + CO.

A cursory treatment of diatomic metal-metal cation

behavior is discussed from the one-photon dissociation

spectrum of Ca2+, the resonant 2-photon dissociation spectrum

of Ni2+, and the threshold photodissociation spectrum of Cr+.














INTRODUCTION


The description of chemical phenomena at a molecular

level is the ultimate goal of any chemist. Unfortunately such

a goal would require a detailed knowledge of the forces

between all the present atoms, a formidable task for any

sizable system. One may, however, dissect a large system or

chemical reaction into smaller model systems consisting of a

few isolated atoms. A small, experimentally tractable system

may then be chosen to model a chemically interesting part of

the extended system; for instance, a solvated ion with its

nearest neighbors or the active atoms in the discrete step of

a reaction mechanism may be modeled. In this way, a

complicated system may be understood by the behavior of its

integral subunits.

Under this philosophy, both experimentalist and theorist

have labored to understand the quantal details of interatomic

interactions in the smallest of such model systems, the

diatomic. Due, in part, to their ease of production and good

stability, many main-group diatomic systems have been

successfully described through the synergistic effort of

experiment and theory.' The forces found in main-group

diatomic molecules, for example H2, N2, and CO, are








2

quintessential examples of covalent interactions. The

understanding of the nature of covalent bonding is currently

being extended to include the effects of d orbitals by the

study of diatomics from the transition-metal series.2

Part of this dissertation will discuss the behavior of

three transition metal diatomic systems specifically, Ni2+,

Cr2+, and Ca2, via spectroscopic information. Although

calcium is not considered a transition-metal, many of its

excited states will involve 3d orbitals. The interatomic

forces in these systems are expected to display some covalent

character, but also, inductive and electrostatic forces will

be present since the diatomic systems are charged.

Interestingly, a molecular orbital picture for the neutral

analogues, Cr2 and Ca2, suggests an adiabatic bond order of six

and zero, respectively. Experimentally, the chromium neutral

dimer has been found to have a surprisingly small bond

strength. While the calcium dimer is found to be bound via

van der Waals forces in difference to the zero bond order

prediction of molecular orbital theory.

The importance of d orbitals in chemical interactions

extends beyond their role in metal-metal bonding to their

ability to lower the activation barrier for many reactions.

Transition metal containing molecules and surfaces are

important in the catalysis of many chemical reactions both at

interfaces3 and in solution.4 The effectiveness of such

catalysts is derived, in part, from partially-filled d









3

orbitals that provide low-energy, short-term electron sites

along the reaction coordinate. Much insight will be gained by

an accurate description of the pair potential between a

transition metal and a reactant. Within this dissertation we

will present the results from the spectroscopically probed

system of V(OCO)+. Photodissociation spectra of this system

reveal an energy barrier of 1.6 eV to cleave a carbon-oxygen

bond to form VO'and CO. The bond energy of the carbon-oxygen

bond is ca. 5.43 eV in the gas phase molecule.5

As previously mentioned, the cations of homonuclear

diatomic molecules will exhibit non-covalent interactions as

well as covalent interactions. Empirically, an interaction

may be described as consisting of some percentage of the

following types of force: covalent, electrostatic, inductive,

and dispersive. Although covalent interactions are important,

they cannot account for the behavior of solute-solvent

chemistry, or surface adsorption, for example. Solute-solvent

behavior, especially ion-solvent systems, will be dominated by

electrostatic and inductive forces.

Small gas-phase isolated systems, consisting of an ion

solvated with a number of water or ammonia molecules, have

been used as models of solute-solvent behavior before.6'7'8'9'10

These high-pressure mass spectrometric studies are able to

quantify the thermodynamics of solvent-ion binding as a

function of the number of solvent molecules. However, due to

their size, the solvated ions have not been spectroscopically









4

probed, and therefore little is known about the configuration

or potential energy surface of these systems.

To simplify the study of electrostatic and inductive

forces, one may isolate a specific pair (an ion with an atom

or molecule) that contains virtually no covalent forces.

Through the formalism of classical electrostatics, the

interactions between ions, dipoles and other multipoles may be

expressed as the sum of separate contributions. The

attractive part of an electrostatic potential for a metal ion

and a water molecule would consist of a charge-dipole term, a

charge induced-dipole term, and a charge-quadrupole term.

As an initial step in understanding the chemical behavior

of a solvated metal ion, one may begin with the study of the

most chemically simple solvent imaginable, a rare gas. A

rare-gas atom possesses no permanent dipole, and it is

virtually inert. The metal ion to which this polarizable

partner is bound will have a considerably lower ionization

potential: therefore, charge transfer is minimal. A single

cation with a rare-gas adduct will display binding

interactions that are dominated by inductive forces, and

provide an ideal system to begin the understanding of physical

forces found in solution chemistry. All solvents, monatomic

or polyatomic, will have an inductive contribution to the

total solvation energy.

A rare-gas solvent is not novel. Liquid krypton and

liquid argon have been used to slow the kinetics of metastable








5

transition-metal carbonyl reactions."'12 Significant effort has

also been given to the isolation of charged species in rare-

gas matrices.13"14'"5 But how isolated are these ions? As will

be shown, the interaction of a transition-metal cation is

significant, ca. 0.5 eV. Thus, for optical studies of ions in

a matrix, large spectral shifts may be expected. It is

reasonable that the behavior of cation rare-gas systems be

described in order to understand the role of the matrix

environment with an ionic species.

Within this dissertation, spectroscopically acquired data

will be presented on several small cluster ions, specifically,

the number of atoms in the systems = 2 10, that exhibit

binding dominated by electrostatic or inductive forces. Major

emphasis is placed on the characterization of several

transition-metal cations with rare-gas adducts. The

understanding of the nature of inductive forces from these

systems will then lend support to the analysis of metal

cations with physisorbed or electrostatically bound polyatomic

molecules such as N2, CO2, or H20. Direct comparison between

the systems of VRg+ (Rg = Ar, Kr) and V-H20O suggests that

inductive forces will contribute significantly to the aqueous

solvation energy of a monovalent cation.

In some cases, the vibrational information for metal-

cation rare-gas diatomic systems is so extensive that over 80%

of the total bound levels, which cover ca. 99% of the

potential energy surface, are experimentally observed. This








6

provides a unique opportunity to accurately determine both the

vibrational frequency, and dissociation energy. In addition,

the extensive vibronic data may be used to parameterize some

simple analytic potential functions over the full potential

surface. An accurate knowledge of the pair potential will

provide a powerful tool with which extended solutions may be

modeled.














EXPERIMENT


Overview



The experimental apparatus was designed to generate and

gas-phase isolate a variety of internally-cold cluster ions

for photo-interrogation. Both types of systems presented in

this dissertation, metal-metal and metal-ligand, require

unique conditions for optimal production. Inductively bound

species, by nature, such as transition-metal rare-gas

diatomics are particularly troublesome to make routinely due

to their weak binding interactions. Sufficient quantities of

refractory material must be atomized, ionized, and then

internally cooled before physisorption of rare-gas atoms to

the ionic site is possible. Production of transition-metal

rare-gas species, therefore, involves an extreme change in

temperature, spanning vaporization to condensation. This

seemingly improbable set of conditions is achieved by the

combination of a laser driven plasma and supersonic expansion.

A laser driven plasma is seeded within an inert carrier

gas, usually helium. Collisional cooling initializes cluster

formation. Subsequent adiabatic expansion results in the

generation of a variety of internally cool aggregates. Such








8

techniques have been successfully used to generate internally

cool neutral clusters of refractory material previously.'6

This technique has also been applied with success to the

formation of both negative and positive metal cluster ions.7

Mass selection of the molecular ion beam provides a

microscopic window into the success of the expansion technique

for generating a given system. A variety of experimental

conditions, such as the backing pressure and laser

vaporization fluence, may be adjusted to maximize the

production of a desired chemical system. The experiment will

often generate a variety of cluster sizes. Effective mass

selection and detection require a fundamental understanding,

and intelligent incorporation, of various static and pulsed

ion optics. Once the mass components of the molecular ion

beam are established, photointerrogation may be performed with

a confident knowledge of the species under study.

Due to the nature of the expansion and the pumping

limitations of the apparatus, the experiment is pulsed at 9.1

Hz. Limiting the total throughput by lowering the duty cycle

of the gas allows one to maintain a high jet density and not

exceed the pumping capacity of the apparatus. However, the

pulsed nature of the experiment demands real time computer

control over the many events that occur in a cycle. A custom

computer program controls the relative timing of the

vaporization laser, the carrier gas pulse, the acceleration

stack, and the dissociation laser.










Accelerator


Target
Nozzle









Electric
Sector


Vaporization
Laser


Ion Optics


MCP Detector


Tunable
Dissociation
Laser


Figure 1. Experimental Apparatus.
The figure displays a sketch of the experimental apparatus.
A plasma is generated at the upper left of the figure in the
beam source at high pressure by the second harmonic of a
Nd3+:YAG laser. Ions and neutrals then supersonically expand
in an inert carrier (ca. 99 % He), cool, and then travel
through differential pumping orifices (skimmers) and into the
accelerator of a custom time-of-flight mass spectrometer.
Here, positive or negative ions may be extracted at 900 to the
supersonic beam axis with a kinetic energy of ca. 1.45 keV.
Mass separation takes place as the ions pass through a 2.45 m
flight tube containing focussing and deflection optics.
Fragmentation of any ions is detected by laboratory kinetic
energy analysis performed by a l270electrostatic sector at the
end of this flight tube. Laser photoexcitation may occur
colinearly, as shown in the figure, or may intersect the beam
at 900 prior to entrance of the electrostatic sector.


Skimmers












Figure 1 displays the salient features of the

experimental apparatus that was used for this research. The

experiment is detailed below by following the journey of a

cluster ion from inception to mass selection to

photodissociation.




Beam Generation



The start of an experimental cycle occurs in the beam

source and is marked by the birth of a chemical system.

Production of a desired system is achieved when the surface of

a sample rod is laser vaporized within the high pressure pulse

of a carrier gas. Focussed light of a Quantel Nd 3:YAG

laser (model 580), via the second harmonic (532 nm), will

generate a plasma. Laser light, 7 ns in duration, is

typically chosen in the range of 15-40 mJ/pulse. The light is

focused to a point smaller than 1 mm in diameter. This

corresponds to a photon fluence of ca. 108 W/cm2 (lower limit)

at the rod surface. The laser generated plasma is thermally

quenched in the carrier gas through collisions. Carrier gas

for the present research is either pure He, for metal-metal

clustering, or a mixture that has a small percentage (ca. 1-2%

mole fraction) of ligand (L) in helium. As will be shown, an

assortment ML systems, where L = Ne, Ar, Kr, CO2, or N,, may








11

be generated from the appropriate gas mixture. Three-body

collisions initialize clustering to form a variety of M, or

MjI neutral and ionic clusters.

Figure 2 displays a cross section of the source assembly

used to house the sample rod and provide a reaction zone where

the nascent clusters may be formed. Optimizing the

configuration of a nozzle source is rather enigmatic.

Nucleation to molecular species is kinetically controlled and

therefore critically dependant on the local pressure in the

plasma generation zone. With low gas density, typically only

a single adduct is observed to physisorb to a metal cation.

The clustering efficiency improves with an increase in carrier

gas density; a direct reflection of the fact that both

three-body and two-body collisions will increase with

pressure. However, too much gas pressure has been observed to

quench the positive ion beam and is believed to be due to

electron recombination with the positive ions.

Note, the onset of expansion is similar to quenching a

reaction; the observance of ionic species is an attestment to

the fact that the cluster ensemble is not at thermodynamic

equilibrium. Even the vibrational and rotational temperatures

for a given molecular species are known not to correspond to

the same temperature after an expansion.18 Molecular

vibrations equilibrate more slowly than rotational degrees of

freedom and will therefore be at a higher temperature with

respect to the translational temperature of the beam.















Transition Metal Rod
STeflon Spacer





Laser (532 nm) Gas Inlet





Stainless
Steel Block O-Ring

Precision Bearing

Figure 2. Cross Section of Source Block.
This figure displays a sketch of the source block used for
generation of metal-cation rare-gas systems. The channel to
the right of the sample rod allows laser access for plasma
generation and exit orifice for expanding carrier gas. The
plasma is collisionally thermalized in the carrier gas pulse
within the channel prior to expansion. Three-body collisions
initialize the aggregation of cluster systems. The rod is
mounted in precision bearings to ensure a wobble-free
rotation. O-rings seal off the volume near the sample plasma
generation zone to maximize the carrier gas density thereby
maximizing the cooling/clustering capability.








13

Nonetheless, an estimated 5,000 to 10,000 internally cool M2+

and/or ML may be routinely generated 9.1 times a second.

A given vaporization laser pulse produces a finite number

of neutral and ionic atoms. Yield for a desired species is

then in competition with the production of other clusters for

the available material. In attempts to produce rare-gas

ligated metal cations, metal-metal clusters have been observed

at the expense of metal-ligand systems for higher carrier gas

pressures.9 The, presumably, more weakly bound metal-ligand

systems would find the collisional frequency, and therefore

the progression to equilibrium imposed by a high pressure

regime deleterious while in competition with more strongly

bound metal-metal systems. Unfortunately, one may not easily

predict the exact source conditions necessary to generate a

particular system.

Several theoretical and experimental studies have been

done to characterize the cooling properties of supersonic

expansions. For compressible, adiabatic, and isentropic flow,

the following relations for temperature (T), pressure (P), and

density (p) in terms of mach number (M) and heat capacity

ratio (7) have been derived:20


Ti 2L) I( -1 1+ y { )M12
2 22 yi2
Ti \Pil Pi) 1 + ( 11)M2
2








14

These relations are valid for compressible flow of a gas that

is confined in varying area channels. The first two

qualities are the familiar adiabatic relations that may be

found in any thermodynamic textbook.2' For an adiabatic

expansion of an ideal gas, a drop in pressure will be

accompanied by a reduction in temperature. The last term

expresses the physical characteristics of a system to the mach

number. From this term, one observes that an adiabatic

expansion of a gas will results in an increase in the mach

number.

The mach number is defined as v/a where v refers to the

mass flow velocity and 'a' is the local speed of sound. The

speed of sound is a function of temperature given by (TRT/m)1'.

J. B. Anderson and J. B. Fenn22 have determined the limiting

flow velocity as mach number approaches infinity as (5/7y) a.

Initial source temperature will determine the speed-of-sound.

Notice that a high mach number does not reflect a large mass

velocity but rather a reduction of the local speed-of-sound as

the gas expands from a high pressure region to a low pressure

region. High mach numbers are therefore desirable because

they correspond to a small translational velocity distribution

and hence a cold beam.

Using the above pressure relationship, Eq. (1), it is

possible to calculate the exit mach number of a nozzle with a

known pressure ratio. The cross sectional area, A, of the








15

channel is related to the mach number and heat capacity ratio

with the following equation:20

1 + ( -)M2 2T
A2 I 2 (2)
A M2 1 + ( )M, 2
2


Immediately, one may determine the pressure conditions in

which the nozzle is choked23 (also referred to as an

underexpanded condition); i.e., for what cross-sectional area

in a diverging nozzle is M = 1. The ratio of background to

reservoir pressure for a monatomic gas is 0.487. This ratio

under typical experimental conditions of our apparatus is ca.

10-8. The expansion for the apparatus is supersonic: it is so

supersonic that the above equation results in an unrealistic

nozzle exit-mach number of 80.

Obviously, as the molecular density drops from a decrease

in pressure, a point is reached in which the molecules can no

longer communicate. The beam becomes discontinuous and a

terminal mach number is reached. J. P. Toennies and

K. Winkelmann2 have determined the terminal mach number as a

function of downfield distance (x) normalized to the nozzle

diameter (x/d) for various pod. The variable po is stagnation

pressure and the quantity pod is proportional to the

bimolecular collision frequency.

One may estimate the quantity of pod experimentally to

determine the terminal mach number for a typical set of








16

conditions. For our apparatus, the stagnation pressure may be

determined from a knowledge of the flow rate and the volume of

a single gas pulse. Flow rate is easily measured and is ca.

100 SCCM (standard cubic centimeters per minute) with an

applied cylinder pressure of ca. 70 psi. The temporal width

of the gas pulse is determined by varying the plasma

generation event within the gas pulse. Presence of seeded

ions reveals a pulse width of ca. 1.0 msec. The volume of gas

per pulse is found from the product of the nozzle cross

section area, the pulse width, and the gas velocity as

3.8 cm3/pulse, or, at the experimental cycle of 9.1 Hz,

35 cm3/sec. The ratio of flow rates, before and after

expansion, multiplied by the backing pressure will estimate

the pressure in the nozzle channel as ca. 30.7 torr. The

quantity pod, with a nozzle diameter of ca. 2 mm, is ca. 6.0

torr-cm and corresponds to a terminal mach number of ca. 10.

This is considered a low to moderate expansion for our

apparatus. More extreme pressure drops are possible that

would correspond to a terminal mach number of ca. 20.

Several versions of nozzle blocks, in which the channel

and exit orifice configurations were varied, have been tried.

The one described below is particularly suited to the

generation of weakly bound ML species (refer to Figure 2).

The source block is made of stainless steel with outer

dimensions of 3.17 cm by 3.17 cm by 3.81 cm. A central gas

channel of length 3.17 cm and diameter 2.2 mm perpendicularly









17

bisects the sample rod through-hole. At the exit end of the

gas channel is a diverging 180 cone ca. 6.4 mm depth. O-rings

capture the sample rod and make a hermetic seal on either side

of the gas flow channel equidistant from the center at 1.7 mm.

The rotating rod is supported by precision bearings. Teflon

spacers provide further rod support and apply the necessary

force to make the o-rings seal. The total volume, excluding

the gas inlet and exit channel volume, around the rod is ca.

49 mm3, which is about 40% of the total possible gas volume in

the block. A pulse of gas originates upstream, 6.3 mm from

the rotating rod and subsequently flows around the

circumference of the rod before exiting down a 1.9 cm long

channel.

A commercial solenoid valve (General Valve series 9)

controls the carrier gas pulse. An exit orifice of 0.76 mm

diameter is plugged with a Kelef popet in the de-energized

state. The valve is overdriven' with an electrical pulse of

150 V and ca. 150 Asec in duration. This extreme pounding

will shorten the lifetime of the Kelef popet and necessitate

its replacement after several weeks of operation.

Nevertheless, a gas pulse of ca. 1.0 ms, which corresponds to

a flow rate of ca. 40-500 SCCM, will result at the

experimental cycle of 9.1 Hz. The flow-rate is adjustable

with backing pressure and limited by the diffusion pump



*Manufacturer's recommendation for continuous duty is 28
volts.








18

throughput. Interactive computer control allows the timing

adjustment of the vaporization laser impingement on the rod

surface to coincide within the gas pulse.

The resulting cluster neutral and ion ensemble expands

from the high pressure region of the nozzle channel into a

500 L aluminum cylindrical chamber (inner diameter 114 cm and

height 61 cm) evacuated by three diffusion pumps. Conversion

of the random motion of the gas/cluster ensemble within the

nozzle channel into directed flow upon adiabatic expansion

results in a supersonic beam. A supersonic nozzle will

therefore convert enthalpy into kinetic energy. The cooling

properties of this technique have routinely generated diatomic

species with vibrational temperatures of less than 60 K and

rotational temperatures of 5 K.25 From the observance of

blackbody radiation, a temperature change of 7,000 K to a few

Kelvin has occurred in a fraction of a second.

The neutral/ion cluster ensemble traverses two

differential-pumping orifices. Passage through these regions

is gained through two conical, 550, electroformed skimmers

that are positioned 12 cm and 60 cm downstream of the nozzle

exit with apertures of 1.0 and 1.5 cm, respectively. The

skimmers define regions of successively lower vacuum pressure

and skim out a region within the mach bottle of the supersonic

expansion.'" The main chamber, in which the molecular beam

first expands, is pumped by two differential pumps, a 10"








19

(NRC) and a 6" (Varian model VHS-6) that provide an operating

pressure of 105 torr via a total pumping speed of 9600 1/s.

The two skimmers mark the entrance and exit of a wedge

shaped sector that is 15% of the total volume of the main

expansion chamber. This region is pumped separately by a 6"

diffusion pump with a water cooled baffle. Under operation

the background pressure in this region is ca. 10" torr.




Mass Selection



The second downfield skimmer stands at the entrance of

the acceleration stack of a time-of-flight mass spectrometer.

After ca. 110 cm of travel and 620 Asec, the cluster ensemble

reaches the center of the stack. In this region, ions, either

positive or negative, may be extracted at 900 to the molecular

beam. A computer triggered acceleration pulse imports ca.

1.45 keV of kinetic energy to the cluster ions in a two-stage,

Wiley-McLaren accelerator.26 The first stage contains the

weaker field, 35 V/cm, with the second stage being

considerably larger at 1450 V/cm. This allows one to maximize

temporal resolution of ions at the detector (2.45 m downfield)

by correcting for space deviations at the accelerator. The

space deviation is defined by the skimmers mentioned earlier.

The electrical pulse is supplied by a Cober (model 605P) high








20

voltage pulse generator that is capable of delivering 1.5 keV

pulse with i 100 ns risetime.

The acceleration stack consists of seven, stainless steel

parallel plates (dimension 15.24 by 15.24 cm by 1.6 mm thick)

separated by 1.0 cm Teflon insulating spacers. Ions enter the

low field region in the rear of the stack approximately

between the second and third plates. All plates have

centrally located slots of 2.54 cm by 7.62 cm to allow for

unhindered ion passage. Two of the seven plates, which define

the high field region, are grided with 90% open screen to keep

the field region flat. The ratio of the high and low electric

fields may be optimized with a simple voltage divider by

maximizing the mass resolution at the detector. Discrete

components are used to minimize capacitance thus keeping the

acceleration pulse sharp. The voltage divider consists of a

network of resistors and a high voltage switch. Five

internal, i.e., within the vacuum hardware, 1.0 kn, 1%-

tolerance glass resistors determine the low field strength.

The last plate is grounded so that the ions are in a

field-free region upon departure from the acceleration stack.

The acceleration stack marks the beginning of a time-of-

flight mass spectrometer (TOFMS). Ions are subjected to a

variety of deflecting and focusing optics before detection by

dual microchannel plates. Horizontal deflectors correct for

the forward momentum of the expanded molecular beam. Two

electrostatic einzel lenses make a parallel to point focusing








21

device for the ions. Each einzel assembly consists of three

cylindrical aluminum tubes of length 7.62 cm and inner

diameter of 6.99 cm. The three concentric elements are spaced

6.35 mm apart. An applied potential of 450 V (positive

potential for cations) on the central einzel element provides

an ion focal length of ca. 85 cm for 1450 keV ions.

After 2.45 m of travel, the ions are detected by a dual

microchannel plate detector. Ideally the acceleration stack

imparts equal kinetic energy to all species; thus, arrival

time is proportional to the square of the mass-to-charge

ratio. Figure 3 displays the parent mass distribution for

cobalt cation with physisorbed helium atoms. The ability to

physisorb multiple helium atoms to a cation nucleation site

attests to the extreme cooling capabilities of the apparatus.

Also, notice that mass peaks are well separated with the four

amu spacing among CoHe,+ peaks being well resolved. Unit mass

resolution is possible with the primary mass resolving power

of ca. 300 at 100 amu.

The ion detector consists of two Galileo microchannel

platesn (MCP) captured in a custom assemblage. The two plates

are separated by a 0.127 nm nickel-lifesaver shim that

electrically contacts the outer perimeter while leaving the

detection area open. Metal shim provides an electrical

connection for a resistive voltage divider. An individual

microchannel plate in this configuration has been biased with

up to 900 V without a breakdown. Incoming ions generate





















CU












50 60 70 80 90 100
AMU
Figure 3. Mass Spectrum of Cobalt Helide Cations.
The figure displays a portion of the parent mass spectrum,
relative abundance versus amu, for a single cobalt cation with
several physisorbed helium atoms. The naked cobalt cation at
58 amu is shown off scale to reveal the helium substituents;
it is approximately a factor of eight larger than CoHe,+. The
ability to physisorb several helium atoms, upwards of seven
(shaded in black for emphasis), is an attestment to the
cooling and clustering property of the supersonic expansion.








23

secondary electrons in the dual detector. These ions are

detected at a stainless steel electrode ca. 2.8 mm behind the

exit surface of the second microchannel plate. The gain of an

MCP is ca. 107. Detection efficiency is exponential as a

function of gain voltage with roughly a factor of five

increase in signal level per one-hundred volts of bias.

Single ion detection is possible although not preferred for

optical studies.

Slight electrical modification is required to mass select

negative species. All potentials of electrostatic ion optics

and the acceleration stack are merely reversed in polarity.

Only the detector assembly requires special handling.

Regardless of the polarity of the ions, secondary electrons

must still be generated and detected. For detection of

cations, a negative potential is applied to the entrance MCP.

Conversely, for detecting anions a positive potential must be

applied to the entrance MCP but the electrical bias must

ensure that secondary electrons are accelerated through the

second MCP. This problem may be overcome by floating the

entire assembly with respect to ground. Proper electrical

connections are discussed in Appendix A. Figure 4 displays a

parent mass spectrum for anions of aluminum. Mass resolution

is similar to that of a cation mass spectrum.

Before detection, a 1270 electrostatic sector turns the

ions off the flight tube axis."'29 The electrostatic sector is

a kinetic energy analyzer. A field strength of 600 V/cm































AMU


Figure 4. Mass Spectrum of Aluminum Anions.
The figure displays the cluster anions of aluminum over a mass
region of 100 to 700 amu. This region of the mass
distribution encompasses clusters anions of 5 to 25 aluminum
atoms. Notice the anion A113' is relatively larger than any
other anion in the beam and represents a 'magic number'.








25

for this optic is necessary to turn parent ions of 1.45 keV

kinetic energy. The aluminum sector provides an ion path on

an 8.9 cm radius with a channel width of 2 cm. The sector

electrodes are 7 cm wide. Resolution is proportional to the

radius and is a function of the initial velocity spread of the

ions. The magic 1270 17' angle between entrance and exit

apertures has been found to optimize the refocusing and

resolving properties of an electrostatic sector.

Collision induced dissociation (CID), metastable decay,

and photoinduced dissociation of a parent molecule may be

observed by tuning the sector field to transmit fragment ions

of lower kinetic energy. The daughter ions will arrive at the

same time of the parent ions but at a proportionately smaller

kinetic energy. The first generation of this sector had a

1.27 cm entrance and exit aperture and gave a kinetic energy

resolving power of ca. 10. In a later version of the sector,

the apertures were narrowed to 4.7 mm, thereby limiting the

off-axis velocity spread at the entrance without significant

parent throughput loss. This configuration increased the

resolving power to 15. Figure 5 displays a sector scan of

Co,+ photodissociated with a fixed laser frequency of

28 169 cm1 and power of 35 mJ/pulse.

An electrostatic sector in tandem with a TOF is a

powerful combination. This combination allows one to mass

select a given parent ion, perform some experiment on that

parent, then mass select the fragments.




















C




O
0






(L
+ c-




50 100 150 200 300 400 500 600 700
AMU




Figure 5. Photofragmentation of Co8+.
This figure displays the photofragments of Cog+ with 355 nm
light. The field strength of the 1270 electrostatic sector is
scanned to transmit fragment ions from a given parent system.
The parent mass of 472 amu is not displayed under the gain
conditions of the detector. Secondary mass resolving power is
about 15.








27

Optical Spectroscopy



The ability to mass select provides only moderate insight

into the chemical behavior of molecular systems. For this

experiment it is considered a prerequisite for optical

interrogation. Optical analysis will directly access the

quantal details of a system. Such information is invaluable

for describing the interatomic forces among the bound atoms.

The tunable light source for this experiment is a Quantel

(model 581) Nd3:YAG pumped dye laser that provides both fixed

and tunable light. The laser is timed to photo-intersect the

ion packet prior to entrance of the 1270. The sector may then

be scanned to observe the photo-induced fragments at a fixed

frequency, as discussed in the preceding section, or, a

particular fragment may be monitored as a function of

wavelength.

The visible region is accessed through a variety of

organic dyes dissolved in methanol. A total range of 540 cm'

to 780 cm"' may be easily reached with approximately seven

different dyes. The dye laser tunes over the fluorescence

region of each dye. Figure 6 displays the laser intensity as

a function of wavelength for 532 nm pumped rhodamine R6G

(C28H31N203Cl) .30 This particular dye will allow access to a ca.

25 nm (700 cmu') wavelength region centered at 590 nm. The

picture symbolizes the 'tuning curve' for the dye. The R6G

dye has a conversion efficiency of ca. 20% with a 200 mJ/pulse















bu-
_.
E 40


u)
"30-
L.
20-

-J
: 10



578

Figure 6.
The figure
wavelength
particular
(700 cm'-).


583 588 593 598 603 608
wavelength (nm)
Laser Dye Curve for Rhodamine R6G.
displays the dye laser intensity as a function of
(tuning curve) for rhodamine R6G dye. This
dye will access a wavelength region of ca. 25 nm








29

pump beam. Many of the photodissociation spectra presented

in this dissertation result from scanning in several different

dye regions. These scans must be combined, with good overlap,

to form a complete photodissociation picture.

The dissociation laser scans linearly in time with

respect to wavelength. Several pairs of points taken manually

relate the wavelength to a computer generated data index. The

computer-collected photodissociated event is then correlated

to a wavelength position. Unfortunately, normal optical

optimization and play in the mechanical parts of the scanning

mechanism may cause consecutive scans to be different by as

much as 0.1 nm. This corresponds to an unacceptable 2.5 cm1'

error at 630 nm. For this reason, the spectra are calibrated

to a primary standard.

Optical spectra may be calibrated with optogalvanic

transitions found in a neon discharge. A conventional neon

indicator lamp is powered by a current-limited power supply at

ca. 100 V (DC) and 10.0 mA. A 4% reflection of the primary

beam off a turning optic intersects the discharge region of

the neon bulb. Simultaneous scanning of optogalvanic

transitions with the photodissociation event provides an

accurate method to determine the absolute wavelength position

of the dye laser. These optogalvanic line positions are well

known and may be used a primary standard.3132

Figure 7 displays an optogalvanic spectrum over the

region 580 to 720 nm. Notice that optogalvanic transitions















C)

O



oL
O






580 620 660 700 740
Wavelength (nm)
Figure 7. Optogalvanic Transitions for Neon.
This figure displays the optogalvanic transitions found in a
neon discharge lamp over the wavelength region 580 to 720 nm.
Incident laser light may enhance or deplete charge carriers in
the discharge region, thus changing the resistance of the lamp
and appearing as either a positive or negative going
electrical signal across a capacitively coupled load. The
line position are well known and provide a primary standard
for calibration of optical spectra taken with a pulsed laser
in the visible region. The small gap in the spectrum near
684 nm is due to the poor overlap of two dye regions (see text
for explanation).











Table 1. Optogalvanic Positions for Neon.
Laser Dye" nm cm' sign Source
R610 585.250 17,086.72 b,c
588.190 17,001.31 + b,c
594.483 16,821.34 + b,c
597.553 16,734.92 + b,c
R640 603.000 16,583.75 b,c
607.434 16,462.69 b,c
609.616 16,403.77 b,c
612.845 16,317.34 b,c
614.306 16,278.53 + b,c
616.359 16,224.31 + b,c
621.728 16,084.20 + b,c
626.650 15,957.87 + b,c
630.479 15,860.96 b,c
633.443 15,786.74 + b,c
DCM
638.299 15,666.64 b,c
640.225 15,619.51 + b,c
650.653 15,369.18 b,c
653.288 15,307.18 + b,c
DCM/LD 659.895 15,153.93 b
667.828 14,973.92 b
671.704 14,887.51 b
692.947 14,431.12 b
696.543 14,356.615 + d
702.405 14,236.801 + d
LD-700 703.241 14,219.88 + b
717.394 13,939.34 b
724.517 13,802.30 b
743.890 13,442.85 b


aCommon name. bRef.[31].


CRef.[32].


may occur in either the positive or negative direction

corresponding to an increase or decrease in the charge

carriers in the discharge region. Table 1 provides a list of

optogalvanic transitions easily observed on the wavelength

region of 585 to 740 nm. These transitions were taken in air

and are grouped according to the dye region in which they are


observed.


dRef.


[33].








32

After the first attempt to calibrate the Quantel laser

scan box to optogalvanic transitions, it was determined that

the laser did not scan linearly in time but had a systematic

and increasing deviation. Figure 8 shows the error of the

Quantel dye laser readout as a function of wavelength. This

annoying error is easily corrected by a least-linear-squares

method relating the Quantel scan box to the optogalvanic

transitions.

Once the scan data has been corrected to air wavelength

it must then be corrected to vacuum. This is done by using

the dry air refractive index of 1.0002926.03) Simply multiply

the optogalvanic corrected air wavelength by the refractive

index to get the vacuum number. Conversion to wavenumbers is

accomplished by taking the inverse of the wavelength and

multiplying by the correct conversion factor of 107 nm/cm.

Finally, for those spectra that are taken along the ion

flight tube axis one must correct the frequency for the

Doppler shift. For absorption, the Doppler shift is

determined by the following equation:m



V observed 3
Corrected (1-V/C)



where v is frequency in wavenumbers, v is the ion velocity and

c is the speed of light.














0.20
E

> 0.16
-D -
.
0
0.12 .



5 0.08


690 700 710 720 730
Observed Wavelength (nm)
Figure 8. Error in Quantel Dye Laser.
The figure displays the error (the literature value for an
optogalvanic transitions minus the quantel scanbox readout) of
the Quantel dye laser as a function of wavelength.
Optogalvanic transitions for neon are used as a primary
standard and compared to the readout offered from the Quantel
laser system. The dye laser has provisions to correct the
wavelength for a constant value. However, as the plot
confirms, the error (shown as solid squares) as a function of
wavelength describes a line with slope as well as intercept.
This plot was derived from a single uninterrupted scan.












The ion speed is calculated from the kinetic energy that

the ion receives in the acceleration stack of the mass

spectrometer. The ion speed may be calculated with the

following equation (non-relativistic approximation):3

v = 1.3891m() (4)



where K is the imparted kinetic energy in volts, m is the mass

in amu. The velocity, v, will then be in cm/jsec.

Figure 9 displays the Doppler shift for a

photodissociation band of V(OCO)' V + OCO. Comparing the

photodissociation spectra of coaxial (top spectrum) and cross

beam (bottom spectrum) laser excitation, one observes that the

coaxial spectrum is red shifted by 2.93 cm1'. This suggests

the kinetic energy imparted to the ions in the acceleration

stack of the time-of-flight is ca. 1.45 keV. Apparently the

acceleration stack is quite efficient; recall that the applied

voltage in the TOF acceleration stack is 1.5 keV.

The tunable laser system is capable of scanning at

different rates. For preliminary scans, a faster scan rate

(0.6 nm/min.) is used to economize the data acquisition time.

Eventually some photodissociation spectra demand a closer look

and therefore a slower scan rate (0.04 nm/min.) to utilize the

narrow linewidth. The dye laser resolution is ca. 0.2 cm-1 at

16 000 cm1. In this event, several repeating but slow scans















S__ Doppler
/ Shift




-c-










Photoexcitation of V(OCO).
The figure displays the Doppler shift for coaxial excitation
upper scan) and cross beam excitation (middle curve) of a band
in the photodissociation spectrum of V(OCO)+ V + OCO. The
lower scan corresponds to a wavelength interference pattern of
an etalon with free a spectral range of ca. 1.73 cm-. The
Doppler shift of 2.93 cm'1 corresponds to a parent ion kinetic
energy of 1.45 keV. This is consistent with the applied
acceleration voltage of 1.5 keV.








36

may be done over an interesting region of the spectrum.

These repeating scans may be averaged to increase the

signal-to-noise ratio. Unfortunately, accurate overlay of

multiple spectra is complicated by the poor re-setablity of

the mechanical grating drive. An optical device that has

been found useful for aligning separate but repeating scans is

an etalon. An etalon is an interferometer; constructive and

destructive interference is a function of incident wavelength.

This interference may be monitored simultaneously with the

photodissociation event for a given scan. The peaks

corresponding to constructive interference may be easily

aligned between different scans. See the bottom trace of

Figure 9 for an example of an etalon scan.




Computer Control



The experiment would be impossible to run without

computer control. Within the experimental time period of

approximately 100 msec, sample generation, mass selection, and

optical interrogation all occur. Experimental success depends

the proper timing of many events: in chronological order, the

carrier gas pulse, the vaporization laser light, the

acceleration stack pulse, and the dissociation laser light.

To ensure success, data collection, relative timing of

experimental events, and waveform digitization are all








37

controlled with a personal computer and a CAMAC (Computer

AutoMated data Acquisition and Control)36 crate.

Optical interrogation of the ion beam demands precise

timing control. This is especially important for cross-beam

optical interrogation because the spread in arrival time of a

given ion size is roughly 100 nsec. Even fluctuations in the

power line will affect the acceleration stack voltage, and are

easily seen in the arrival time of the ion packet for

photodissociation in a cross-beam configuration. Critical

timing parameters are controlled by a LeCroy model 4222

programmable delay generator that has 200 psec accuracy.

Precise timing control demands that the computer operate

in real-time. This is accomplished with a custom computer

program that make use of the internal clock of a personal

computer. All timing pulses are initiated at 9.1 Hz by an

interrupt routine. Other computer tasks are suspended in the

background until the experimental timing sequence is

completed. The computer code (C language) for the real-time

control and data acquisition of the experimental apparatus is

included in Appendix B.

Electrical signals induced in the MCP detector by cluster

ions are pre-amplified by a factor of 100 (Pacific video

amplifier) before digitation by a 100MHz transient recorder

(DSP model 2001S transient recorder). Time-of-flight mass

spectra are recorded and averaged at the experimental rate of








38

9.1 Hz. Optical spectra are recorded in single sweep fashion.

Low resolution optical scans require about one hour for 20 nm.




Signal Optimization



When making transition-metal rare-gas systems care must

be taken before experimentation to minimize perennial oxide

and water contaminants. These contaminants preferentially

bind to the transition-metal cation and hence minimize the

amount of desirable ML product. Gas mixtures are prepared by

a specially dedicated manifold system. Typically, a 50 L

cylinder is pumped out thoroughly to remove any contaminants.

When possible, gas is delivered in the appropriate amount from

a new and fully pressurized cylinder. This insures that the

partial pressure of volatile contaminants in the tank is at a

minimum.

Stainless steel gas lines leading into the vacuum chamber

are pumped for 8 hrs then purged with the appropriate gas/gas-

mix just before an experimental run. Further precautions

against water contamination warrants the use of a Molesieve

trap in a liquid nitrogen bath. The Molesieve is housed in a

copper coil. The copper coil represents the only non-

stainless tubing in the gas inlet system. The gas line is set

up so that the copper tubing may be optionally bypassed.








39

Sample rod and source block preparation also requires

similar scrutiny. All transition metal rods are ca. 99% pure

with the exception of the chromium rod. This rod was plated

locally and no effort has been made to characterize its

purity. The transition metal rod is lightly filed or sanded

to remove surface contaminants and to crudely smooth the

surface. The source-block channel is meticulously cleaned

with Q-tips and methanol. The entire stainless steel block is

then ultrasonicated in a soap solution for 5 min, another

5 min. in methanol, and then two successive 5 min. intervals

in water. After this cleaning process the source block is

heated to 2000C for ca. 10 min to remove water. Expediently,

the sample rod is secured within the nozzle block, appropriate

connections are made, and the assemblage is placed back in the

vacuum chamber before it can cool.

For the production of V(HOH)+, water is a desirable

component of the carrier gas. To cluster water, a two-stage

pressure system is incorporated. A pure tank of helium

provides the backing pressure of 100 psi to a small ca.

200 cm3 cylinder. About 2 ml of water is placed in this

cylinder. This corresponds to approximately 0.3% mole

fraction of water in carrier gas. A second regulator controls

the final gas-valve backing pressure.

In addition to worrying about contaminants one must also

optimize the signal-to-noise (S/N). There are three major

factors that influence the signal-to-noise ratio









40

significantly: the gas pulse, the rod surface, and the

vaporization laser stability. Unfortunately, little can be

done to improve shot-to-shot stability of the laser system.

However, vibrations may be minimized with a solid table and

sturdy optical mounts.

The valve is adjusted to produce a reasonable flow rate

in the 'sweet spot'. Figure 10 displays a picture of the flow

rate verse the applied electrical pulse duration. Notice that

the flow rate has a local minimum near 158 psec corresponding

to ca. 100 sccm. For best stability the electrical pulse is

set to this minimum. Overall S/N critically depends on

pressure fluctuation and therefore it is best to minimize flow

rate fluctuation by minimizing the first derivative of this

curve.

The rod is constantly turned at 1/3 RPM with a Hurst

synchronous motor to prevent burning a hole in the surface and

therefore to maintain long term signal-to-noise stability.

The journey of a cluster ion from inception to detection

has been followed. The combination of a laser generated

plasma with a supersonic expansion enables one to produce

virtually any imaginable system. The use of two mass

selection stages provides superb control over parent and

daughter ions. This particular apparatus is quite facile at

producing weakly bound ions for the purpose of optical

probing.










250


200 Sweet
Spot

0150 I


S100 "" "

o -

50 -



120 130 140 150 160 170 180
Electrical Pulse Width (psec)
Figure 10. Sweet Spot of Solenoid Pulse Valve.
The figure displays flow characteristics of the solenoid valve
as a function of applied electrical pulse width. Flow rate is
measured in standard cubic centimeters per minute (SCCM). In
the de-energized state the solenoid valve is closed with the
aid of a stiff spring. The valve may be opened against the
force of the spring with a 150 V electrical pulse. The figure
displays a unique position, the 'sweet spot', which
corresponds to a local minimum in flowrate. Mechanically, a
dynamic equilibrium between the restoring force of the spring
and the opening force of the electromagnet will result in the
limitation of popet bouncing. In addition, operating the
valve at the sweet spot minimizes fluctuations in flowrate
with any change in valve behavior, i.e. the first derivative
of this curve is small in the vicinity of the minimum.














INDUCTIVELY BOUND DIATOMICS


Threshold to Photodissociation



This chapter is dedicated to the presentation and

analysis of data obtained from the photodissociation of

several cation, rare-gas containing, diatomic systems. The

photophysics leading to dissociation may be divided loosely

into two types depending on the lifetime of the dissociative

event. If the lifetime is very short, as in direct

dissociation, only a broad spectrum will be observed. This is

the case for the photodissociation of NiAr+ and CrAr. In

contrast to this behavior, the lifetime of the photoexcited

state may be sufficiently short to be observed in

photodissociation, but sufficiently long to reveal vibrational

and rotational information. The systems, specifically VAr+,

VKr+, CoAr+, CoKr, ZrAr*, and CaKr, all display resonant

transitions, i.e., bound-bound vibronic transitions, followed

by dissociation. Obviously, more information may be garnered

from the systems that display vibrational transitions than

from those that display only a featureless threshold. But

also, the analysis of these systems is more demanding and will

therefore deferred to the next section. We will introduce








43

the analysis of metal rare-gas diatomics with the systems of

NiAr+ and CrAr+, which display only a featureless threshold.

Nonetheless, a featureless threshold is quite informative.

Figure 11 displays the photofragmentation of

NiAr* Ni+ + Ar as a function of dissociation laser frequency

on the interval from 17 400 to 18 100 cm7. The production of

Ar is not observed as a photoproduct of NiAr* at these photon

energies as expected from the large disparity in the

ionization potential of the two atoms: IP(Ar) = 15.755 eV and

IP(Ni) = 7.633 eV.37 Internal electronic excitation of the Ar

atom is not energetically possible either; the first excited

state is at 11.54 eV (93 143 cm').37 Excitation of argon would

require the energy of five visible photons in this wavelength

region, an unlikely event. Therefore, photofragmentation of

NiAr+ is monitored as the Ni fragment ion current transmitted

by the 1270 electrostatic sector.

With the high intensity of laser light, a multi-photon

event, i.e., the concerted absorption of two or more photons,

is possible. The Quantel dye laser is capable of delivering

a power fluence of 108 W/cm2 to the ion packet. This

corresponds to a photon fluence of ca. 1017 photons/cm2 in the

visible region which is more than sufficient for the process

of multiphoton absorption.

Of course the probability for a multiphoton event will

depend on exact nature of the transition involved. One-photon

dissociation cross sections of resonant transitions have been

















C



I -
O






II I I
a-











17400 17600 17800 18000
Laser Frequency (wavenumber)
Figure 11. Photodissociation Threshold for NiAr+.
The figure displays the relative photofragmentation of
NiAr Ni + Ar as a function of laser frequency over the
interval 17 400 to 18 100 cmn'. A jump in the one photon
photofragmentation is observed at 17 984 cm-1 indicating a
threshold for producing excited 2F712 Ni ions. This
establishes the binding energy of NiAr* as 0.55 eV.








45

estimated at the aforementioned power for MRg+ systems as

5 x 10-17 cm2.0 Thus, one in five photons that cross the

interaction region defined by the cross section will result in

dissociation. A two-photon cross section will be smaller.

Nonetheless, two-photon processes have been observed under

similar laser power in the photodissociation of Ni2*.09 In any

case, correct analysis of an optical transition is necessary

the for accurate description of chemical behavior.

Figure 12 displays the relative Ni photocurrent as a

function of incident laser fluence. The laser fluence

dependence of the dissociation yield at 18 020 cm-' (ca. 40 cm1

above the dissociation edge) shows a linear fragmentation

response over a range of 0.5 to 8.0 mJ/pulse cm2. Recall, in

a weak field approximation the absorption intensity is

proportional to the incident light intensity (Beer-Lambert

Law).40 Thus, a linear relation between fragmentation and

laser fluence indicates that the photodissociation at this

energy involves a simple one-photon absorption event. This

leaves no ambiguity as to the value of the excitation energy

imparted to the NiAr by the laser.

Under the normal operating conditions of the mass

spectrometer, a trace amount of Ni from NiAr* is observed

from collision-induced dissociative processes. The data

presented here are in the form such that the small CID

contribution to the dissociation has been nullified.








46










0

+
2








0 2 4 6 8
Laser Fluence (mJ/pulse)
Figure 12. Laser Fluence Dependence for Photodissociation of
NiAr*.
The figure displays the fluence dependence for the
photodissociation of NiAr at the wavelength of ca. 554 nm.
This wavelength position is to the blue of the
photodissociation threshold of displayed in Figure 11. A
linear curve for the fluence dependence determines that the
threshold is one photon is nature.












To within the signal-to-noise of the present data, the

photodissociation action spectrum of NiAr+ in the region of

18 000 cm"1 appears as a featureless edge. Presumably, this

indicates the onset of a photodissociation threshold, i.e.,

the point at which the laser photon has just enough energy to

produce (excited state) products with zero kinetic energy.

Therefore, one may attribute the edge energy of 2.23 eV

(17 984 cm"-) as the sum of the binding energy of NiAr+ and

some promotion energy in the isolated Ni ion. The absence of

any vibrational or electronic hot band features associated

with the threshold at 17 984 cm-1 implies extensive cooling of

the NiAr+ emanating from the supersonic-expansion ion source.

Since it is energetically impossible to excite the argon

atom in the probed spectral region, the absorption spectrum of

NiAr must be similar to the absorption of the bare Ni ion.

Consultation of the energy levels of Ni shows that electric

dipole allowed transitions would not be expected within the

manifold of states arising from the 3d9 configuration since

all of these states have the same parity. The lowest,

fully-allowed electronic state corresponding to 3d84p

configuration (and electric dipole connected to the ground

state) is 6.39 eV(37 above the 2D5/2 ground state of Ni. The

photodissociation of NiAr+ appears to occur through a weakly

allowed one-photon transition at 2.3 eV where no isolated Ni+

transitions are expected. However, the ground state system is















; V

58 +
SNiAr+ j

o __ 60NiAr+







17970 17980 17990 18000
Laser Frequency (wavenumber)
Figure 13. Isotopic Shift for Photodissociation of NiAr+.
The figure displays a closeup of the region near the
photodissociation threshold displays a spectroscopic shift for
two isotopes of NiAr+. The lighter isotope, 58Ni40Ar+ (dotted
line), is shifted 0.8 0.15 cm1 to the blue of the threshold
for 6Ni4Ar+(solid line). This shift corresponds to a ground
state vibrational frequency of 235 50 cm1.








49

undoubtedly bound and, thus, the magnitude of the observed

diabetic limit would be larger than any suspected separated

atomic limit energy. One possible assignment of the

photodissociation feature in Figure 11 is the threshold for

production of 2F,7 Ni and 'S Ar. The transition derives its

nature from the parity forbidden, but spin allowed

3d84s (2F7t) 3d9 (2D512) transition in isolated Ni+. If this is

the case, the NiAr+ ground state binding energy (Do) is the

difference between the Ni+ 2F,72 2Ds2 transition energy of

1.68 eV (13 550.3 cm-1) and the observed threshold energy of

2.23 eV, or 0.55 eV.

Since nickel has several naturally occurring isotopes

("Ni, 6"Ni predominantly at 68.3% and 26% respectively)33 it is

possible to simultaneously measure the photodissociation

spectrum of both isotopes. Figure 13 displays a closeup of

the region near the diabetic threshold at 17 970 to

18 000 cm'. The isotope shift between the photodissociation

features of 58Ni40Ar+ and 60Ni40Ar is 0.8 0.15 cm- with the

heavier isotope being shifted to higher energy. This shift

corresponds to the difference in the vibrational energy of the

ground state of these two species. An equation relating the

isotopic shift to the vibrational frequency and the reduced

mass is easily derived from the definition of the force

constant, k = A(2rw)2.(41 After some manipulation, the

vibrational frequency may be expressed in terms of the isotope

shift, Ap, as follows:








50

2Av
e (1 p)

The variable p is the square root of the ratio of reduced

masses. Presumably, this vibrational energy is zero point and

the ground state vibrational frequency of NiAr* may be

determined as ca. 235 50 cm'.

Besides NiAr+, the photodissociation spectrum of CrAr

also displays a threshold in the visible region. Figure 14

displays the photodissociation spectrum for the process CrAr

SCr* + Ar over the region of 14 440 to 14 700 cm1l. A

significant increase in photodissociation intensity is seen to

begin at 14 500 cm7' which marks the onset to a diabetic

dissociation into excited fragments. Perturbations due to

background states irregularly modulate the photodissociation

spectrum for photon energies above 14 490cm'.

The separated atomic configuration of the photofragments

for the dissociation is Cr+(6D) + Ar(IS). The excited atomic

state electronic configuration of the transition metal cation

is in accord with the only spin allowed transition" within ca.

6 eV of the ground state, Cr(6S). The large disparity in

ionization potentials (IP(Ar) IP(Cr) = 9.0eV)3 between Cr

and Ar indicates that Cr is the only possible charged

photoproduct. Dissociation into excited state Ar atoms is

also impossible, as previously discussed in NiAr* system,

since the first excited state lies ca. 11.5 eV above the

ground state. Due to the cooling the parent ions suffers in



















0
4-0




0
CL


MI





I I I I I I I I I I I I

14440 14480 14520 14560 14600 14640 14680
Laser Frequency (wavenumbers)
Figure 14. Photodissociation Threshold for CrAr+.
The figure displays the relative photofragmentation spectrum
of CrAr Cr+ + Ar as a function of laser frequency over the
region of 14 440 to 14 700 cm'. The onset to a one-photon
diabetic dissociation limit corresponding to the separated
atomic levels of Cr+(6D) and Ar('S) is marked with an
arrowhead. The ground state binding energy of this molecule
is determined from this threshold and the Cr* promotion energy
to be 0.29 0.04 eV.









52

Table 2. Ground State Spectroscopic Parameters for NiAr+ and
CrAr*.


"Metal ion atomic configuration in separated atom limit.



the supersonic expansion, the origin of the optical feature

is assumed to be the vibrationless level of the molecules.

Similar fluence dependence measurements as performed in NiAr

confirm that the diabetic threshold corresponds to a one-

photon event. The adiabatic dissociation energy may then be

determined by subtraction of the atomic promotion energy in

Cr from the observed diabetic dissociation limit to yield

0.29 .04 eV for CrAr. The uncertainty in the adiabatic

dissociation limit arises from the uncertainty in the J state

of the Cr* ion upon dissociation.

Unfortunately, isotopic information is not reliable for

CrAr, unlike that of NiAr. Attempts to determine the

isotopic shift of 2Cr40Ar+ versus 5Cr40Ar+ (and/or mCrOAr+),

which occur naturally at 84%, 9.5% (2.4%)" respectively, are

complicated by the rough nature of the photodissociation

spectrum and the relatively low natural abundance of another

isotopically substituted system.


System Config." D, (eV) W (cm') k, (N/m)

NiAr+ 3d9 0.55 235 77

CrAr 3d5 0.29








53

Both systems discussed in this section, NiAr+ and CrAr*,

have similar properties. A singly-charged cation is

physisorbed to a rare-gas atom. Spectroscopy performed in the

visible region on these systems, results in a

photodissociation feature that is derived from an excited

state of the cation. Neither excitation nor charge transfer

of the rare-gas atom is energetically impossible. In

addition, all photodissociation events correspond to a one-

photon excitation. The spectroscopically determined

characteristics of NiAr'and CrAr+ are listed in Table 2.

Since there is little likelihood of any formal charge

residing on the Ar atom in either NiAr+ or CrAr, a good

approximation of the nature of the binding in these molecules

may be derived from a picture of an almost unperturbed

transition-metal cation with a polarized Ar atom. The binding

forces would be dominated by simple charge induced-dipole

forces. If this is the case, the attractive part of a

classical potential surface is proportional to l/r4.02 Thus,

the binding energy for a given system is significantly

dependent on the internuclear separation. This would explain

the difference in adiabatic binding energy between NiAr and

CrAr. The respective valence electronic configuration is

(3d9) for Ni and (3d5) for Cr. Allowing for d orbital

contraction across the transition-metal row, one would expect

that the NiAr system, having the smaller radius, would be

bound by more than the CrAr.








54

Resonant Photodissociation of VAr and VKr+



The diatomics VAr+ and VKr* will be the first systems to

be discussed that display resonant photodissociation of bound

levels. The kind of data manipulation found in this section

is representative of the remaining systems discussed in this

chapter. For the sake of completeness, the results of the

data analysis are included in each section. A detailed

treatment of vibrational fitting and the application of the

LeRoy-Bernstein procedure for determination of the

dissociation limit is included in this section. The

determination of vibrational numbering through isotopic

analysis is postponed to the ZrAr section.

One may notice that the line positions for the systems of

VAr, VKr+, CoAr*, CoKr presented in this Chapter have been

revised from previously published data.43'38 This was before we

were aware of the nonlinearity of the Quantel scan box (see

experimental section). Correct wavelength positions will be

published in a future paper that will include recently

acquired results for the photodissociation spectra of VXe* and

CoXe. All vibronic line positions listed in this

Dissertation are accurate to ca. 1.5 cmu.

Figure 15 displays a portion of the one-photon resonant

photodissociation spectrum for the process of VAr V* + Ar

over the visible region of 16 150 to 16 650 cm'. A series of

bound-bound vibronic transitions belonging to an excited state

















I--




WI)








16150 16250 16350 16450 16550 16650
Laser Frequency (wavenumber)



Figure 15. Resonant Photodissociation of VAr+.
This figure displays a portion of the one-photon resonant
photodissociation spectrum of VAr. Relative V photocurrent
ordinatee) is displayed as a function of laser frequency
(abssisa). The horizontal axis indicates zero
photodissociation. No Ar+ photofragments are observed in this
spectral region. Note the strong upper state vibronic
progression converging to a diabetic dissociation limit at
16 581 cm1. Note also, the perturbation occurring near
16 330 cml and the weak bands belonging to different
progressions evident in the red end of the figure. The
spectrum above 16 600 cm' is weak and apparently continuous
indicating a direct bound-continuum photodissociation at these
regions.









56

of VAr+ is evident. At this excitation energy,

photoproduction of Ar (similarly, Kr is not observed from

VKr+) is not possible due to the large disparity of ionization

potential of the atoms. The ionization potentials37 of Kr, Ar,

and V are 13.996 eV, 15.755 eV, and 6.74 eV, respectively.

Under the normal operating conditions of the mass

spectrometer, a trace amount of V+ from VAr+ is observed from

collision-induced dissociation with the residual He gas (ca.

1 x 10' Torr) in the flight tube. For this system, collision-

induced dissociation (CID) produces only a small, and

relatively constant background to the photoproduction yield

and may be nullified. The bottom of the horizontal axis of

Figure 15 therefore corresponds to zero photo-production of

V+.

The portion of the spectrum shown in Figure 15 is

especially revealing. A progression of red-degraded vibronic

bands converges to a diabetic dissociation limit of 16 581 cm'

at which point the spectrum becomes continuous. More than one

upper state progression is evident (see particularly the red

end of the spectrum) and numerous perturbations indicate that

the upper state of these transitions interact, as shown by two

closely spaced bands near 16 330 cm'. The upper state

anharmonicity is also made apparent by the diminishing

interval among transitions with increasing laser frequency.

The resonant photodissociation spectrum for VKr is

similar to that of VAr+. This spectrum also displays a








57

vibrational progression, but unlike the spectrum of VAr it is

not visibly perturbed by another state. The band shapes in

both these spectra demonstrate partially resolved rotational

structure indicative of a large increase in average

internuclear distance upon photoexcitation and a cold

( < 10 K) initial rotational distribution of the parent

molecule. No electronic or vibrational hot bands have been

assigned for either molecule. The partially resolved

rotational structure of the vibronic transitions places a

lower limit on the lifetime of the upper levels of the

transition at 10 ps. The upper limit to the excited state

lifetime is placed by the time between excitation and kinetic

energy analysis, about 5 js for travel time in the 1270

electrostatic sector.

Dissociation laser fluence dependence, for both V-(rare

gas) systems, of the resonant photodissociation transitions

indicates a one-photon absorption event is responsible for the

photoproduction of V*. A more thorough description of using

laser fluence dependence to determine the number of photons of

a given photodissociation feature was given in the section of

NiAr*. Poor temporal/spatial quality of the excitation source

unfortunately prevents accurate absolute cross-section

measurements. However, the strongest photodissociation

transitions have cross sections of ca. 10-17 cm2.











Table 3. Line positions for 51V40Ar+ and S"V"Kr+ in wavenumbers.
VAr VKr
v' Observed o-c" v' Observed o-c'
1 15303.0 0.73 2 15548.0 0.82
2 15387.9 -0.83 3 15639.1 1.56
3 15470.7 -0.76 5 15807.7 -2.35
4 15550.4 -0.13 6 15891.1 -1.18
5 15625.9 -0.11 7 15971.4 -0.55
6 15698.4 0.43 8 16049.3 0.24
7 15766.9 0.52 9 16123.8 0.17
8 15832.2 0.70 10 16195.7 0.10
9 15893.9 0.69 11 16265.5 0.37
10 15952.1 0.44 12 16331.7 -0.49
11 16007.5 0.47 13 16397.0 0.23
12 16059.0 -0.19 14 16459.1 0.14
13 16108.0 -0.20 15 16519.3 0.51
14 16152.5 -1.83 16 16576.0 -0.20
15 16192.9 -4.66 17 16631.2 -0.13
*15 16199.3 1.76 18 16685.8 1.63
16 16239.0 1.09 19 16734.9 0.12
17 16276.1 0.69 20 16784.2 1.12
18 16310.3 0.11 21 16829.6 0.35
19 16339.9 -2.55 22 16872.2 -1.00
*19 16344.3 1.87 23 16915.8 0.82
20 16372.7 0.70 24 16954.0 -0.55
21 16398.3 -0.77 25 16991.0 -1.18
*21 16401.9 2.85 26 17026.5 -1.12
22 16423.9 0.22 27 17060.7 -0.41
23 16445.9 -0.03 28 17092.5 -0.11
24 16465.4 -0.47 29 17121.8 -0.29
25 16482.6 -0.88 30 17149.6 0.04
26 16498.9 -0.11 31 17176.5 1.34
27 16512.7 0.26 32 17199.4 0.46
28 16524.3 0.56 33 17222.3 1.50
29 16534.3 1.23 34 17243.1 2.35
30 16543.0 2.41 35 17262.5 3.49
31 16550.7 4.52 36 17279.2 3.83
32 16556.9 6.90 37 17296.5 6.47
33 16562.0 9.78 38 17311.3 8.24
34 16566.4 13.70 39 17323.4 9.08
35 16570.0 18.38 40 17337.1 13.19
36 16572.8 23.76 41 17348.2 16.31
37 16575.1 30.07 42 17358.2 19.93
(a) Observed minus calculated.
(*) Extra lines due to perturbation.












Table 3 lists the positions of the assigned VKr+ and

VAr+ photodissociation excitation transitions in the interval

from 15 000 to 18 000 cm-'. The most intense point of the

vibronic band (typical width 2-6 cm-1) is taken to be the

vibronic band origin in this analysis. Only the strongest and

least perturbed progression in VAr has been presented. Most

of the transitions for the photoexcitation spectra of VAr* are

attributed to excitation of three upper electronic states, all

of which dissociate into V(5Pj) + Ar('S). Although hampered

by the perturbations and intensity anomalies in the weaker

progressions, one may tentatively assign the dissociation

limit corresponding to the strongest progression as V(S5P2) +

Ar by correlation of the extrapolated molecular dissociation

limits with the fine structure intervals in atomic V. Only

one progression is observed in the VKr spectrum, presumably

corresponding to the most intense transition in VAr. In any

case, the misassignment of the separated atomic limit could

lead to maximum error of 147 cm-1, which corresponds to the 5P3

- 5P2 fine structure interval.

Further evidence for the correct assignment of the

separated atomic limit may be found in the spin-allowed

selection rule for diatomic systems. The ground state atomic

configuration for vanadium cation is 5D, which, upon

combination with a 'S Ar would produce a variety of quintet

molecular terms. Similarly, the excited atomic state, 5p, for








60

V+ would produce quintet molecular terms. The excited state,

which lies ca. 1.68 eV above the ground state, is the only

quintet occurring within 4 eV of the ground state.7 This

argument, of course, is dependent on the exact angular

coupling cases of the two electronic states.



Vibrational Analysis



Vibrational transitions may be fit to third order in (v'

+ 1/2) with the following well-known formula:"

E(v) =Teo+ (v'+1/2) -(jex(v/+/2)2+W. (v'1/2)3. (6)


This allows one to determine the electronic term (T.), the

equilibrium vibrational frequency (aw'), and the anharmonicity

terms, (wx,') and (wYe') of the excited state. For the VAr+

system, the exact vibrational numbering is not known and

therefore represents an arbitrary numbering scheme. However,

the numbering has been chosen to yield a reasonable

vibrational frequency. Accuracy of this numbering scheme will

be tested in the following chapter. The zero of energy for

the vibrational fit and all subsequent manipulations is taken

as the zero-point level of the ground electronic state.

Electronic term T. is determined directly from a fit of the

observed transitions Eq. (6) and is 1/2 c," smaller than the

electronic term commonly denoted45 as T,.










17500


- 17000 V +
E VKr +


S16500- A

C,
S 16000 VAr

LL
. 15500

I /
15000
0 10 20 30 40 50
(v' + 1/2)

Figure 16. Vibrational Fit for VAr+ and VKr+.
The figure displays the vibrational fit of the observed
vibronic transitions for VKr (triangles) and VAr* (squares).
The observed transition are least-squares fit to Eq. (6) to
determine the vibrational frequency and anharmonicities of
each system. The solid lines for each system represent the
calculated levels from the least-squares fit.












Figure 16 displays the calculated and experimental points

for the vibrational fit. The accuracy with which Eq. (6)

describes the observed vibronic structure depends upon the

degree of anharmonicity of the molecular forces and the

existence of any local perturbations between the electronic

states. The best fit is obtained for the lowest vibrational

levels of each system. The residuals to the least squares fit

are also included in Table 3 and, except for very large v'

values, show no significant deviation.

In practice, the criterion for an acceptable vibrational

fit depends upon the behavior of the residuals of the observed

and calculated vibrational levels. If the vibrational

information is sufficient, such as is found in VAr* in which

37 bands are observed, one may fit the levels to several

anharmonic terms. Figure 17 displays the residuals to the

vibrational fit of Eq. (6) to observed levels in VAr. A

vibrational fit, containing one anharmonic term, to the lowest

31 bands (squares) displays a systematic error in the

residuals. This systematic error may be removed by the

inclusion of a second anharmonic term (triangles). Of course

one may continue to fit more vibrational levels with the

addition of more anharmonic terms but this is unrevealing. In

some cases attempts to fit the larger v' often increase the

residual error of the lower states, thus the determination of

w, will be poor. Accurate parameterization of larger v'













35

30- A
E
3 25-
r A
o 20

15-
-o
0)

O A


rA0 5- 1AA 15 2 25 3 35---

S-5 1 A







Figure 17. Residuals to the Vibrational Fit of VAr .
The figure displays the residuals (observed calculated) for
the vibrational fit of the observed bands of VAr1 to Eq. (6).
A least-squares fit to the equation containing one anharmonic
term (squares) and a least-squares fit to the equation contain
two anharmonic terms (triangles). Two entries occur at
U N

o






S= 1 5, 19 and 21 corresponding to a splitting of the






vibrational levels by a perturbation. The plot displays a
pictorial representation of the effect of adding more terms
(v'+ 1/2)








Figure 17. Residuals expansto the Vibrational Fit of nation to
The figure displays the residuals (observed calcula systematic) for
error. Generally, if vibrational fit of the observed bands of VArvailabl to Eq. (6).
A least-squares fit to the equation containing one anharmonic
term (squares) and a least-squares fit to the equation contain



two anharmonic terms are included in the fit of the bottom most
v' = 15, 19 and 21 corresponding to a splitting of the



vibrational levels. The by a perturbation. The plot displays a
pictorial representation of the effect of adding more terms
the Taylor's series expansion of the vibrational equation to
the residuals, specifically, the removal of a systematic
error. Generally, if vibrational information is available two
anharmonic terms are included in the fit of the bottom most
vibrational levels. The number of vibrational levels is
increased until the root-mean-square deviation of the
residuals, in the absence of perturbated states, exceeds
1.5 cm' for those fitted levels.








64

vibrational levels with Eq. (6) is not of significant

consequence as a modified analysis treating the vibrational

levels closest to the dissociation limit will be presented

below.

Absolute vibrational numbering of the transitions listed

in Table 3 is made from the measurement of the spectral shift

among the 6Kr, "Kr, "Kr, and "Kr isotopomers of VKr+. This

yields a unique absolute vibrational numbering for the upper

level of the transition. A detailed description of the

utilization of isotopes for the determination of vibrational

numbering will be addressed in the ZrAr section. At present,

neither the spectrum of 59V36Ar+ nor 5V38Ar+ (0.34% and 0.07%

natural abundance,33 respectively) has been obtained. Without

isotopic substitution, the firm assignment of absolute

vibrational quantum numbers to the VAr transitions listed in

Table 3 is impossible. Thus, the upper state vibrational

quantum number listed in Table 3 is merely an effective

vibrational index, chosen to be close to the absolute value.

The correct numbering is, of course, important for the

vibrational fit and the subsequent determination of the

vibrational frequency and the electronic term. Assignment of

the reddest observed transition to the origin band lowers the

vibrational frequency by ca. 5%.

All of the transitions observed in this study appear to

originate from the ground electronic and vibrationless state

of the molecule: i.e., no hot bands have been identified.








65

This is understandable due to the extensive cooling these ions

suffer in the supersonic expansion. From a conservative

estimate of the sensitivity of the experiment (1% of a strong

transition) and a guess of the ground state vibrational

frequency (200 cm-'; see discussion below), one may infer the

vibrational temperature of these ions to be less than 65 K.

The low internal temperature of the ions simplifies the

spectrum greatly but prevents direct determination of the

ground state vibrational frequency via photodissociation

excitation spectroscopy.

Not all of the electronic states predicted from the

accessible V atomic ion states combined with a 'S rare-gas

atom have been detected in this photodissociation study.

Optical selection rules for absorption would limit the number

of accessible transitions for excitation and not all the upper

levels of those accessible transitions may efficiently

dissociate. The fate of the excited states of these ions is

determined by a competition among radiative stabilization

(fluorescence to a bound level), radiative dissociation

(fluorescence to a dissociative level), and non-radiative

dissociation through direct coupling to a continuum level

(predissociation). Since optical absorption is detected in

this study through a vibrational predissociation of the upper

state on an appropriate time-scale, many transitions in these

molecules may go undetected.








66

LeRoy-Bernstein Derived Dissociation Limits


Vibrational levels near the dissociation limit are poorly

parameterized by a series expansion about equilibrium in

Eq. (6), but are better described by a functional form that

considers the nature of the attractive forces at work at large

internuclear separations. LeRoy and Bernstein4647 have proposed

a procedure for the determination of the dissociation energy

from the observed vibrational levels. Their derivation begins

with the semiclassical WKB" approximation:


(v + 1/2) = 2(2)1/R2 [E(v) U(R) /dR. (8)
h JR (v)


The variable is the reduced mass and E(v) corresponds to the

vh vibrational energy level. The integral bounds are a

function of the integrand where E(v)=U(R2)=U(R1); the variables

R, and R2 refer to the internuclear distance on the repulsive

and attractive potential surface, respectively. At large

internuclear separation, the vibrational index v may be

treated as a continuous variable. The derivative of the above

equation with respect to v results in the following equation:

dv 2 / R2(v)
dEv 2 (2V) 1/2 [E(v) U(R)]-/2dR. (9)
dE(v) h J ^(v)


"WKB approximation will be discussed in the next Chapter.









67

For a diatomic molecule that dissociates according a

-C/R" potential, one may approximate the interatomic potential

in the limit of large R with the potential of the form

U(R) = D (10)
Rn


Dissociation energy is given by the variable D and R is the

internuclear separation. The vibrational eigenvalues may then

be expressed as a function of C and the outer turning point,

R2, of the potential,

E(v) = D (11)
R2


Substitution of U(R) from Eq. (10) into Eq. (9) and then

elimination of C with Eq. (11) from the integrand results in

the following equation:

dv 2 (2 )1/2 R2) R2)n -1RdR.
dE(v) h[D E(v) ]1/2f RR (v)



This integral may be put in a more convenient form by changing

the variable of integration to y = R2(v)/R. The following

equation results:

dv 2 (2i) 1/2 Cl/n R2/R1 dy (13)
dE(v) h[D E(v) ] (1/2+1/n)J y2(y 1)/2


In the limit of R,/R, oo the integral is known33 and results

in an analytic expression involving the r function,48








68

dE(v) hC-1/nnT(1 + l/n) [D E( v) (n2)/2n (14)
dv (2pL)1/2P(1/2 + l/n)


Several terms may be combined to form a constant, K;

K= hC-1/nnr(1 + l/n)
(2xCp)1/2F(1/2 + l/n)


For the molecules under study in this work, the long

range attraction forces between the vanadium atomic ion and

the rare-gas atom will be dominated by simple charge

induced-dipole forces. Therefore C and n in Eq. (10) are

fixed49, respectively, as


2
C =2a n-=4. (16)



In this expression a is the polarizability of the rare-gas

atom. Thus, the constant K is equal to 0.501 and 0.374 (cm*)1/4

for CoAr and CoKr, respectively.

For sufficiently dense vibronic levels, the derivative of

the eigenvalues may be approximated with the following

equation:

dE(v) G(v) = [E(v + 1) E(v 1)] (17)
dv 2


Thus, substitution of the above equation into Eq. (14) results

in an expression that may be easily plotted:

(AG)/3 = [D E(v) ]K4/3. (18)










200

180 A

160 A
m A
140 -

2 120

0 100 -
80

60 VKr+
40- VAr +

20 -
0 -- I i --I I- I i -T-
15800 16200 16600 17000 17400 17800
Transition Frequency (wavenumber)

Figure 18. LeRoy-Bernstein Fit for VAr+ and VKr+.
Dissociation limits of VAr+ and VKr+ from LeRoy-Berstein fit.
A plot of the derivative of the vibrational energy with
respect to vibrational index to the 4/3 power verses
transition frequency (LeRoy-Berstein plot) for the observed
electronic transitions in VKr+ (triangles) and VAr (squares).
For molecules which dissociate under the influence of a -C/r4
attractive force (charge induced-dipole) these data may be
linearly extrapolated (lines) to the abscissa to obtain the
dissociation limit of the excited states of the respective
molecules. The slopes of the extrapolated lines are different
due to the difference in polarizability and reduced mass of
the two molecules and are in accord with predicted values.












Figure 18 shows the dependence of the derivative of the

vibrational energy with respect to the transition frequency

for the band systems observed in VAr+ (squares) and VKr+

(triangles). The plot shows that (AG)43 is indeed linearly

dependent on transition frequency near the dissociation and a

linear least squares extrapolation may be used to estimate the

dissociation limits, D. These extrapolated values are listed

in Table 4. Note that the values of D are not dependent on

the absolute vibrational numbering.

A useful expression may be obtained by the integration

of Eq. (17). The vibrational energy levels near the

dissociation limit will be of the form

[D E(v)] (n-2)/n = [(n-2)/2n] (v,-v)K. (19)


The parameter vD, a constant of integration, is the fictitious

vibrational quantum number of the dissociation limit itself,

i.e. E(vD) = D. Recall that for this discussion the

zero-of-energy for both D and E(v) is taken to be the

zero-point level of the ground state of the molecule. Thus,

a particular electronic state has the diabetic dissociation

energies (in conventional nomenclature) of Do = D E(0) and

De = D T,.

The dissociation energies listed in Table 4 correspond to

the difference in energy between the zero point level of the

molecule and a particular excited state of the V+ + Ar(Kr)









71

Table 4. Spectroscopic Parameter for VAr+ and VKr+.
All values are in (cm') unless otherwise noted.
VAr+ VKr+
Ground Excited Ground Excited

T _15166 15310
e _94.1 98.6

wx __1.95 1.40
wey, 0.011 0.005
k, (N/m) 11.7 18.2

D 48.7 _68.8
D" 16581 17406

Do 2986b 1368c 3811b 2047'

Dc 1415d 2096d
Diabatic threshold
bGround state binding energy determined by D AEa
"Excited state binding energy; D,' = D/ 1/2w~' + 1/4w~x' -
1/8wy,'.
dExcited state equilibrium dissociation energy; D/' = D T,.






separated atoms. It is not possible for these dissociation

limits to correspond to excited argon (krypton) atoms, as

mentioned previously, due to the large, first excitation

energy of the closed-shell rare-gas systems. Comparison of

the observed D values in VAr and VKr with the V+ atomic

energy levels" suggests the assignment of this dissociation

limit as V+ (3d34s 5P,) + Ar/Kr ('S). The identity of the fine

structure level to which excited VAr+ dissociates has been

made by the partial analysis of the weak progressions in the

same spectral region as the transitions listed in Table 3.








72

The transitions presented in Table 3 appear to arise from an

excited state dissociating into V + 5P2. Only one progression

is observed in the VKr+ spectrum, presumably it corresponds to

the most intense transition in VAr, which is a level

dissociating into V 5P2. This is the limit used in the

analysis; misassignment of which could lead to a maximum error

of 147 cm-', the 5P3-_P2 fine structure interval. The adiabatic

dissociation energy of the ground state of VAr or VKr+ is

simply the difference between any experimentally determined

excited state dissociation limit, D, and the isolated V

promotion energy to the state corresponding to that limit.

From Table 4 and the above assignment of the dissociation

limits (V 5P2 5Do = 13594.7311), the adiabatic dissociation

energy for the ground state of VAr and VKr is found to be

2986 cm-1 and 3811 cm-', respectively.

After D has been determined for a particular excited

electronic state, the vibrational binding energy, (D E(v)),

is used to derive the number of bound vibrational levels in

the potential via the application of Eq. (19) to yield VD.

The number of bound levels in each potential surface is the

largest integer less than vD. These values, included in

Table 3, are 48.7 and 68.8 for VAr+ and VKr+respectively.

According to this, one observes approximately 76% and 69% of

the bound vibronic transitions in the potential surface for

VAr and VKr+, respectively.










8

7 -

6 VAr +

5

'4






1
i 4 j j^ VKr i i







0 20 40 60
(vD v)
Figure 19. Vibrational Binding Energy for VAr+ and VKr+.
The Figure displays a plot of the vibrational binding energy
to the 1/4 power versus the vibrational index (v, v) for the
observed excited state of VKr* (triangles) and VAr (circles).
The quantity vD is the hypothetical vibrational index of the
dissociation limit of the potential, i.e., E(vD) = D. The
solid lines are the vibrational binding energies predicted for
VAr* and VKr+ from Eq. (19) and the literature values of the
rare-gas polarizabilities.












Figure 19 shows a plot of the vibrational binding

energies to the 1/4 power versus vibrational quantum number

for the excited states of VKr and VAr+. Also shown in the

figure is the predicted dependence (lines) of vibrational

binding energy for VAr+ and VKr using Eq. (15) and literature

values0" for the rare-gas polarizabilities (1.66 x 10-" cm3 for

Ar and 2.52 x 10-24 cm3 for Kr). One can see that the

theoretical values closely match the experimentally derived

points. The predictive power of this simple model of

vibrational structure implies that inductive forces dominate

the binding in these systems. One may then postulate, that

the attractive part of a potential surface, and for many

Lennard-Jones analytic potentials, the dissociation energy

(see Appendix C), is proportional the a/r4. An increase in

binding energy between the systems VAr and VKr* may therefore

be attributed to the change in polarizability of the rare-gas

partner.



Photodissociation of CoAr and CoKr*



The second group of metal-cation rare-gas systems to be

presented in this Chapter, CoAr+ and CoKr+, also displays

resonant bound-bound transitions in the visible region. These

systems, unlike VAr (Kr), each have three prominent

vibrational progressions in their photoexcitation-dissociation








75

spectrum. The congestion perturbs the spectrum slightly but

it is nevertheless experimentally tractable. Similar

vibrational analysis found in the VAr'(Kr) section is applied

here as well.

Figure 20 displays a portion of the resonant

photodissociation spectrum of CoAr* Co+ + Ar over the region

of 14 800 to 16 300 cm'. Bound quasi-bound transitions for

three progressions are easily observed in this region.

Approximately eleven transitions of one progression, ca.

150 cml in interval, account for the largest peaks in the

figure. Several transitions belonging to another excited

state, within the region 14 800 to 15 450 cm1, are seen to

converge to a diabetic dissociation limit. This portion of

the spectrum is similar in appearance the photodissociation

spectrum of VAr* found the in previous section. Dwarfed

remnants of a third progression may also be observed in the

region of 15 460 to 15 710 cm'. The curved appearance of the

peak intensities, i.e. a drop off in intensity near either end

of this spectrum is a result of the laser dye emission

spectrum (the dye tuning curve, see experimental Chapter) and

does not represent a change in the dissociation cross-section.

The photofragmentation spectrum of CoKr* is similar to

that of CoAr*. This system also displays three prominent

vibronic progressions. Fortunately, isotopic variants of Kr

are naturally occurring and may be used to help assign the

vibrational spectra of these systems. Figure 21 shows the















CD


0


0-i




O
0




14800 15000 15200 15400 15600 15800 16000 16200
Laser Frequency (wavenumber)


Figure 20. Resonant Photodissociation of CoAr+.
This figure displays a portion of the CoAr+ resonant
dissociation spectrum in the visible region. Plotted is the
observed Co* fragment current arising from the one-photon
dissociation of isolated CoAr as a function of incident laser
frequency. The relatively smaller dissociation at the low-
and high-frequency sides of the plot represents a drop-off in
the dissociation laser output intensity and not a systematic
change in the peak dissociation cross-section. Each peak in
the spectrum corresponds to an entire vibronic band, which,
because of the 2 K rotational temperature of the ions has
collapsed to less than 3 cm' FWHM (Full Width Half Maximum).
Three upper-state vibrational progressions corresponding to
three different electronic states are evident in the figure.








77

photofragmentation of CoKr Co + Kr as a function of

dissociation laser frequency in the interval from 15 420 to

15 620 cm'. The top trace shows the photofragmentation of all

naturally occurring Kr isotopic variants of the CoKr* molecule

and the bottom trace shows the photofragmentation of 59Co86Kr+

only (17.37% natural abundance'2) on an increased vertical

scale. The ability to acquire the signal of selected isotopic

variants of a molecular ion considerably simplifies the

spectrum (note the region near 15540 cm-1 in Figure 21) and

facilitates vibrational assignment.

A similar set of experimental conditions applies to the

spectra of CoAr'(Kr) as discussed for the previous rare-gas

containing diatomics. At these photon energies Kr is not

observed as a photoproduct of CoKr (similarly Ar+ is not

observed from CoAr+) as expected from the large disparity in

the ionization potential of the atoms (IP(Kr) = 13.996 eV;

IP(Ar) = 15.755 eV; IP(Co) = 7.86 eV)13. Under the normal

operating conditions of the mass spectrometer, a trace amount

of Co* from CoKr (CoAr) is observed from collision-induced

dissociative processes with residual He gas in the flight tube

of the TOFMS. In the present experiment, collision-induced

dissociation produces a small background to our laser-induced

dissociation yield that is constant and may be easily

nullified. The bottom of the abscissa axis on the

photodissociation spectra of CoAr and CoKr+ therefore

represents zero photodissociation intensity.
























8-





15425 15475 15525 15575 15625
Dissociation Laser Frequency (wavenumber)

Figure 21. Photodissociation Spectrum of CoKr+ Isotopes.
The figure displays a portion of the photoexcitation spectrum
over the region of 15 420 to 15 620 cm' for CoKr+. The top
half of the figure shows the photodissociation, Co' relative
photocurrent as a function of laser frequency, of all
naturally occurring isotopes of CoKr+. In the lower panel,
only the photodissociation of 59Co86Kr* is displayed. Isotopic
shift information is necessary to assign the absolute
vibrational numbering of the observed bands. This region of
the spectrum displays peaks from three prominent progression
that are listed in Table 6.












Dissociation laser fluence dependence of the resonant

photodissociation indicates a one-photon absorption event.

Poor temporal/spatial quality of the excitation source

prevents accurate absolute cross section measurements, but the

strongest photodissociation transitions have cross sections of

ca. of 10-7 cm2. Partially resolved rotational structure on

the vibronic transitions place a lower limit on the lifetime

of the upper levels of the transition at 10 ps. The upper

limit to the excited state lifetime is placed by the time

between excitation and kinetic energy analysis, about

5 Asec. The features in Figure 21 are representative of the

over 100 sharp vibronic bands found in the photodissociation

spectrum of CoKr+ in the region of 18 000 cm-' to below

13 500 cm-1. Most (>95%) of these vibronic transitions fall

into three simple upper state progressions from, presumably,

the same lower vibronic state. We identify these three

progressions as distinct electronic band systems.



Vibrational Analysis



The assigned vibronic positions for the photodissociation

excitation spectra, over the frequency interval of 13 500 to

18 000 cm'', of CoAr+ and CoKr* are listed in Table 5 and

Table 6, respectively. In each case the positions of the

assigned transitions are grouped into three band systems












Line positions of assigned '5Co40Ar+transitions in


wavenumbers.
A-X B-X C-X
v' observe. o-c' v' observ. o-c" v' observ. o-c*


6
7
8
9
10
11
*11
12
*12
13
*13
*13
25
26
27
28
29
30
31
32
33
34
35


14026.3
14149.0
14265.4
14375.7
14488.3
14577.6
14589.7
14677.0
14688.0
14767.1
14773.7
14780.3
15502.2
15536.3
15565.9
15592.6
15616.7
15637.5
15656.7
15672.9
15687.3
15699.5
15710.7


0.87
0.37
-0.71
-2.48
3.59
-8.39
3.75
-5.02
6.02
-5.85
0.77
7.39
-0.22
0.01
-0.50
-0.35
0.76
1.83
4.55
7.53
11.65
16.63
23.35


:


(a) Observed minus calculated
(*) Extra bands due to perturbation.


^


14076.8
14167.2
14254.4
14338.0
14418.7
14494.6
14567.6
14636.6
14701.9
14763.8
14822.5
14877.7
14930.1
14979.3
15025.6
15067.6
15106.7
15142.9
15176.9
15207.7
15236.1
15261.3
15284.9
15305.3
15323.3
15340.2
15354.9
15368.2
15378.9
15388.3
15396.6
15403.6
15409.3
15414.3
15418.5
15421.8


1.01
-0.09
-0.56
-0.68
-0.01
-0.32
0.12
0.04
-0.12
-0.22
-0.14
-0.13
0.23
0.58
1.25
0.57
0.08
-0.38
-0.19
-0.40
-0.29
-0.72
-0.16
-0.27
-0.22
1.02
2.50
4.74
6.68
9.45
13.08
17.52
22.59
28.83
36.07
44.05


14544.7
14714.3
14878.6
15034.7
15184.7
15328.2
15466.1
15598.6
15725.0
15845.1
15960.1
16069.5
16173.8
16272.0
16364.9
16453.0
16535.4
16614.1
16686.0
16754.9
16817.8
16875.9
16930.4
16979.8
17025.0
17066.9
17104.4
17138.8
17169.4
17197.0
17221.8
17243.2
17262.5
17279.6
17294.6
17307.3
17318.3
17327.8
17336.1
17343.1
17348.9
17353.9
17358.0
17361.3
17363.9
17366.1
17367.6


-0.71
-0.36
1.11
0.69
0.40
-0.26
-0.48
-0.16
0.00
-0.48
-0.31
-0.17
0.33
0.11
-0.03
0.11
-0.26
0.67
-0.30
0.54
0.19
-0.34
-0.04
-0.31
-0.44
0.48
1.04
2.67
4.36
7.02
10.66
14.58
20.00
26.81
34.84
43.97
54.52
66.79
80.80
96.55
113.94
133.28
154.28
177.15
201.78
228.39
256.59


Table 5.












Table 6. Line positions of assigned "5Co40Kr+ vibronic transitions
in wavenumbers.
A-X B-X C-X
v' observe. o-cI v' observ. o-c' v' observ. o-c


2
3
4
4
5
*5
6
*6
7
8
9
*9
10
11
13
*13
14
15
16
17
*17
18
*18
19
*19
21
*21
24
*24


13696.5
13835.4
13970.8
13981.0
14098.3
14110.1
14219.7
14233.8
14356.9
14489.0
14605.0
14625.2
14728.6
14840.1
15061.0
15063.3
15167.0
15268.0
15368.0
15455.4
15471.5
15553.0
15566.8
15640.9
15655.8
15818.2
15837.7
16048.2
16057.8


0.14
-0.12
-0.91
9.32
-6.53
5.20
-15.3
-1.22
-5.34
2.59
-2.50
17.67
2.98
-0.63
-0.67
1.64
-0.49
-2.23
-1.99
-11.1
4.98
-7.02
6.83
-9.46
5.49
-3.43
16.04
-6.67
2.86


2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
*30
31
32
33
*33
34
35


14161.4
14270.7
14377.4
14481.4
14583.5
14679.6
14779.6
14873.2
14964.9
15051.0
15138.9
15223.2
15305.2
15384.7
15462.7
15532.5
15604.7
15674.1
15743.3
15803.9
15864.9
15925.5
15984.9
16036.9
16088.3
16139.3
16187.7
16231.3
16273.3
16276.0
16315.8
16355.0
16390.5
16393.3
16426.1
16459.2


1.03
0.61
0.26
-0.26
0.07
-3.01
0.44
0.05
0.44
-2.33
-0.75
-0.25
0.45
1.25
2.93
-1.05
-0.28
0.23
2.96
-0.63
-1.33
-0.05
2.38
-0.26
-1.18
-0.18
0.61
-1.24
-2.42
0.29
-0.74
-0.23
-1.12
1.69
0.31
1.32


(a) Observed minus calculated
(*) Extra lines due to perturbation.


4
5
6
7
8
9
10
11
*11
12
*12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30


15354.4
15495.9
15633.5
15768.4
15899.8
16027.4
16152.4
16273.3
16276.0
16390.5
16393.3
16506.3
16618.4
16725.5
16830.4
16932.3
17030.4
17126.1
17218.2
17306.3
17392.0
17474.1
17553.4
17630.0
17702.9
17773.2
17840.1
17904.2
17964.8


0.35
0.21
-0.41
-0.21
-0.22
-0.66
-0.23
-0.67
2.04
-1.38
1.43
-0.18
0.51
-0.44
-0.33
0.02
-0.21
0.36
0.52
-0.07
0.01
-0.29
-0.37
0.06
-0.14
0.12
0.04
0.18
-0.06








82

labeled C-X, B-X, and A-X. The current labeling is a matter

of convenience; the ground and three observed excited states

are labeled X, A, B, and C, in order of increasing electronic

origin energy. This choice by no means indicates that the 'A'

state observed in this study is the first excited state nor

that no other electronic states lie between the A, B, and C

states. However, the chosen nomenclature is such that the A

(B,C) state of CoAr and CoKr correspond to the same Co+

atomic ion state at the dissociation limit. The most intense

point of the vibronic band (typical width 2-3 cm-'; see

Figure 21) is taken to be the vibronic band origin for the

present analysis. Table 5 and Table 6 also list the

residuals to the least squares fit of the vibronic bands to

the standard14 formula given previously in Eq. (6) from which

the constants T,, we, wxG, wy are derived. As in the analysis

of VAr and VKr, the zero of energy for this fit and all the

following discussion is taken as the zero-point level of the

ground electronic state of the molecule. The accuracy with

which Eq. (6) describes the observed vibronic structure

depends on the degree of anharmonicity of the molecular forces

and the existence of any local perturbations between the

electronic states. The best fit in this study is obtained for

the lowest vibrational levels (v' = 0 25) of the C state of

CoAr* which shows no apparent anomalous behavior. Even for

this state, however, the transition frequencies involving the

highest vibrational levels (v' = 30 46) are severely









18000 .

amm
o 17000 "
E
Q)
16000-


S15000 ALA

LL A
.o 14000-


13000
0 10 20 30 40
(v' + 1/2)

Figure 22. Vibration Fit to Band Origins for CoKr+ States.
This figure displays a least-squares fit to Eq. (6) (solid
curves) of the observed vibrational band origins of the C-X
(solid squares), B-X (triangles) and A-X (open squares)
systems of CoKr. Absolute vibrational numbering is obtained
from isotopic shift information. The molecular constants
obtained from this fit are listed in Table 7.








84

underestimated by Eq (6). and so are not included in the fit.

Complications arise, however, from the local perturbations

that all band systems other than CoAr+ C-X exhibit to some

extent.

Figure 22 shows the vibrational structure of CoKr in a

plot of transition energy of the C-X, B-X, and A-X systems

versus excited state quantum number, (v'+1/2) The solid

curves represent the fit to Eq. (6) and the symbols are the

experimental band origins. Despite the evidence of

perturbation from the missing and extra lines apparent in this

plot the overall fit is quite good. Absolute vibrational

numbering of the transitions shown in Figure 22 and listed in

Table 6 are made from the measurement of the spectral shift

among the 6Kr, "Kr, "Kr, and "Kr isotopomers of CoKr. This

yields a unique absolute vibrational numbering for the C and

B states but the extensive perturbations in the A state make

its vibrational numbering uncertain by 1 quantum.

Figure 22 clearly shows that the three excited electronic

states observed in photodissociation have similar but not

identical vibrational structure. Also from Figure 22, it is

evident that the electronic origin of the A state is lower

than the B state, but the dissociation limit of the A state is

higher than the B state which means that the A and B state

potential curves cross.

The nature and extent of the perturbations present in

this spectrum are varied. A perturbation between the C and B








85

states of CoKr occurs at an accidental degeneracy between the

v' = 11 of the C state and v' = 30 of the B state and again at

v' = 12 and v' = 33 of those states. This perturbation

appears to involve only these two electronic states with an

estimated interaction matrix element of about 3 cm-'. The A

state of this molecule is more severely and ubiquitously

perturbed than the B or C states as is evidenced by the

diminished quality of the fit to Eq. (6) (see Table 6). Extra

lines in this band system arise from perturbations with at

least one otherwise undetected state. The perturbation shifts

in the A-X system indicate a much stronger coupling between

interacting electronic states than is seen in the C-B

perturbation of the same molecule.

At present, neither the spectrum of 59Co36Ar+ nor 59Co3Ar+

(0.34% and 0.07% natural abundance'2, respectively) have been

obtained. Without isotopic substitution, the firm assignment

of absolute vibrational quantum numbers to the CoAr*

transitions listed in Table 5 is impossible. Thus, the upper

state vibrational quantum number listed in Table 5 is merely

an effective vibrational index, chosen to be close to the

absolute value.

All of the transitions observed in this study appear to

originate from the ground electronic and vibrational state of

the molecule, i.e. no hot bands have been identified. This is

understandable due to the extensive cooling these ions suffer

in the supersonic expansion. From a conservative estimate of








86

the sensitivity of the experiment (1% of a strong transition)

and a guess of the ground state vibrational frequency

(200 cm-1; see discussion below), we infer the vibrational

temperature of these ions to be less that 65 K. This is

significantly lower than the vibrational temperatures of

transition metal dimer neutrals16 supersonically expanded under

similar conditions. It is possible that ion-molecule

vibrational relaxation collisions are longer ranged or more

efficient than neutral-neutral V-T collisions, leading to a

lower final vibrational temperature for ions relative to that

of neutrals in the beam. Nonetheless, the low internal

temperature of the ions simplifies the spectrum greatly but

prevents direct determination of the ground state vibrational

frequency by photodissociation excitation spectroscopy.



Determination of dissociation limits



Similar treatment of the vibrational levels near the

dissociation limit is done here as in the treatment of

vibrational levels for the systems of VAr* and VKr*.

Figure 23 shows the dependence of the derivative of the

vibrational energy with respect to the transition frequency

for the C-X, B-X, and A-X band systems of CoAr. The plot

shows that (AG)413 is indeed linearly dependent on transition

frequency near the dissociation and a linear least squares

extrapolation may be used to estimate the dissociation limits,










200


160


S120


< 80 -


40-


0
14500 15500 16500 17500
Transition Frequency (wavenumber)
Figure 23. Dissociation Limits of CoAr+.

The Figure displays a plot of the derivative of the
vibrational energy with respect to vibrational index to the
4/3 power versus transition frequency (LeRoy-Bernstein plot)
for the A (open squares), B(triangles), and C(solid squares)
states of CoAr. For molecules which dissociated under the
influence of a -C/r4 attractive force (charge-induced dipole)
these data may be linearly extrapolated (lines) to the
abscissa to obtain the dissociation limit of the respective
excited states. These limits, D, are listed in Table 7 for
both CoAr+ and CoKr.








88

D. These extrapolated values are listed in Table 7. We must

emphasize that the values of D are not dependent on the

absolute vibrational numbering. Subsequently, the accuracy to

which the ground state binding energy is known is a function

of the LeRoy-Bernstein extrapolation and the correct

assignment of the separated atomic limits. The accuracy of

the excited state vibrational frequency and binding energy

will depend on the correct vibrational assignment.

The dissociation energies, D, listed in Table 7

correspond to the difference in energy between the zero point

level of the molecule and a particular excited state of the

Co+ + Ar(Kr) separated atoms. It is not possible for these


Table 7. Experimental Molecular Constants for 59Co4Ar+ and
59Co"Kr+ in cm1.

CoAr+ CoKr+
State A B C A B C

T, 13081 13380 14458 13336 13874 14674

w,' 165.4 120.9 175.8 148 117.8 159.0
WOx' 3.20 2.21 3.28 1.47 1.36 1.76

WcY/' 0.017 0.011 0.016 -0.002 0.003 0.003
k, (N/m) 38.5 20.6 40.1 44.8 28.4 51.7

v_ 55.3 55.6 88.9 93.5
Db 15758 15433 17370 17395 16840 18911
D,'( 2595 1993 2825 3985 2886 4158
D/e 2677 2053 2912 4059 2945 4237
aNumber of bound vibrational levels.
bDiabatic threshold.
CExcited state binding energy;D/'=D/ -1/20'/+1/4cf/-l1/8'y/.
dExcited state equilibrium dissociation energy; D,' = D T,.








89

dissociation limits to correspond to excited argon(krypton)

atoms. Comparison of the observed D values in CoAr* and CoKr*

with the Co* atomic energy levels37 suggests the assignment of

the C state dissociation limit as 3d8 3P2 Co + 'S Ar(Kr) and

the B state limit as 3d74s 3F2 Co + 'S Ar(Kr) at 13 261.1 cm-'

and 11 321.5 cm-' above separated 3d8 F4 Co+ + 'S Ar(Kr)

(ground state) atoms, respectively. This places the A state

dissociation at 11 645 cm-n above ground state atoms where no

Co electronic states presently are assigned. This

observation does not, at present, invalidate the assignment of

the C and B state limits because a number of predicted Co*

atomic terms are still undetected in this energy region.

The adiabatic dissociation energy of the ground state of

CoAr* or CoKr is simply the difference between any

experimentally determined excited state dissociation limit, D,

and the isolated Co+ promotion energy to the state

corresponding to that limit. From Table 7 and the above

assignment of the B and C state limits, the adiabatic

dissociation energies of the X states of CoAr* and CoKr are

found to be 4110 cm-1 and 5585 cm-1, respectively.

Once D has been determined for a particular excited

electronic state, the vibrational binding energy, (D E(v)),

is used to derive the number of bound vibrational levels in

the potential via the application of Eq.(3) to yield vD. The

number of bound levels in each potential is the largest

integer less than vD. These values are listed in Table 7.




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kí ¿,n?
SPECTROSCOPIC CHARACTERIZATION OF NOVEL CLUSTER IONS
By
DANIEL E. LESSEN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1992

ACKNOWLEDGEMENTS
The completion of this work would not have been possible
without the help of the other members of the research group:
Dr. Philip Brucat, my principal advisor, and fellow graduate
student Robert Asher. Dr. Brucat, served as scientific
mentor, motivator and friend. His enthusiasm in the quest for
scientific knowledge was infectious. In the beginning years
of my graduate career, it was Phil who taught me the art of
many different occupations besides chemist: namely,
electrician, machinist, plumber, and computer programmer.
I would like to thank Robert Asher, not only for his
friendship, but for sharing the physical and mental burden of
operating the experimental apparatus. Much of the research
presented in this Dissertation is a consequence of effective
teamwork between Robert and myself.
Special thanks go to my wife, Christine, for her patience
and support in all those trying moments.
I dedicate this Dissertation to my parents. Without
their support throughout my educational career I would not
have succeeded in this accomplishment.
ii

TABLE OF CONTENTS
ACKNOWLEDGEMENTS ii
LIST OF TABLES V
LIST OF FIGURES vii
ABSTRACT X
INTRODUCTION 1
EXPERIMENT 7
Overview 7
Beam Generation 10
Mass Selection 19
Optical Spectroscopy 27
Computer Control 36
INDUCTIVELY BOUND DIATOMICS 42
Threshold to Photodissociation 42
Resonant Photodissociation of VAr+ and VKr+ ... 54
Photodissociation of CoAr+ and CoKr+ 74
Resonant Photodissociation of ZrAr+ 91
Photodissociation of CaKr+ 105
Discussion 108
DIATOMIC POTENTIAL ENERGY SURFACES 116
Analytic Potentials 116
Vibrational Eigenvalues from the WKB
Approximation 119
METAL RARE-GAS CLUSTERS 133
METAL CATIONS WITH PHYSISORBED POLYATOMICS 143
Predissociation of V(OCO)+ 143
Vibration Structure of Electrostatically Bound V+-
(H20) 154
Resonant Photodissociation of V(NH3)+ 162
Resonant Photodissociation of Cr(N2) + 165
Resonant Photodissociation of Ca(N2)+ 167
iii

METAL-METAL SYSTEMS 171
Threshold Photodissociation of Cr2+ 186
Photodissociation of Ca2+ 194
CONCLUSIONS 199
APPENDIX A ELECTRICAL CIRCUITS 203
APPENDIX B COMPUTER CODE 205
WKB Grid Program 205
CAMAC Low Level Routines 213
CAMAC Header File 220
Control Program 220
Supporting Assembly Language Routines 258
APPENDIX C ANALYTIC PAIR POTENTIALS 284
Lennard-Jones Potentials 284
Born-Meyer Potential 291
APPENDIX D UNASSIGNED PHOTODISSOCIATION SPECTRA . . . 295
REFERENCES 303
BIOGRAPHICAL SKETCH 310
iv

LIST OF TABLES
Table 1. Optogalvanic Positions for Neon 31
Table 2. Ground State Spectroscopic Parameters for
NiAr+ and CrAr+ 52
Table 3. Line positions for 51v40Ar+ and 51v84Kr+ in
wavenumbers 58
Table 4. Spectroscopic Parameter for VAr+ and VKr+. . 71
Table 5. Line positions of assigned 59Co40Ar +
transitions in wavenumbers 80
Table 6. Line positions of assigned 59Co40Kr+ vibronic
transitions in wavenumbers 81
Table 7. Experimental Molecular Constants for 59Co40Ar+
and 59CoMKr+ in cm'1 88
Table 8. Line Positions for assigned vibronic
transitions of 90Zr40Ar+ in wavenumbers 94
Table 9. Unassigned line positions (cm1) for 90Zr40Ar+
grouped by progression 94
Table 10. Spectroscopic Parameters of Excited State in
ZrAr+ 98
Table 11. Dissociation Energy for ZrAr+ Excited
States 101
Table 12. Ground State Adiabatic Bond Strength. . . . 109
Table 13. Spectroscopic Parameters for Excited
States 109
Table 14. WKB Parameterization of Born-Meyer Potential
with Experimental Eigenvalues 125
Table 15. Line Positions for R2PD of Ni2+ (cm1). . . . 181
v

Table
16.
Excited State
Parameters for Metal-Ligands.
200
Table
17.
Ground State Adiabatic Bond Strength. . . .
201
Table
18.
Lennard-Jones
[8,4] Relations
288
Table
20.
Lennard-Jones
[6,4] Relations
289
Table
22 .
Lennard-Jones
[12,4] Relations
290
vi

LIST OF FIGURES
Figure 1. Experimental Apparatus 9
Figure 2. Cross Section of Source Block 12
Figure 3. Mass Spectrum of Cobalt Helide Cations. . . 22
Figure 4. Mass Spectrum of Aluminum Anions 24
Figure 5. Photofragmentation of Co8+ 26
Figure 6. Laser Dye Curve for Rhodamine R6G 28
Figure 7. Optogalvanic Transitions for Neon 30
Figure 8. Error in Quantel Dye Laser. 33
Figure 9. Doppler Shift for Coaxial versus Cross beam
Photoexcitation of V(0C0)+ 35
Figure 10. Sweet Spot of Solenoid Pulse Valve 41
Figure 11. Photodissociation Threshold for NiAr+. . . 44
Figure 12. Laser Fluence Dependence for
Photodissociation of NiAr+ 46
Figure 13. Isotopic Shift for Photodissociation of
NiAr+ 48
Figure 14. Photodissociation Threshold for CrAr+. ... 51
Figure 15. Resonant Photodissociation of VAr+ 55
Figure 16. Vibrational Fit for VAr+ and VKr+ 61
Figure 17. Residuals to the Vibrational Fit of VAr+. . 63
Figure 18. LeRoy-Bernstein Fit for VAr+ and VKr+. . . 69
Figure 19. Vibrational Binding Energy for VAr+ and
VKr+ 73
vii

Figure 20. Resonant Photodissociation of CoAr+. ... 76
Figure 21. Photodissociation Spectrum of CoKr+
Isotopes 78
Figure 22. Vibration Fit to Band Origins for CoKr+ States83
Figure 23. Dissociation Limits of CoAr+ 87
Figure 24. Vibrational Binding Energy for CoAr+ and
CoKr+ States 90
Figure 25. Resonant Photodissociation of ZrAr+. ... 92
Figure 26. Isotopic Shifts for ZrAr+ 97
Figure 27. Vibrational Fit of ZrAr+ 99
Figure 28. ZrAr+ C State Dissociation Limit 103
Figure 29. Photodissociation of CaKr+ 107
Figure 30. RMS Contour Plot of CoKr+ C state 123
Figure 31. Potential Energy Curves of CoKr+ Excited
States 127
Figure 32. WKB Error for Morse Potential 129
Figure 33. Residuals to WKB 131
Figure 34. Potential Energy Surfaces for VKr+ 132
Figure 35. Mass Spectra for the Uniquely Stable
CoAr6+ 135
Figure 36. Relative Abundance of VArn+ and CoArn+. . . 138
Figure 37. Collision Induced Dissociation of CoAru+. . 140
Figure 38. Stick Plot of V(OCO)+ Photodissociation. . 145
Figure 39. Photoexcitation Spectrum of V(OCO)+. . . . 148
Figure 40. [VO+]/[V+] Branching Ratio 150
Figure 41. Energetics for Photodissociation of VC02+. 153
Figure 42. Resonant Photofragmentation Spectrum of
V(H20)+ 156
viii

Figure 43. Isotope Shifts of V+(18OH2) minus V+(16OH2). . 159
Figure 44. Photodissociation Spectra of Deuterated
Isotopes of V(Water)+ 161
Figure 45. Resonant Photodissociation of V(NH3)+. . . 163
Figure 46. Photodissociation Threshold for Cr(N2)+ -*•
Cr+ + N2 166
Figure 47. Vibrationally Excited Photofragments of
Ca (N2) + 168
Figure 48. Mass Spectrum of Argon Seeded Nickel Beam. 173
Figure 49. Photofragmentation of Ni2Ar+ 177
Figure 50. Resonant Two-Photon Dissociation of Ni2+. . 180
Figure 51. Photodissociation Threshold of Cr2+ -*• Cr+ + Crl87
Figure 52. Cr2+ Photodissociation Mechanisms 189
Figure 53. R2PD of Cr2+ 191
Figure 54. Resonant Photodissociation of Ca2+ 195
Figure 55. Valve Driver Circuit 203
Figure 56. Bias Conditions for MicroChannel Plate
Detector 204
Figure 57. Photodissociation Spectrum of Fe2+ 296
Figure 58. Photodissociation of NiO+ -» Ni+ +0. ... 297
Figure 59. Photodissociation Spectrum of ZrOAr+ -*â–  ZrO+
+ Ar 298
Figure 60. Photodissociation Spectrum for Zr(0C0)+ -*â– 
Zr+ + 0C0 299
Figure 61. Photodissociation of Co(HOH)+ -*• Co+ + H20. 300
Figure 62. Photodissociation of Co(OCO)+ -» Co+ + C02. 301
Figure 63. Photodissociation of Co(NN)+ -* Co+ + N2. . 302
ix

Abstract of Dissertation Presented to the Graduate
School of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy
SPECTROSCOPIC CHARACTERIZATION OF NOVEL CLUSTER IONS
By
Daniel E. Lessen
December 1992
Chairman: Philip J. Brucat
Major Department: Chemistry
A variety of molecular ions, many without conventional
covalent bonds, have been generated by adiabatic supersonic
expansion of a laser driven plasma and spectroscopically
probed in the visible region. Photofragmentation of these
mass selected ions with a tunable visible laser reveals
spectroscopic parameters of both excited and ground states.
Specifically, the spectra of the systems of Cr(N2)+, CrAr+, and
NiAr+, exhibit a sharp change in photodissociation cross
section corresponding to a diabatic threshold from which the
ground state binding energy is determined. Resonant
photodissociation spectra display sharp vibronic features of
bound quasi-bound transitions corresponding to excited state
vibrational progressions for the inductively bound diatomic
systems of VAr+, VKr+, CoAr+, CoKr+, CaKr+, and ZrAr+.
Often, analysis of the vibronic transitions for a given system
x

will accurately determine the excited state vibrational
frequency, anharmonicities, and electronic origin besides the
ground and excited state binding energy. Additionally,
vibrational structure for many of these diatomic systems is
used to parameterize a variety of analytic potentials that
incorporate a charge-induced dipole attractive term via the
semiclassical Wentzel-Kramers-Brillouin method.
Transition metal cations with physisorbed polyatomic
adducts are spectroscopically probed in the visible region.
Resonant photodissociation spectra of V(H20)+, V(C02)+, and
V(NH3)+ are discussed. The photodissociation spectrum of
V (H20)+ reveals an electrostatically bound system. The
resonant photodissociation of the system V(C02)+ displays two
distinct dissociation pathways that arise from the same
photoexcited state: V(OCO)+ - V+ + C02 and V(OCO)+ - V0+ + CO.
A cursory treatment of diatomic metal-metal cation
behavior is discussed from the one-photon dissociation
spectrum of Ca2+, the resonant 2-photon dissociation spectrum
of Ni2+, and the threshold photodissociation spectrum of Cr2+.
xi

INTRODUCTION
The description of chemical phenomena at a molecular
level is the ultimate goal of any chemist. Unfortunately such
a goal would reguire a detailed knowledge of the forces
between all the present atoms, a formidable task for any
sizable system. One may, however, dissect a large system or
chemical reaction into smaller model systems consisting of a
few isolated atoms. A small, experimentally tractable system
may then be chosen to model a chemically interesting part of
the extended system; for instance, a solvated ion with its
nearest neighbors or the active atoms in the discrete step of
a reaction mechanism may be modeled. In this way, a
complicated system may be understood by the behavior of its
integral subunits.
Under this philosophy, both experimentalist and theorist
have labored to understand the quantal details of interatomic
interactions in the smallest of such model systems, the
diatomic. Due, in part, to their ease of production and good
stability, many main-group diatomic systems have been
successfully described through the synergistic effort of
experiment and theory.1 The forces found in main-group
diatomic molecules, for example H2, N2, and CO, are
1

2
quintessential examples of covalent interactions. The
understanding of the nature of covalent bonding is currently
being extended to include the effects of d orbitals by the
study of diatomics from the transition-metal series.2
Part of this dissertation will discuss the behavior of
three transition metal diatomic systems specifically, Ni2+,
Cr2+, and Ca2+, via spectroscopic information. Although
calcium is not considered a transition-metal, many of its
excited states will involve 3d orbitals. The interatomic
forces in these systems are expected to display some covalent
character, but also, inductive and electrostatic forces will
be present since the diatomic systems are charged.
Interestingly, a molecular orbital picture for the neutral
analogues, Cr2 and Ca2, suggests an adiabatic bond order of six
and zero, respectively. Experimentally, the chromium neutral
dimer has been found to have a surprisingly small bond
strength. While the calcium dimer is found to be bound via
van der Waals forces in difference to the zero bond order
prediction of molecular orbital theory.
The importance of d orbitals in chemical interactions
extends beyond their role in metal-metal bonding to their
ability to lower the activation barrier for many reactions.
Transition metal containing molecules and surfaces are
important in the catalysis of many chemical reactions both at
interfaces3 and in solution.4 The effectiveness of such
catalysts is derived, in part, from partially-filled d

3
orbitals that provide low-energy, short-term electron sites
along the reaction coordinate. Much insight will be gained by
an accurate description of the pair potential between a
transition metal and a reactant. Within this dissertation we
will present the results from the spectroscopically probed
system of V(OCO)+. Photodissociation spectra of this system
reveal an energy barrier of 1.6 eV to cleave a carbon-oxygen
bond to form VO+and CO. The bond energy of the carbon-oxygen
bond is ca. 5.43 eV in the gas phase molecule.5
As previously mentioned, the cations of homonuclear
diatomic molecules will exhibit non-covalent interactions as
well as covalent interactions. Empirically, an interaction
may be described as consisting of some percentage of the
following types of force: covalent, electrostatic, inductive,
and dispersive. Although covalent interactions are important,
they cannot account for the behavior of solute-solvent
chemistry, or surface adsorption, for example. Solute-solvent
behavior, especially ion-solvent systems, will be dominated by
electrostatic and inductive forces.
Small gas-phase isolated systems, consisting of an ion
solvated with a number of water or ammonia molecules, have
been used as models of solute-solvent behavior before.6,7,8’9’10
These high-pressure mass spectrometric studies are able to
quantify the thermodynamics of solvent-ion binding as a
function of the number of solvent molecules. However, due to
their size, the solvated ions have not been spectroscopically

4
probed, and therefore little is known about the configuration
or potential energy surface of these systems.
To simplify the study of electrostatic and inductive
forces, one may isolate a specific pair (an ion with an atom
or molecule) that contains virtually no covalent forces.
Through the formalism of classical electrostatics, the
interactions between ions, dipoles and other multipoles may be
expressed as the sum of separate contributions. The
attractive part of an electrostatic potential for a metal ion
and a water molecule would consist of a charge-dipole term, a
charge induced-dipole term, and a charge-quadrupole term.
As an initial step in understanding the chemical behavior
of a solvated metal ion, one may begin with the study of the
most chemically simple solvent imaginable, a rare gas. A
rare-gas atom possesses no permanent dipole, and it is
virtually inert. The metal ion to which this polarizable
partner is bound will have a considerably lower ionization
potential: therefore, charge transfer is minimal. A single
cation with a rare-gas adduct will display binding
interactions that are dominated by inductive forces, and
provide an ideal system to begin the understanding of physical
forces found in solution chemistry. All solvents, monatomic
or polyatomic, will have an inductive contribution to the
total solvation energy.
A rare-gas solvent is not novel. Liquid krypton and
liquid argon have been used to slow the kinetics of metastable

5
transition-metal carbonyl reactions.11’12 Significant effort has
also been given to the isolation of charged species in rare-
gas matrices.13,14,15 But how isolated are these ions? As will
be shown, the interaction of a transition-metal cation is
significant, ca. 0.5 eV. Thus, for optical studies of ions in
a matrix, large spectral shifts may be expected. It is
reasonable that the behavior of cation rare-gas systems be
described in order to understand the role of the matrix
environment with an ionic species.
Within this dissertation, spectroscopically acquired data
will be presented on several small cluster ions, specifically,
the number of atoms in the systems = 2 -*• 10, that exhibit
binding dominated by electrostatic or inductive forces. Major
emphasis is placed on the characterization of several
transition-metal cations with rare-gas adducts. The
understanding of the nature of inductive forces from these
systems will then lend support to the analysis of metal
cations with physisorbed or electrostatically bound polyatomic
molecules such as N2, C02, or H20. Direct comparison between
the systems of VRg+ (Rg = Ar, Kr) and V-H20+ suggests that
inductive forces will contribute significantly to the aqueous
solvation energy of a monovalent cation.
In some cases, the vibrational information for metal-
cation rare-gas diatomic systems is so extensive that over 80%
of the total bound levels, which cover ca. 99% of the
potential energy surface, are experimentally observed. This

6
provides a unique opportunity to accurately determine both the
vibrational frequency, and dissociation enerqy. In addition,
the extensive vibronic data may be used to parameterize some
simple analytic potential functions over the full potential
surface. An accurate knowledqe of the pair potential will
provide a powerful tool with which extended solutions may be
modeled.

EXPERIMENT
Overview
The experimental apparatus was designed to generate and
gas-phase isolate a variety of internally-cold cluster ions
for photo-interrogation. Both types of systems presented in
this dissertation, metal-metal and metal-ligand, require
unique conditions for optimal production. Inductively bound
species, by nature, such as transition-metal rare-gas
diatomics are particularly troublesome to make routinely due
to their weak binding interactions. Sufficient quantities of
refractory material must be atomized, ionized, and then
internally cooled before physisorption of rare-gas atoms to
the ionic site is possible. Production of transition-metal
rare-gas species, therefore, involves an extreme change in
temperature, spanning vaporization to condensation. This
seemingly improbable set of conditions is achieved by the
combination of a laser driven plasma and supersonic expansion.
A laser driven plasma is seeded within an inert carrier
gas, usually helium. Collisional cooling initializes cluster
formation. Subsequent adiabatic expansion results in the
generation of a variety of internally cool aggregates. Such
7

8
techniques have been successfully used to generate internally
cool neutral clusters of refractory material previously.16
This technique has also been applied with success to the
formation of both negative and positive metal cluster ions.17
Mass selection of the molecular ion beam provides a
microscopic window into the success of the expansion technique
for generating a given system. A variety of experimental
conditions, such as the backing pressure and laser
vaporization fluence, may be adjusted to maximize the
production of a desired chemical system. The experiment will
often generate a variety of cluster sizes. Effective mass
selection and detection require a fundamental understanding,
and intelligent incorporation, of various static and pulsed
ion optics. Once the mass components of the molecular ion
beam are established, photointerrogation may be performed with
a confident knowledge of the species under study.
Due to the nature of the expansion and the pumping
limitations of the apparatus, the experiment is pulsed at 9.1
Hz. Limiting the total throughput by lowering the duty cycle
of the gas allows one to maintain a high jet density and not
exceed the pumping capacity of the apparatus. However, the
pulsed nature of the experiment demands real time computer
control over the many events that occur in a cycle. A custom
computer program controls the relative timing of the
vaporization laser, the carrier gas pulse, the acceleration
stack, and the dissociation laser.

9
Figure 1. Experimental Apparatus.
The figure displays a sketch of the experimental apparatus.
A plasma is generated at the upper left of the figure in the
beam source at high pressure by the second harmonic of a
Nd3+:YAG laser. Ions and neutrals then supersonically expand
in an inert carrier (ca. 99 % He) , cool, and then travel
through differential pumping orifices (skimmers) and into the
accelerator of a custom time-of-flight mass spectrometer.
Here, positive or negative ions may be extracted at 90° to the
supersonic beam axis with a kinetic energy of ca. 1.45 keV.
Mass separation takes place as the ions pass through a 2.45 m
flight tube containing focussing and deflection optics.
Fragmentation of any ions is detected by laboratory kinetic
energy analysis performed by a 127°electrostatic sector at the
end of this flight tube. Laser photoexcitation may occur
colinearly, as shown in the figure, or may intersect the beam
at 90° prior to entrance of the electrostatic sector.

10
Figure 1 displays the salient features of the
experimental apparatus that was used for this research. The
experiment is detailed below by following the journey of a
cluster ion from inception to mass selection to
photodissociation.
Beam Generation
The start of an experimental cycle occurs in the beam
source and is marked by the birth of a chemical system.
Production of a desired system is achieved when the surface of
a sample rod is laser vaporized within the high pressure pulse
of a carrier gas. Focussed light of a Quantel Nd+3:YAG
laser (model 580) , via the second harmonic (532 nm) , will
generate a plasma. Laser light, 7 ns in duration, is
typically chosen in the range of 15-40 mJ/pulse. The light is
focussed to a point smaller than 1 mm in diameter. This
corresponds to a photon fluence of ca. 108 W/cm2 (lower limit)
at the rod surface. The laser generated plasma is thermally
quenched in the carrier gas through collisions. Carrier gas
for the present research is either pure He, for metal-metal
clustering, or a mixture that has a small percentage (ca. 1-2%
mole fraction) of ligand (L) in helium. As will be shown, an
assortment ML+ systems, where L = Ne, Ar, Kr, C02, or N2, may

11
be generated from the appropriate gas mixture. Three-body
collisions initialize clustering to form a variety of Mx or
MxLy neutral and ionic clusters.
Figure 2 displays a cross section of the source assembly
used to house the sample rod and provide a reaction zone where
the nascent clusters may be formed. Optimizing the
configuration of a nozzle source is rather enigmatic.
Nucleation to molecular species is kinetically controlled and
therefore critically dependant on the local pressure in the
plasma generation zone. With low gas density, typically only
a single adduct is observed to physisorb to a metal cation.
The clustering efficiency improves with an increase in carrier
gas density; a direct reflection of the fact that both
three-body and two-body collisions will increase with
pressure. However, too much gas pressure has been observed to
quench the positive ion beam and is believed to be due to
electron recombination with the positive ions.
Note, the onset of expansion is similar to quenching a
reaction; the observance of ionic species is an attestment to
the fact that the cluster ensemble is not at thermodynamic
equilibrium. Even the vibrational and rotational temperatures
for a given molecular species are known not to correspond to
the same temperature after an expansion.18 Molecular
vibrations equilibrate more slowly than rotational degrees of
freedom and will therefore be at a higher temperature with
respect to the translational temperature of the beam.

12
Transition Metal Rod
Teflon Spacer
Laser (532 nm)
Gas Inlet
Stainless
Steel Block
Precision Bearing
O-Ring
Figure 2. Cross Section of Source Block.
This figure displays a sketch of the source block used for
generation of metal-cation rare-gas systems. The channel to
the right of the sample rod allows laser access for plasma
generation and exit orifice for expanding carrier gas. The
plasma is collisionally thermalized in the carrier gas pulse
within the channel prior to expansion. Three-body collisions
initialize the aggregation of cluster systems. The rod is
mounted in precision bearings to ensure a wobble-free
rotation. O-rings seal off the volume near the sample plasma
generation zone to maximize the carrier gas density thereby
maximizing the cooling/clustering capability.

13
Nonetheless, an estimated 5,000 to 10,000 internally cool M2+
and/or ML+ may be routinely generated 9.1 times a second.
A given vaporization laser pulse produces a finite number
of neutral and ionic atoms. Yield for a desired species is
then in competition with the production of other clusters for
the available material. In attempts to produce rare-gas
ligated metal cations, metal-metal clusters have been observed
at the expense of metal-ligand systems for higher carrier gas
pressures.19 The, presumably, more weakly bound metal-ligand
systems would find the collisional frequency, and therefore
the progression to equilibrium imposed by a high pressure
regime deleterious while in competition with more strongly
bound metal-metal systems. Unfortunately, one may not easily
predict the exact source conditions necessary to generate a
particular system.
Several theoretical and experimental studies have been
done to characterize the cooling properties of supersonic
expansions. For compressible, adiabatic, and isentropic flow,
the following relations for temperature (T), pressure (P), and
density (p) in terms of mach number (M) and heat capacity
ratio (7) have been derived:20

14
These relations are valid for compressible flow of a gas that
is confined in varying area channels. The first two
equalities are the familiar adiabatic relations that may be
found in any thermodynamic textbook.21 For an adiabatic
expansion of an ideal gas, a drop in pressure will be
accompanied by a reduction in temperature. The last term
expresses the physical characteristics of a system to the mach
number. From this term, one observes that an adiabatic
expansion of a gas will results in an increase in the mach
number.
The mach number is defined as v/a where v refers to the
mass flow velocity and 'a' is the local speed of sound. The
speed of sound is a function of temperature given by (7RT/m)1/2.
J. B. Anderson and J. B. Fenn22 have determined the limiting
flow velocity as mach number approaches infinity as (5/7)1/2a.
Initial source temperature will determine the speed-of-sound.
Notice that a high mach number does not reflect a large mass
velocity but rather a reduction of the local speed-of-sound as
the gas expands from a high pressure region to a low pressure
region. High mach numbers are therefore desirable because
they correspond to a small translational velocity distribution
and hence a cold beam.
Using the above pressure relationship, Eq. (1) , it is
possible to calculate the exit mach number of a nozzle with a
known pressure ratio. The cross sectional area, A, of the

15
channel is related to the mach number and heat capacity ratio
with the following equation:20
^2
Mi
M,
1 + (^-^)M22
1 +
2 (Y—1)
(2)
Immediately, one may determine the pressure conditions in
which the nozzle is choked23 (also referred to as an
underexpanded condition); i.e., for what cross-sectional area
in a diverging nozzle is M = 1. The ratio of background to
reservoir pressure for a monatomic gas is 0.487. This ratio
under typical experimental conditions of our apparatus is ca.
1CT8. The expansion for the apparatus is supersonic: it is so
supersonic that the above equation results in an unrealistic
nozzle exit-mach number of 80.
Obviously, as the molecular density drops from a decrease
in pressure, a point is reached in which the molecules can no
longer communicate. The beam becomes discontinuous and a
terminal mach number is reached. J. P. Toennies and
K. Winkelmann24 have determined the terminal mach number as a
function of downfield distance (x) normalized to the nozzle
diameter (x/d) for various p0d. The variable p0 is stagnation
pressure and the quantity Pyd is proportional to the
bimolecular collision frequency.
One may estimate the quantity of p0d experimentally to
determine the terminal mach number for a typical set of

16
conditions. For our apparatus, the stagnation pressure may be
determined from a knowledge of the flow rate and the volume of
a single gas pulse. Flow rate is easily measured and is ca.
100 SCCM (standard cubic centimeters per minute) with an
applied cylinder pressure of ca. 70 psi. The temporal width
of the gas pulse is determined by varying the plasma
generation event within the gas pulse. Presence of seeded
ions reveals a pulse width of ca. 1.0 msec. The volume of gas
per pulse is found from the product of the nozzle cross
section area, the pulse width, and the gas velocity as
3.8 cm3/pulse, or, at the experimental cycle of 9.1 Hz,
35 cm3/sec. The ratio of flow rates, before and after
expansion, multiplied by the backing pressure will estimate
the pressure in the nozzle channel as ca. 30.7 torr. The
quantity p0d, with a nozzle diameter of ca. 2 mm, is ca. 6.0
torr-cm and corresponds to a terminal mach number of ca. 10.
This is considered a low to moderate expansion for our
apparatus. More extreme pressure drops are possible that
would correspond to a terminal mach number of ca. 20.
Several versions of nozzle blocks, in which the channel
and exit orifice configurations were varied, have been tried.
The one described below is particularly suited to the
generation of weakly bound M+L species (refer to Figure 2).
The source block is made of stainless steel with outer
dimensions of 3.17 cm by 3.17 cm by 3.81 cm. A central gas
channel of length 3.17 cm and diameter 2.2 mm perpendicularly

17
bisects the sample rod through-hole. At the exit end of the
gas channel is a diverging 18° cone ca. 6.4 mm depth. O-rings
capture the sample rod and make a hermetic seal on either side
of the gas flow channel equidistant from the center at 1.7 mm.
The rotating rod is supported by precision bearings. Teflon
spacers provide further rod support and apply the necessary
force to make the o-rings seal. The total volume, excluding
the gas inlet and exit channel volume, around the rod is ca.
49 mm3, which is about 40% of the total possible gas volume in
the block. A pulse of gas originates upstream, 6.3 mm from
the rotating rod and subsequently flows around the
circumference of the rod before exiting down a 1.9 cm long
channel.
A commercial solenoid valve (General Valve series 9)
controls the carrier gas pulse. An exit orifice of 0.76 mm
diameter is plugged with a Kelef popet in the de-energized
state. The valve is overdriven* with an electrical pulse of
150 V and ca. 150 ¿isec in duration. This extreme pounding
will shorten the lifetime of the Kelef popet and necessitate
its replacement after several weeks of operation.
Nevertheless, a gas pulse of ca. 1.0 ms, which corresponds to
a flow rate of ca. 40-500 SCCM, will result at the
experimental cycle of 9.1 Hz. The flow-rate is adjustable
with backing pressure and limited by the diffusion pump
‘Manufacturer's recommendation for continuous duty is 28
volts.

18
throughput. Interactive computer control allows the timing
adjustment of the vaporization laser impingement on the rod
surface to coincide within the gas pulse.
The resulting cluster neutral and ion ensemble expands
from the high pressure region of the nozzle channel into a
500 L aluminum cylindrical chamber (inner diameter 114 cm and
height 61 cm) evacuated by three diffusion pumps. Conversion
of the random motion of the gas/cluster ensemble within the
nozzle channel into directed flow upon adiabatic expansion
results in a supersonic beam. A supersonic nozzle will
therefore convert enthalpy into kinetic energy. The cooling
properties of this technique have routinely generated diatomic
species with vibrational temperatures of less than 60 K and
rotational temperatures of 5 K.25 From the observance of
blackbody radiation, a temperature change of 7,000 K to a few
Kelvin has occurred in a fraction of a second.
The neutral/ion cluster ensemble traverses two
differential-pumping orifices. Passage through these regions
is gained through two conical, 55°, electroformed skimmers
that are positioned 12 cm and 60 cm downstream of the nozzle
exit with apertures of 1.0 and 1.5 cm, respectively. The
skimmers define regions of successively lower vacuum pressure
and skim out a region within the mach bottle of the supersonic
expansion.18 The main chamber, in which the molecular beam
first expands, is pumped by two differential pumps, a 10”

19
(NRC) and a 6" (Varían model VHS-6) that provide an operating
pressure of 10'5 torr via a total pumping speed of 9600 1/s.
The two skimmers mark the entrance and exit of a wedge
shaped sector that is 15% of the total volume of the main
expansion chamber. This region is pumped separately by a 6"
diffusion pump with a water cooled baffle. Under operation
the background pressure in this region is ca. 10‘6 torr.
Mass Selection
The second downfield skimmer stands at the entrance of
the acceleration stack of a time-of-flight mass spectrometer.
After ca. 110 cm of travel and 620 jusec, the cluster ensemble
reaches the center of the stack. In this region, ions, either
positive or negative, may be extracted at 90° to the molecular
beam. A computer triggered acceleration pulse imports ca.
1.45 keV of kinetic energy to the cluster ions in a two-stage,
Wiley-McLaren accelerator.26 The first stage contains the
weaker field, 35 V/cm, with the second stage being
considerably larger at 1450 V/cm. This allows one to maximize
temporal resolution of ions at the detector (2.45 m downfield)
by correcting for space deviations at the accelerator. The
space deviation is defined by the skimmers mentioned earlier.
The electrical pulse is supplied by a Cober (model 605P) high

20
voltage pulse generator that is capable of delivering 1.5 keV
pulse with < 100 ns risetime.
The acceleration stack consists of seven, stainless steel
parallel plates (dimension 15.24 by 15.24 cm by 1.6 mm thick)
separated by 1.0 cm Teflon insulating spacers. Ions enter the
low field region in the rear of the stack approximately
between the second and third plates. All plates have
centrally located slots of 2.54 cm by 7.62 cm to allow for
unhindered ion passage. Two of the seven plates, which define
the high field region, are grided with 90% open screen to keep
the field region flat. The ratio of the high and low electric
fields may be optimized with a simple voltage divider by
maximizing the mass resolution at the detector. Discrete
components are used to minimize capacitance thus keeping the
acceleration pulse sharp. The voltage divider consists of a
network of resistors and a high voltage switch. Five
internal, i.e., within the vacuum hardware, 1.0 ki), ± 1%-
tolerance glass resistors determine the low field strength.
The last plate is grounded so that the ions are in a
field-free region upon departure from the acceleration stack.
The acceleration stack marks the beginning of a time-of-
flight mass spectrometer (TOFMS). Ions are subjected to a
variety of deflecting and focusing optics before detection by
dual microchannel plates. Horizontal deflectors correct for
the forward momentum of the expanded molecular beam. Two
electrostatic einzel lenses make a parallel to point focusing

21
device for the ions. Each einzel assembly consists of three
cylindrical aluminum tubes of length 7.62 cm and inner
diameter of 6.99 cm. The three concentric elements are spaced
6.35 mm apart. An applied potential of 450 V (positive
potential for cations) on the central einzel element provides
an ion focal length of ca. 85 cm for 1450 keV ions.
After 2.45 m of travel, the ions are detected by a dual
microchannel plate detector. Ideally the acceleration stack
imparts equal kinetic energy to all species; thus, arrival
time is proportional to the square of the mass-to-charge
ratio. Figure 3 displays the parent mass distribution for
cobalt cation with physisorbed helium atoms. The ability to
physisorb multiple helium atoms to a cation nucleation site
attests to the extreme cooling capabilities of the apparatus.
Also, notice that mass peaks are well separated with the four
amu spacing among CoHen+ peaks being well resolved. Unit mass
resolution is possible with the primary mass resolving power
of ca. 300 at 100 amu.
The ion detector consists of two Galileo microchannel
plates27 (MCP) captured in a custom assemblage. The two plates
are separated by a 0.127 nm nickel-lifesaver shim that
electrically contacts the outer perimeter while leaving the
detection area open. Metal shim provides an electrical
connection for a resistive voltage divider. An individual
microchannel plate in this configuration has been biased with
up to 900 V without a breakdown. Incoming ions generate

22
50
Figure 3.
60 70 80 90
AMU
Mass Spectrum of Cobalt Helide Cations.
100
The figure displays a portion of the parent mass spectrum,
relative abundance versus amu, for a single cobalt cation with
several physisorbed helium atoms. The naked cobalt cation at
58 amu is shown off scale to reveal the helium substituents;
it is approximately a factor of eight larger than CoHe2+. The
ability to physisorb several helium atoms, upwards of seven
(shaded in black for emphasis), is an attestment to the
cooling and clustering property of the supersonic expansion.

23
secondary electrons in the dual detector. These ions are
detected at a stainless steel electrode ca. 2.8 mm behind the
exit surface of the second microchannel plate. The gain of an
MCP is ca. 107. Detection efficiency is exponential as a
function of gain voltage with roughly a factor of five
increase in signal level per one-hundred volts of bias.
Single ion detection is possible although not preferred for
optical studies.
Slight electrical modification is required to mass select
negative species. All potentials of electrostatic ion optics
and the acceleration stack are merely reversed in polarity.
Only the detector assembly requires special handling.
Regardless of the polarity of the ions, secondary electrons
must still be generated and detected. For detection of
cations, a negative potential is applied to the entrance MCP.
Conversely, for detecting anions a positive potential must be
applied to the entrance MCP but the electrical bias must
ensure that secondary electrons are accelerated through the
second MCP. This problem may be overcome by floating the
entire assembly with respect to ground. Proper electrical
connections are discussed in Appendix A. Figure 4 displays a
parent mass spectrum for anions of aluminum. Mass resolution
is similar to that of a cation mass spectrum.
Before detection, a 127° electrostatic sector turns the
ions off the flight tube axis. 28,29 The electrostatic sector is
a kinetic energy analyzer. A field strength of 600 V/cm

Relative Intensity
24
AMU
Figure 4. Mass Spectrum of Aluminum Anions.
The figure displays the cluster anions of aluminum over a mass
region of 100 to 700 amu. This region of the mass
distribution encompasses clusters anions of 5 to 25 aluminum
atoms. Notice the anion Aln+ is relatively larger than any
other anion in the beam and represents a 'magic number'.

25
for this optic is necessary to turn parent ions of 1.45 keV
kinetic energy. The aluminum sector provides an ion path on
an 8.9 cm radius with a channel width of 2 cm. The sector
electrodes are 7 cm wide. Resolution is proportional to the
radius and is a function of the initial velocity spread of the
ions. The magic 127° 17' angle between entrance and exit
apertures has been found to optimize the refocusing and
resolving properties of an electrostatic sector.
Collision induced dissociation (CID), metastable decay,
and photoinduced dissociation of a parent molecule may be
observed by tuning the sector field to transmit fragment ions
of lower kinetic energy. The daughter ions will arrive at the
same time of the parent ions but at a proportionately smaller
kinetic energy. The first generation of this sector had a
1.27 cm entrance and exit aperture and gave a kinetic energy
resolving power of ca. 10. In a later version of the sector,
the apertures were narrowed to 4.7 mm, thereby limiting the
off-axis velocity spread at the entrance without significant
parent throughput loss. This configuration increased the
resolving power to 15. Figure 5 displays a sector scan of
Co8+ photodissociated with a fixed laser frequency of
28 169 cm'1 and power of 35 mJ/pulse.
An electrostatic sector in tandem with a TOF is a
powerful combination. This combination allows one to mass
select a given parent ion, perform some experiment on that
parent, then mass select the fragments.

26
AMU
Figure 5. Photofragmentation of Co8+.
This figure displays the photofragments of Co8+ with 355 nm
light. The field strength of the 127° electrostatic sector is
scanned to transmit fragment ions from a given parent system.
The parent mass of 472 amu is not displayed under the gain
conditions of the detector. Secondary mass resolving power is
about 15.

27
Optical Spectroscopy
The ability to mass select provides only moderate insight
into the chemical behavior of molecular systems. For this
experiment it is considered a prerequisite for optical
interrogation. Optical analysis will directly access the
quantal details of a system. Such information is invaluable
for describing the interatomic forces among the bound atoms.
The tunable light source for this experiment is a Quantel
(model 581) Nd+3:YAG pumped dye laser that provides both fixed
and tunable light. The laser is timed to photo-intersect the
ion packet prior to entrance of the 127°. The sector may then
be scanned to observe the photo-induced fragments at a fixed
frequency, as discussed in the preceding section, or, a
particular fragment may be monitored as a function of
wavelength.
The visible region is accessed through a variety of
organic dyes dissolved in methanol. A total range of 540 cm'1
to 780 cm'1 may be easily reached with approximately seven
different dyes. The dye laser tunes over the fluorescence
region of each dye. Figure 6 displays the laser intensity as
a function of wavelength for 532 nm pumped rhodamine R6G
(C2gH3,N203Cl) .30 This particular dye will allow access to a ca.
25 nm (700 cm'1) wavelength region centered at 590 nm. The
picture symbolizes the 'tuning curve' for the dye. The R6G
dye has a conversion efficiency of ca. 20% with a 200 mJ/pulse

28
wavelength (nm)
Figure 6. Laser Dye Curve for Rhodamine R6G.
The figure displays the dye laser intensity as a function of
wavelength (tuning curve) for rhodamine R6G dye. This
particular dye will access a wavelength region of ca. 25 nm
(700 cm1) .

29
pump beam. Many of the photodissociation spectra presented
in this dissertation result from scanning in several different
dye regions. These scans must be combined, with good overlap,
to form a complete photodissociation picture.
The dissociation laser scans linearly in time with
respect to wavelength. Several pairs of points taken manually
relate the wavelength to a computer generated data index. The
computer-collected photodissociated event is then correlated
to a wavelength position. Unfortunately, normal optical
optimization and play in the mechanical parts of the scanning
mechanism may cause consecutive scans to be different by as
much as 0.1 nm. This corresponds to an unacceptable 2.5 cm"1
error at 630 nm. For this reason, the spectra are calibrated
to a primary standard.
Optical spectra may be calibrated with optogalvanic
transitions found in a neon discharge. A conventional neon
indicator lamp is powered by a current-limited power supply at
ca. 100 V (DC) and 10.0 mA. A 4% reflection of the primary
beam off a turning optic intersects the discharge region of
the neon bulb. Simultaneous scanning of optogalvanic
transitions with the photodissociation event provides an
accurate method to determine the absolute wavelength position
of the dye laser. These optogalvanic line positions are well
known and may be used a primary standard.31,32
Figure 7 displays an optogalvanic spectrum over the
region 580 to 720 nm. Notice that optogalvanic transitions

30
13
O -
o
580 620 660 700 740
Wavelength (nm)
Figure 7. Optogalvanic Transitions for Neon.
This figure displays the optogalvanic transitions found in a
neon discharge lamp over the wavelength region 580 to 720 nm.
Incident laser light may enhance or deplete charge carriers in
the discharge region, thus changing the resistance of the lamp
and appearing as either a positive or negative going
electrical signal across a capacitively coupled load. The
line position are well known and provide a primary standard
for calibration of optical spectra taken with a pulsed laser
in the visible region. The small gap in the spectrum near
684 nm is due to the poor overlap of two dye regions (see text
for explanation).

31
Table 1. Optogalvanic Positions for Neon.
Laser Dye*
nm
cm-1
sign
Source
R610
585.250
17,086.72
-
b, c
588.190
17,001.31
+
b, c
594.483
16,821.34
+
b, c
597.553
16,734.92
+
b, c
R640
603.000
16,583.75
-
b, c
607.434
16,462.69
-
b, c
609.616
16,403.77
-
b, c
612.845
16,317.34
-
b, c
614.306
16,278.53
+
b, c
616.359
16,224.31
+
b, c
621.728
16,084.20
+
b, c
626.650
15,957.87
+
b, c
630.479
15,860.96
-
b, c
DCM
633.443
15,786.74
+
b, c
638.299
15,666.64
-
b, c
640.225
15,619.51
+
b, c
650.653
15,369.18
-
b, c
653.288
15,307.18
+
b, c
DCM/LD
659.895
15,153.93
-
b
667.828
14,973.92
-
b
671.704
14,887.51
-
b
692.947
14,431.12
-
b
696.543
14,356.615
+
d
702.405
14,236.801
+
d
LD-700
703.241
14,219.88
+
b
717.394
13,939.34
-
b
724.517
13,802.30
-
b
743.890
13,442.85
-
b
“Common name.
bRef. [31] .
cRef. [32] .
dRef.
[33] .
may occur in either the positive or negative direction
corresponding to an increase or decrease in the charge
carriers in the discharge region. Table 1 provides a list of
optogalvanic transitions easily observed on the wavelength
region of 585 to 740 nm. These transitions were taken in air
and are grouped according to the dye region in which they are
observed

32
After the first attempt to calibrate the Quantel laser
scan box to optogalvanic transitions, it was determined that
the laser did not scan linearly in time but had a systematic
and increasing deviation. Figure 8 shows the error of the
Quantel dye laser readout as a function of wavelength. This
annoying error is easily corrected by a least-linear-squares
method relating the Quantel scan box to the optogalvanic
transitions.
Once the scan data has been corrected to air wavelength
it must then be corrected to vacuum. This is done by using
the dry air refractive index of 1.0002926.^ Simply multiply
the optogalvanic corrected air wavelength by the refractive
index to get the vacuum number. Conversion to wavenumbers is
accomplished by taking the inverse of the wavelength and
multiplying by the correct conversion factor of 107 nm/cm.
Finally, for
those spectra that
are
taken along
the
ion
flight tube axis
one must correct
the
frequency
for
the
Doppler shift.
For absorption,
the
Doppler shift
is
determined by the
following equation:
34
,, _ ' observed
''corrected (l~v/c) ' '
where v is frequency in wavenumbers, v is the ion velocity and
c is the speed of light.

33
The figure displays the error (the literature value for an
optogalvanic transitions minus the quantel scanbox readout) of
the Quantel dye laser as a function of wavelength.
Optogalvanic transitions for neon are used as a primary
standard and compared to the readout offered from the Quantel
laser system. The dye laser has provisions to correct the
wavelength for a constant value. However, as the plot
confirms, the error (shown as solid squares) as a function of
wavelength describes a line with slope as well as intercept.
This plot was derived from a single uninterrupted scan.

34
The ion speed is calculated from the kinetic energy that
the ion receives in the acceleration stack of the mass
spectrometer. The ion speed may be calculated with the
following equation (non-relativistic approximation):35
(4)
where K is the imparted kinetic energy in volts, m is the mass
in amu. The velocity, v, will then be in cm/jusec.
Figure 9 displays the Doppler shift for a
photodissociation band of V(OCO)+ -> V+ + 0C0. Comparing the
photodissociation spectra of coaxial (top spectrum) and cross
beam (bottom spectrum) laser excitation, one observes that the
coaxial spectrum is red shifted by 2.93 cm'1. This suggests
the kinetic energy imparted to the ions in the acceleration
stack of the time-of-flight is ca. 1.45 keV. Apparently the
acceleration stack is quite efficient; recall that the applied
voltage in the TOF acceleration stack is 1.5 keV.
The tunable laser system is capable of scanning at
different rates. For preliminary scans, a faster scan rate
(0.6 nm/min.) is used to economize the data acquisition time.
Eventually some photodissociation spectra demand a closer look
and therefore a slower scan rate (0.04 nm/min.) to utilize the
narrow linewidth. The dye laser resolution is ca. 0.2 cm'1 at
16 000 cm'1. In this event, several repeating but slow scans

35
16141 16143 16145 16147 16149
Laser Frequency (wavenumber)
Figure 9. Doppler Shift for Coaxial versus Cross beam
Photoexcitation of V(OCO)+.
The figure displays the Doppler shift for coaxial excitation
upper scan) and cross beam excitation (middle curve) of a band
in the photodissociation spectrum of V(OCO)+ -*• V+ + 0C0. The
lower scan corresponds to a wavelength interference pattern of
an etalon with free a spectral range of ca. 1.73 cm1. The
Doppler shift of 2.93 cm'1 corresponds to a parent ion kinetic
energy of 1.45 keV. This is consistent with the applied
acceleration voltage of 1.5 keV.

36
may be done over an interesting region of the spectrum.
These repeating scans may be averaged to increase the
signal-to-noise ratio. Unfortunately, accurate overlay of
multiple spectra is complicated by the poor re-setablity of
the mechanical grating drive. An optical device that has
been found useful for aligning separate but repeating scans is
an etalon. An etalon is an interferometer; constructive and
destructive interference is a function of incident wavelength.
This interference may be monitored simultaneously with the
photodissociation event for a given scan. The peaks
corresponding to constructive interference may be easily
aligned between different scans. See the bottom trace of
Figure 9 for an example of an etalon scan.
Computer Control
The experiment would be impossible to run without
computer control. Within the experimental time period of
approximately 100 msec, sample generation, mass selection, and
optical interrogation all occur. Experimental success depends
the proper timing of many events: in chronological order, the
carrier gas pulse, the vaporization laser light, the
acceleration stack pulse, and the dissociation laser light.
To ensure success, data collection, relative timing of
experimental events, and waveform digitization are all

37
controlled with a personal computer and a CAMAC (Computer
AutoMated data Acquisition and Control)36 crate.
Optical interrogation of the ion beam demands precise
timing control. This is especially important for cross-beam
optical interrogation because the spread in arrival time of a
given ion size is roughly 100 nsec. Even fluctuations in the
power line will affect the acceleration stack voltage, and are
easily seen in the arrival time of the ion packet for
photodissociation in a cross-beam configuration. Critical
timing parameters are controlled by a LeCroy model 4222
programmable delay generator that has ± 200 psec accuracy.
Precise timing control demands that the computer operate
in real-time. This is accomplished with a custom computer
program that make use of the internal clock of a personal
computer. All timing pulses are initiated at 9.1 Hz by an
interrupt routine. Other computer tasks are suspended in the
background until the experimental timing sequence is
completed. The computer code (C language) for the real-time
control and data acquisition of the experimental apparatus is
included in Appendix B.
Electrical signals induced in the MCP detector by cluster
ions are pre-amplified by a factor of 100 (Pacific video
amplifier) before digitation by a 100MHz transient recorder
(DSP model 2001S transient recorder) . Time-of-flight mass
spectra are recorded and averaged at the experimental rate of

38
9.1 Hz. Optical spectra are recorded in single sweep fashion.
Low resolution optical scans require about one hour for 20 nm.
Signal Optimization
When making transition-metal rare-gas systems care must
be taken before experimentation to minimize perennial oxide
and water contaminants. These contaminants preferentially
bind to the transition-metal cation and hence minimize the
amount of desirable ML+ product. Gas mixtures are prepared by
a specially dedicated manifold system. Typically, a 50 L
cylinder is pumped out thoroughly to remove any contaminants.
When possible, gas is delivered in the appropriate amount from
a new and fully pressurized cylinder. This insures that the
partial pressure of volatile contaminants in the tank is at a
minimum.
Stainless steel gas lines leading into the vacuum chamber
are pumped for 8 hrs then purged with the appropriate gas/gas-
mix just before an experimental run. Further precautions
against water contamination warrants the use of a Molesieve
trap in a liquid nitrogen bath. The Molesieve is housed in a
copper coil. The copper coil represents the only non¬
stainless tubing in the gas inlet system. The gas line is set
up so that the copper tubing may be optionally bypassed.

39
Sample rod and source block preparation also requires
similar scrutiny. All transition metal rods are ca. 99% pure
with the exception of the chromium rod. This rod was plated
locally and no effort has been made to characterize its
purity. The transition metal rod is lightly filed or sanded
to remove surface contaminants and to crudely smooth the
surface. The source-block channel is meticulously cleaned
with Q-tips and methanol. The entire stainless steel block is
then ultrasonicated in a soap solution for 5 min, another
5 min. in methanol, and then two successive 5 min. intervals
in water. After this cleaning process the source block is
heated to 200°C for ca. 10 min to remove water. Expediently,
the sample rod is secured within the nozzle block, appropriate
connections are made, and the assemblage is placed back in the
vacuum chamber before it can cool.
For the production of V(H0H)+, water is a desirable
component of the carrier gas. To cluster water, a two-stage
pressure system is incorporated. A pure tank of helium
provides the backing pressure of 100 psi to a small ca.
200 cm3 cylinder. About 2 ml of water is placed in this
cylinder. This corresponds to approximately 0.3% mole
fraction of water in carrier gas. A second regulator controls
the final gas-valve backing pressure.
In addition to worrying about contaminants one must also
optimize the signal-to-noise (S/N). There are three major
factors that influence the signal-to-noise ratio

40
significantly: the gas pulse, the rod surface, and the
vaporization laser stability. Unfortunately, little can be
done to improve shot-to-shot stability of the laser system.
However, vibrations may be minimized with a solid table and
sturdy optical mounts.
The valve is adjusted to produce a reasonable flow rate
in the 'sweet spot'. Figure 10 displays a picture of the flow
rate verse the applied electrical pulse duration. Notice that
the flow rate has a local minimum near 158 /¿sec corresponding
to ca. 100 seem. For best stability the electrical pulse is
set to this minimum. Overall S/N critically depends on
pressure fluctuation and therefore it is best to minimize flow
rate fluctuation by minimizing the first derivative of this
curve.
The rod is constantly turned at 1/3 RPM with a Hurst
synchronous motor to prevent burning a hole in the surface and
therefore to maintain long term signal-to-noise stability.
The journey of a cluster ion from inception to detection
has been followed. The combination of a laser generated
plasma with a supersonic expansion enables one to produce
virtually any imaginable system. The use of two mass
selection stages provides superb control over parent and
daughter ions. This particular apparatus is quite facile at
producing weakly bound ions for the purpose of optical
probing.

41
The figure displays flow characteristics of the solenoid valve
as a function of applied electrical pulse width. Flow rate is
measured in standard cubic centimeters per minute (SCCM). In
the de-energized state the solenoid valve is closed with the
aid of a stiff spring. The valve may be opened against the
force of the spring with a 150 V electrical pulse. The figure
displays a unique position, the 'sweet spot', which
corresponds to a local minimum in flowrate. Mechanically, a
dynamic equilibrium between the restoring force of the spring
and the opening force of the electromagnet will result in the
limitation of popet bouncing. In addition, operating the
valve at the sweet spot minimizes fluctuations in flowrate
with any change in valve behavior, i.e. the first derivative
of this curve is small in the vicinity of the minimum.

INDUCTIVELY BOUND DIATOMICS
Threshold to Photodissociation
This chapter is dedicated to the presentation and
analysis of data obtained from the photodissociation of
several cation, rare-gas containing, diatomic systems. The
photophysics leading to dissociation may be divided loosely
into two types depending on the lifetime of the dissociative
event. If the lifetime is very short, as in direct
dissociation, only a broad spectrum will be observed. This is
the case for the photodissociation of NiAr+ and CrAr+. In
contrast to this behavior, the lifetime of the photoexcited
state may be sufficiently short to be observed in
photodissociation, but sufficiently long to reveal vibrational
and rotational information. The systems, specifically VAr+,
VKr+, CoAr+, CoKr+, ZrAr+, and CaKr+, all display resonant
transitions, i.e., bound-bound vibronic transitions, followed
by dissociation. Obviously, more information may be garnered
from the systems that display vibrational transitions than
from those that display only a featureless threshold. But
also, the analysis of these systems is more demanding and will
therefore deferred to the next section. We will introduce
42

43
the analysis of metal rare-gas diatomics with the systems of
NiAr+ and CrAr+, which display only a featureless threshold.
Nonetheless, a featureless threshold is quite informative.
Figure 11 displays the photofragmentation of
NiAr+ -» Ni+ + Ar as a function of dissociation laser frequency
on the interval from 17 400 to 18 100 cm'1. The production of
Ar+ is not observed as a photoproduct of NiAr+ at these photon
energies as expected from the large disparity in the
ionization potential of the two atoms: IP(Ar) = 15.755 eV and
IP(Ni) = 7.633 eV.37 Internal electronic excitation of the Ar
atom is not energetically possible either; the first excited
state is at 11.54 eV (93 143 cm'1).37 Excitation of argon would
require the energy of five visible photons in this wavelength
region, an unlikely event. Therefore, photofragmentation of
NiAr+ is monitored as the Ni+ fragment ion current transmitted
by the 127° electrostatic sector.
With the high intensity of laser light, a multi-photon
event, i.e., the concerted absorption of two or more photons,
is possible. The Quantel dye laser is capable of delivering
a power fluence of 108 W/cm2 to the ion packet. This
corresponds to a photon fluence of ca. 1017 photons/cm2 in the
visible region which is more than sufficient for the process
of multiphoton absorption.
Of course the probability for a multiphoton event will
depend on exact nature of the transition envolved. One-photon
dissociation cross sections of resonant transitions have been

44
17400 17600 [ 17800 ' 18000
Laser Frequency (wavenumber)
Figure 11. Photodissociation Threshold for NiAr+.
The figure displays the relative photofragmentation of
NiAr+ -*â–  Ni+ + Ar as a function of laser frequency over the
interval 17 400 to 18 100 cm1. A jump in the one photon
photofragmentation is observed at 17 984 cm'1 indicating a
threshold for producing excited 2F7/2 Ni+ ions. This
establishes the binding energy of NiAr+ as 0.55 eV.

45
estimated at the aforementioned power for MRg+ systems as
5 x 10'17 cm2.(38) Thus, one in five photons that cross the
interaction region defined by the cross section will result in
dissociation. A two-photon cross section will be smaller.
Nonetheless, two-photon processes have been observed under
similar laser power in the photodissociation of Ni2+.(39) In any
case, correct analysis of an optical transition is necessary
the for accurate description of chemical behavior.
Figure 12 displays the relative Ni+ photocurrent as a
function of incident laser fluence. The laser fluence
dependence of the dissociation yield at 18 020 cm"1 (ca. 40 cm"1
above the dissociation edge) shows a linear fragmentation
response over a range of 0.5 to 8.0 mJ/pulse cm"2. Recall, in
a weak field approximation the absorption intensity is
proportional to the incident light intensity (Beer-Lambert
Law) .40 Thus, a linear relation between fragmentation and
laser fluence indicates that the photodissociation at this
energy involves a simple one-photon absorption event. This
leaves no ambiguity as to the value of the excitation energy
imparted to the NiAr+ by the laser.
Under the normal operating conditions of the mass
spectrometer, a trace amount of Ni+ from NiAr+ is observed
from collision-induced dissociative processes. The data
presented here are in the form such that the small CID
contribution to the dissociation has been nullified.

46
0 2 4 6 8
Laser Fluence (mJ/pulse)
Figure 12. Laser Fluence Dependence for Photodissociation of
NiAr+.
The figure displays the fluence dependence for the
photodissociation of NiAr+ at the wavelength of ca. 554 nut.
This wavelength position is to the blue of the
photodissociation threshold of displayed in Figure 11. A
linear curve for the fluence dependence determines that the
threshold is one photon is nature.

47
To within the signal-to-noise of the present data, the
photodissociation action spectrum of NiAr+ in the region of
18 000 cm"1 appears as a featureless edge. Presumably, this
indicates the onset of a photodissociation threshold, i.e.,
the point at which the laser photon has just enough energy to
produce (excited state) products with zero kinetic energy.
Therefore, one may attribute the edge energy of 2.2 3 eV
(17 984 cm'1) as the sum of the binding energy of NiAr+ and
some promotion energy in the isolated Ni+ ion. The absence of
any vibrational or electronic hot band features associated
with the threshold at 17 984 cm'1 implies extensive cooling of
the NiAr+ emanating from the supersonic-expansion ion source.
Since it is energetically impossible to excite the argon
atom in the probed spectral region, the absorption spectrum of
NiAr+ must be similar to the absorption of the bare Ni+ ion.
Consultation of the energy levels of Ni+ shows that electric
dipole allowed transitions would not be expected within the
manifold of states arising from the 3d9 configuration since
all of these states have the same parity. The lowest,
fully-allowed electronic state corresponding to 3d84p
configuration (and electric dipole connected to the ground
state) is 6.3 9 eV(37) above the 2D5/2 ground state of Ni+. The
photodissociation of NiAr+ appears to occur through a weakly
allowed one-photon transition at 2.3 eV where no isolated Ni+
transitions are expected. However, the ground state system is

48
1 1 1 1 1 i i i i | i i i i
17970 17980 17990 18000
Laser Frequency (wavenumber)
Figure 13. Isotopic Shift for Photodissociation of NiAr+.
The figure displays a closeup of the region near the
photodissociation threshold displays a spectroscopic shift for
two isotopes of NiAr+. The lighter isotope, 58Ni40Ar+ (dotted
line), is shifted 0.8 ± 0.15 cm'1 to the blue of the threshold
for 60Ni40Ar+(solid line). This shift corresponds to a ground
state vibrational frequency of 235 ± 50 cm'1.

49
undoubtedly bound and, thus, the magnitude of the observed
diabatic limit would be larger than any suspected separated
atomic limit energy. One possible assignment of the
photodissociation feature in Figure 11 is the threshold for
production of 2f7/2 Ni+ and 's Ar. The transition derives its
nature from the parity forbidden, but spin allowed
3d84s (2F7/2) - 3d9 (2D5/2) transition in isolated Ni+. If this is
the case, the NiAr+ ground state binding energy (D0) is the
difference between the Ni + 2f7/2 - 2D5/2 transition energy of
1.68 eV (13 550.3 cm"1) and the observed threshold energy of
2.23 eV, or 0.55 eV.
Since nickel has several naturally occurring isotopes
(58Ni, 60Ni predominantly at 68.3% and 26% respectively)33 it is
possible to simultaneously measure the photodissociation
spectrum of both isotopes. Figure 13 displays a closeup of
the region near the diabatic threshold at 17 970 to
18 000 cm"1. The isotope shift between the photodissociation
features of 58Ni40Ar+ and 60Ni40Ar+ is 0.8 ± 0.15 cm'1 with the
heavier isotope being shifted to higher energy. This shift
corresponds to the difference in the vibrational energy of the
ground state of these two species. An equation relating the
isotopic shift to the vibrational frequency and the reduced
mass is easily derived from the definition of the force
constant, k = /¿(27tgjc)2.(41) After some manipulation, the
vibrational frequency may be expressed in terms of the isotope
shift, Av, as follows:

50
The variable p is the square root of the ratio of reduced
masses. Presumably, this vibrational energy is zero point and
the ground state vibrational frequency of NiAr+ may be
determined as ca. 235 ± 50 cm1.
Besides NiAr+, the photodissociation spectrum of CrAr+
also displays a threshold in the visible region. Figure 14
displays the photodissociation spectrum for the process CrAr+
-*• Cr+ + Ar over the region of 14 440 to 14 700 cm'1. A
significant increase in photodissociation intensity is seen to
begin at 14 500 cm'1 which marks the onset to a diabatic
dissociation into excited fragments. Perturbations due to
background states irregularly modulate the photodissociation
spectrum for photon energies above 14 490cm'1.
The separated atomic configuration of the photofragments
for the dissociation is Cr+(6D) + Ar(*S) . The excited atomic
state electronic configuration of the transition metal cation
is in accord with the only spin allowed transition37 within ca.
6 eV of the ground state, Cr+(6S). The large disparity in
ionization potentials (IP(Ar) - IP(Cr) = 9.0eV)37 between Cr
and Ar indicates that Cr+ is the only possible charged
photoproduct. Dissociation into excited state Ar atoms is
also impossible, as previously discussed in NiAr+ system,
since the first excited state lies ca. 11.5 eV above the
ground state. Due to the cooling the parent ions suffers in

51
14440 14480 14520 14560 14600 14640 14680
Laser Frequency (wavenumbers)
Figure 14. Photodissociation Threshold for CrAr+.
The figure displays the relative photofragmentation spectrum
of CrAr+ -*• Cr+ + Ar as a function of laser frequency over the
region of 14 440 to 14 700 cm'1. The onset to a one-photon
diabatic dissociation limit corresponding to the separated
atomic levels of Cr+(6D) and Ar(’S) is marked with an
arrowhead. The ground state binding energy of this molecule
is determined from this threshold and the Cr+ promotion energy
to be 0.29 ± 0.04 eV.

52
Table 2. Ground State Spectroscopic Parameters for NiAr+ and
CrAr+.
System
Conf ig.a)
D0 (eV)
we (cm‘)
K (N/m)
NiAr+
3d9
0.55
235
77
CrAr+
3d5
0.29
"Metal ion atomic configuration in separated atom limit.
the supersonic expansion, the origin of the optical feature
is assumed to be the vibrationless level of the molecules.
Similar fluence dependence measurements as performed in NiAr+
confirm that the diabatic threshold corresponds to a one-
photon event. The adiabatic dissociation energy may then be
determined by subtraction of the atomic promotion energy in
Cr+ from the observed diabatic dissociation limit to yield
0.29 ± .04 eV for CrAr+. The uncertainty in the adiabatic
dissociation limit arises from the uncertainty in the J state
of the Cr+ ion upon dissociation.
Unfortunately, isotopic information is not reliable for
CrAr+, unlike that of NiAr+. Attempts to determine the
isotopic shift of 52Cr40Ar+ versus 53Cr40Ar+ (and/or ^Cr^Ar4) ,
which occur naturally at 84%, 9.5% (2.4%)33 respectively, are
complicated by the rough nature of the photodissociation
spectrum and the relatively low natural abundance of another
isotopically substituted system.

53
Both systems discussed in this section, NiAr+ and CrAr+,
have similar properties. A singly-charged cation is
physisorbed to a rare-gas atom. Spectroscopy performed in the
visible region on these systems, results in a
photodissociation feature that is derived from an excited
state of the cation. Neither excitation nor charge transfer
of the rare-gas atom is energetically impossible. In
addition, all photodissociation events correspond to a one-
photon excitation. The spectroscopically determined
characteristics of NiAr+and CrAr+ are listed in Table 2.
Since there is little likelihood of any formal charge
residing on the Ar atom in either NiAr+ or CrAr+, a good
approximation of the nature of the binding in these molecules
may be derived from a picture of an almost unperturbed
transition-metal cation with a polarized Ar atom. The binding
forces would be dominated by simple charge induced-dipole
forces. If this is the case, the attractive part of a
classical potential surface is proportional to l/r4.(42) Thus,
the binding energy for a given system is significantly
dependent on the internuclear separation. This would explain
the difference in adiabatic binding energy between NiAr+ and
CrAr+. The respective valence electronic configuration is
(3d9) for Ni+ and (3d5) for Cr+. Allowing for d orbital
contraction across the transition-metal row, one would expect
that the NiAr+ system, having the smaller radius, would be
bound by more than the CrAr+.

54
Resonant Photodissociation of VAr+ and VKr+
The diatomics VAr+ and VKr+ will be the first systems to
be discussed that display resonant photodissociation of bound
levels. The kind of data manipulation found in this section
is representative of the remaining systems discussed in this
chapter. For the sake of completeness, the results of the
data analysis are included in each section. A detailed
treatment of vibrational fitting and the application of the
LeRoy-Bernstein procedure for determination of the
dissociation limit is included in this section. The
determination of vibrational numbering through isotopic
analysis is postponed to the ZrAr+ section.
One may notice that the line positions for the systems of
VAr+, VKr+, CoAr+, CoKr+ presented in this Chapter have been
revised from previously published data. 43,38 This was before we
were aware of the nonlinearity of the Quantel scan box (see
experimental section). Correct wavelength positions will be
published in a future paper that will include recently
acquired results for the photodissociation spectra of VXe+ and
CoXe+. All vibronic line positions listed in this
Dissertation are accurate to ca. ± 1.5 cm'1.
Figure 15 displays a portion of the one-photon resonant
photodissociation spectrum for the process of VAr+ -* V+ + Ar
over the visible region of 16 150 to 16 650 cm'1. A series of
bound-bound vibronic transitions belonging to an excited state

55
16150 16250 16350 16450 16550 16650
Laser Frequency (wavenumber)
Figure 15. Resonant Photodissociation of VAr+.
This figure displays a portion of the one-photon resonant
photodissociation spectrum of VAr+. Relative V+ photocurrent
(ordinate) is displayed as a function of laser frequency
(abssisa). The horizontal axis indicates zero
photodissociation. No Ar+ photofragments are observed in this
spectral region. Note the strong upper state vibronic
progression converging to a diabatic dissociation limit at
16 581 cm'1. Note also, the perturbation occurring near
16 330 cm'1 and the weak bands belonging to different
progressions evident in the red end of the figure. The
spectrum above 16 600 cm"1 is weak and apparently continuous
indicating a direct bound-continuum photodissociation at these
regions.

56
of VAr+ is evident. At this excitation energy,
photoproduction of Ar+ (similarly, Kr+ is not observed from
VKr+) is not possible due to the large disparity of ionization
potential of the atoms. The ionization potentials37 of Kr, Ar,
and V are 13.996 eV, 15.755 eV, and 6.74 eV, respectively.
Under the normal operating conditions of the mass
spectrometer, a trace amount of V+ from VAr+ is observed from
collision-induced dissociation with the residual He gas (ca.
1 x 10'7 Torr) in the flight tube. For this system, collision-
induced dissociation (CID) produces only a small, and
relatively constant background to the photoproduction yield
and may be nullified. The bottom of the horizontal axis of
Figure 15 therefore corresponds to zero photo-production of
V+.
The portion of the spectrum shown in Figure 15 is
especially revealing. A progression of red-degraded vibronic
bands converges to a diabatic dissociation limit of 16 581 cm'1
at which point the spectrum becomes continuous. More than one
upper state progression is evident (see particularly the red
end of the spectrum) and numerous perturbations indicate that
the upper state of these transitions interact, as shown by two
closely spaced bands near 16 330 cm"1. The upper state
anharmonicity is also made apparent by the diminishing
interval amoung transitions with increasing laser frequency.
The resonant photodissociation spectrum for VKr+ is
similar to that of VAr+. This spectrum also displays a

57
vibrational progression, but unlike the spectrum of VAr+ it is
not visibly perturbed by another state. The band shapes in
both these spectra demonstrate partially resolved rotational
structure indicative of a large increase in average
internuclear distance upon photoexcitation and a cold
( < 10 K) initial rotational distribution of the parent
molecule. No electronic or vibrational hot bands have been
assigned for either molecule. The partially resolved
rotational structure of the vibronic transitions places a
lower limit on the lifetime of the upper levels of the
transition at 10 ps. The upper limit to the excited state
lifetime is placed by the time between excitation and kinetic
energy analysis, about 5 jus for travel time in the 127°
electrostatic sector.
Dissociation laser fluence dependence, for both V+-(rare
gas) systems, of the resonant photodissociation transitions
indicates a one-photon absorption event is responsible for the
photoproduction of V+. A more thorough description of using
laser fluence dependence to determine the number of photons of
a given photodissociation feature was given in the section of
NiAr+. Poor temporal/spatial quality of the excitation source
unfortunately prevents accurate absolute cross-section
measurements. However, the strongest photodissociation
transitions have cross sections of ca. 1017 cm2.

58
Table 3. Line positions for 51V40Ar+ and 51VMKr+ in wavenumbers.
V'
VAr +
Observed
o-ca
V'
VKr+
Observed
o-ca
1
15303.0
0.73
2
15548.0
0.82
2
15387.9
-0.83
3
15639.1
1.56
3
15470.7
-0.76
5
15807.7
-2.35
4
15550.4
-0.13
6
15891.1
-1.18
5
15625.9
-0.11
7
15971.4
-0.55
6
15698.4
0.43
8
16049.3
0.24
7
15766.9
0.52
9
16123.8
0.17
8
15832.2
0.70
10
16195.7
0.10
9
15893.9
0.69
11
16265.5
0.37
10
15952.1
0.44
12
16331.7
-0.49
11
16007.5
0.47
13
16397.0
0.23
12
16059.0
-0.19
14
16459.1
0.14
13
16108.0
-0.20
15
16519.3
0.51
14
16152.5
-1.83
16
16576.0
-0.20
15
16192.9
-4.66
17
16631.2
-0.13
*15
16199.3
1.76
18
16685.8
1.63
16
16239.0
1.09
19
16734.9
0.12
17
16276.1
0.69
20
16784.2
1.12
18
16310.3
0.11
21
16829.6
0.35
19
16339.9
-2.55
22
16872.2
-1.00
*19
16344.3
1.87
23
16915.8
0.82
20
16372.7
0.70
24
16954.0
-0.55
21
16398.3
-0.77
25
16991.0
-1.18
*21
16401.9
2.85
26
17026.5
-1.12
22
16423.9
0.22
27
17060.7
-0.41
23
16445.9
-0.03
28
17092.5
-0.11
24
16465.4
-0.47
29
17121.8
-0.29
25
16482.6
-0.88
30
17149.6
0.04
26
16498.9
-0.11
31
17176.5
1.34
27
16512.7
0.26
32
17199.4
0.46
28
16524.3
0.56
33
17222.3
1.50
29
16534.3
1.23
34
17243.1
2.35
30
16543.0
2.41
35
17262.5
3.49
31
16550.7
4.52
36
17279.2
3.83
32
16556.9
6.90
37
17296.5
6.47
33
16562.0
9.78
38
17311.3
8.24
34
16566.4
13.70
39
17323.4
9.08
35
16570.0
18.38
40
17337.1
13.19
36
16572.8
23.76
41
17348.2
16.31
37
16575.1
30.07
42
17358.2
19.93
(a) Observed minus calculated.
(*) Extra lines due to perturbation.

59
Table 3 lists the positions of the assigned VKr+ and
VAr+ photodissociation excitation transitions in the interval
from 15 000 to 18 000 cm-1. The most intense point of the
vibronic band (typical width 2-6 cm-1) is taken to be the
vibronic band origin in this analysis. Only the strongest and
least perturbed progression in VAr+ has been presented. Most
of the transitions for the photoexcitation spectra of VAr+ are
attributed to excitation of three upper electronic states, all
of which dissociate into V+(5Pj) + Ar('S). Although hampered
by the perturbations and intensity anomalies in the weaker
progressions, one may tentatively assign the dissociation
limit corresponding to the strongest progression as V+(5P2) +
Ar by correlation of the extrapolated molecular dissociation
limits with the fine structure intervals in atomic V+. Only
one progression is observed in the VKr+ spectrum, presumably
corresponding to the most intense transition in VAr+. In any
case, the misassignment of the separated atomic limit could
lead to maximum error of 147 cm'1, which corresponds to the 5P3
- 5P2 fine structure interval.
Further evidence for the correct assignment of the
separated atomic limit may be found in the spin-allowed
selection rule for diatomic systems. The ground state atomic
configuration for vanadium cation is 5D, which, upon
combination with a ‘S Ar would produce a variety of quintet
molecular terms. Similarly, the excited atomic state, 5P, for

60
V+ would produce quintet molecular terms. The excited state,
which lies ca. 1.68 eV above the ground state, is the only
quintet occurring within 4 eV of the ground state.37 This
argument, of course, is dependent on the exact angular
coupling cases of the two electronic states.
Vibrational Analysis
Vibrational transitions may be fit to third order in (v'
+ 1/2) with the following well-known formula:44
E{v) =Teo+u'e(v'+l/2) -(¿ex/e{v'+l/2)2+uey'e(v,+ l/2):i. (6)
This allows one to determine the electronic term (T^) , the
equilibrium vibrational frequency (go/), and the anharmonicity
terms, (coexe') and (ci>eye') of the excited state. For the VAr+
system, the exact vibrational numbering is not known and
therefore represents an arbitrary numbering scheme. However,
the numbering has been chosen to yield a reasonable
vibrational frequency. Accuracy of this numbering scheme will
be tested in the following chapter. The zero of energy for
the vibrational fit and all subsequent manipulations is taken
as the zero-point level of the ground electronic state.
Electronic term Teo is determined directly from a fit of the
observed transitions Eq. (6) and is 1/2 coe" smaller than the
electronic term commonly denoted45 as Te.

61
O 10 20 30 40 50
(v' + 1/2)
Figure 16. Vibrational Fit for VAr+ and VKr+.
The figure displays the vibrational fit of the observed
vibronic transitions for VKr+ (triangles) and VAr+ (squares).
The observed transition are least-squares fit to Eq. (6) to
determine the vibrational frequency and anharmonicities of
each system. The solid lines for each system represent the
calculated levels from the least-squares fit.

62
Figure 16 displays the calculated and experimental points
for the vibrational fit. The accuracy with which Eq. (6)
describes the observed vibronic structure depends upon the
degree of anharmonicity of the molecular forces and the
existence of any local perturbations between the electronic
states. The best fit is obtained for the lowest vibrational
levels of each system. The residuals to the least squares fit
are also included in Table 3 and, except for very large v'
values, show no significant deviation.
In practice, the criterion for an acceptable vibrational
fit depends upon the behavior of the residuals of the observed
and calculated vibrational levels. If the vibrational
information is sufficient, such as is found in VAr+ in which
37 bands are observed, one may fit the levels to several
anharmonic terms. Figure 17 displays the residuals to the
vibrational fit of Eq. (6) to observed levels in VAr+. A
vibrational fit, containing one anharmonic term, to the lowest
31 bands (squares) displays a systematic error in the
residuals. This systematic error may be removed by the
inclusion of a second anharmonic term (triangles). Of course
one may continue to fit more vibrational levels with the
addition of more anharmonic terms but this is unrevealing. In
some cases attempts to fit the larger v' often increase the
residual error of the lower states, thus the determination of
a)e will be poor. Accurate parameterization of larger v'

63
(V + 1/2)
Figure 17. Residuals to the Vibrational Fit of VAr+.
The figure displays the residuals (observed - calculated) for
the vibrational fit of the observed bands of VAr+ to Eq. (6).
A least-squares fit to the equation containing one anharmonic
term (squares) and a least-squares fit to the equation contain
two anharmonic terms (triangles). Two entries occur at
v' = 15, 19 and 21 corresponding to a splitting of the
vibrational levels by a perturbation. The plot displays a
pictorial representation of the effect of adding more terms
the Taylor's series expansion of the vibrational equation to
the residuals, specifically, the removal of a systematic
error. Generally, if vibrational information is available two
anharmonic terms are included in the fit of the bottom most
vibrational levels. The number of vibrational levels is
increased until the root-mean-square deviation of the
residuals, in the absence of perturbated states, exceeds
1.5 cm'1 for those fitted levels.

64
vibrational levels with Eq. (6) is not of significant
consequence as a modified analysis treating the vibrational
levels closest to the dissociation limit will be presented
below.
Absolute vibrational numbering of the transitions listed
in Table 3 is made from the measurement of the spectral shift
among the 86Kr, MKr, 83Kr, and 82Kr isotopomers of VKr+. This
yields a unique absolute vibrational numbering for the upper
level of the transition. A detailed description of the
utilization of isotopes for the determination of vibrational
numbering will be addressed in the ZrAr+ section. At present,
neither the spectrum of 59V36Ar+ nor 59V38Ar+ (0.34% and 0.07%
natural abundance,33 respectively) has been obtained. Without
isotopic substitution, the firm assignment of absolute
vibrational quantum numbers to the VAr+ transitions listed in
Table 3 is impossible. Thus, the upper state vibrational
quantum number listed in Table 3 is merely an effective
vibrational index, chosen to be close to the absolute value.
The correct numbering is, of course, important for the
vibrational fit and the subsequent determination of the
vibrational frequency and the electronic term. Assignment of
the reddest observed transition to the origin band lowers the
vibrational frequency by ca. 5%.
All of the transitions observed in this study appear to
originate from the ground electronic and vibrationless state
of the molecule: i.e., no hot bands have been identified.

65
This is understandable due to the extensive cooling these ions
suffer in the supersonic expansion. From a conservative
estimate of the sensitivity of the experiment (1% of a strong
transition) and a guess of the ground state vibrational
frequency (200 cm-1; see discussion below) , one may infer the
vibrational temperature of these ions to be less than 65 K.
The low internal temperature of the ions simplifies the
spectrum greatly but prevents direct determination of the
ground state vibrational frequency via photodissociation
excitation spectroscopy.
Not all of the electronic states predicted from the
accessible V+ atomic ion states combined with a ‘S rare-gas
atom have been detected in this photodissociation study.
Optical selection rules for absorption would limit the number
of accessible transitions for excitation and not all the upper
levels of those accessible transitions may efficiently
dissociate. The fate of the excited states of these ions is
determined by a competition among radiative stabilization
(fluorescence to a bound level), radiative dissociation
(fluorescence to a dissociative level), and non-radiative
dissociation through direct coupling to a continuum level
(predissociation). Since optical absorption is detected in
this study through a vibrational predissociation of the upper
state on an appropriate time-scale, many transitions in these
molecules may go undetected.

66
LeRov-Bernstein Derived Dissociation Limits
Vibrational levels near the dissociation limit are poorly
parameterized by a series expansion about equilibrium in
Eq. (6) , but are better described by a functional form that
considers the nature of the attractive forces at work at large
internuclear separations. LeRoy and Bernstein46,47 have proposed
a procedure for the determintion of the dissociation energy
from the observed vibrational levels. Their derivation begins
with the semiclassical WKB” approximation:
(v + 1/2) *4(2p)1/2[SiM [E(v) ~ U(R) ] 1/2dR. (8)
h Jrx (v)
The variable /¿ is the reduced mass and E(v) corresponds to the
Vth vibrational energy level. The integral bounds are a
function of the integrand where E (v) =U (R2) =U (R,) ; the variables
R, and R2 refer to the internuclear distance on the repulsive
and attractive potential surface, respectively. At large
internuclear separation, the vibrational index v may be
treated as a continuous variable. The derivative of the above
equation with respect to v results in the following equation:
= -Í (2|i)1/2 [E(v) - U(R) ] -V2dR. (9)
dE{v) h I , ,
J Rj. (v)
'WKB approximation will be discussed in the next Chapter.

67
For a diatomic molecule that dissociates according a
-C/Rnpotential, one may approximate the interatomic potential
in the limit of large R with the potential of the form
U{R) = D ~ — . (10)
Rn
Dissociation energy is given by the variable D and R is the
internuclear separation. The vibrational eigenvalues may then
be expressed as a function of C and the outer turning point,
R2, of the potential,
E(v)
(11)
Substitution of U(R) from Eq. (10) into Eq. (9) and then
elimination of C with Eq. (11) from the integrand results in
the following equation:
dv = 2(2^....-2 [*2M [ ^{v)a -1] dR
dE(v) h[D - E(v) ] 1/2JRiM Rn
(12)
This integral may be put in a more convenient form by changing
the variable of integration to y = R2(v)/R. The following
equation results:
dv = 2(2 [i)1/2c1/n f**'**- dy (13)
dE(v) h[D - E(v) ] (1/2+1/n) Ji y2[y - l)1/2‘
In the limit of R2/Ri -*â–  00 the integral is known33 and results
in an analytic expression involving the T function,48

68
dE{v) = hC~1/nriT (1 + 1 /n) [D _ E, ), dv (27i|i)1/2r(l/2 + 1/n)
Several terms may be combined to form a constant, K;
K _ hC~1/nnT (1 + 1/n) ,15)
(2tih) 1/2r(l/2 + 1/n) '
For the molecules under study in this work, the long
range attraction forces between the vanadium atomic ion and
the rare-gas atom will be dominated by simple charge
induced-dipole forces. Therefore C and n in Eq. (10) are
fixed49, respectively, as
C = , n = 4. (16)
In this expression a is the polarizability of the rare-gas
atom. Thus, the constant K is equal to 0.501 and 0.374 (cm1)1/4
for CoAr+ and CoKr+, respectively.
For sufficiently dense vibronic levels, the derivative of
the eigenvalues may be approximated with the following
equation:
. ^(v) = - EÍV-1)] (17)
dv 2
Thus, substitution of the above equation into Eq. (14) results
in an expression that may be easily plotted:
(aG) 4/3 = [D - E(v) ] i64/3 .
(18)

69
200
180
160
140
£2 120
o 100
<
^ 80
60
40
20
0
15800 16200 16600 17000 17400 17800
Transition Frequency (wavenumber)
Figure 18. LeRoy-Bernstein Fit for VAr+ and VKr+.
Dissociation limits of VAr+ and VKr+ from LeRoy-Berstein fit.
A plot of the derivative of the vibrational energy with
respect to vibrational index to the 4/3 power verses
transition frequency (LeRoy-Berstein plot) for the observed
electronic transitions in VKr+ (triangles) and VAr+ (squares).
For molecules which dissociate under the influence of a -C/r4
attractive force (charge induced-dipole) these data may be
linearly extrapolated (lines) to the abscissa to obtain the
dissociation limit of the excited states of the respective
molecules. The slopes of the extrapolated lines are different
due to the difference in polarizability and reduced mass of
the two molecules and are in accord with predicted values.

70
Figure 18 shows the dependence of the derivative of the
vibrational energy with respect to the transition freguency
for the band systems observed in VAr+ (sguares) and VKr+
(triangles) . The plot shows that (aG)4/3 is indeed linearly
dependent on transition freguency near the dissociation and a
linear least sguares extrapolation may be used to estimate the
dissociation limits, D. These extrapolated values are listed
in Table 4. Note that the values of D are not dependent on
the absolute vibrational numbering.
A useful expression may be obtained by the integration
of Eg. (17). The vibrational energy levels near the
dissociation limit will be of the form
[D - E{v) ] = [ {n-2)/2n] (vD-v) K. (19)
The parameter vD, a constant of integration, is the fictitious
vibrational guantum number of the dissociation limit itself,
i.e. E (vD) = D.
Recall
that
for
this discussion
the
zero-of-energy for
both D
and
E(v)
is taken to be
the
zero-point level of the ground state of the molecule. Thus,
a particular electronic state has the diabatic dissociation
energies (in conventional nomenclature) of D0 = D — E(0) and
De = D - Tm.
The dissociation energies listed in Table 4 correspond to
the difference in energy between the zero point level of the
molecule and a particular excited state of the V+ + Ar(Kr)

71
Table 4. Spectroscopic Parameter for VAr+ and VKr+.
All values
are in (cm1) unless
otherwise
noted.
VAr+
VKr+
Ground
Excited
Ground
Excited
T
xeo
15166
15310
we
94.1
98.6
wexe
1.95
1.40
ueye
0.011
0.005
K (N/m)
11.7
18.2
v D
48.7
68.8
D“
16581
17406
D0
2986b
13 68c
3811b
2047c
Dec
1415d
2 096d
“Diabatic tl
ireshold
bGround state binding energy determined by D - AEatomic
‘Excited state binding energy; D0' = D/ - l/2ooe' + l/4o)cxx' -
l/SCO^e'-
dExcited state equilibrium dissociation energy; D/ = D - T^.
separated atoms. It is not possible for these dissociation
limits to correspond to excited argon (krypton) atoms, as
mentioned previously, due to the large, first excitation
energy of the closed-shell rare-gas systems. Comparison of
the observed D values in VAr+ and VKr+ with the V+ atomic
energy levels37 suggests the assignment of this dissociation
limit as V+ (3d34s 5Pj) + Ar/Kr (1S) . The identity of the fine
structure level to which excited VAr+ dissociates has been
made by the partial analysis of the weak progressions in the
same spectral region as the transitions listed in Table 3.

72
The transitions presented in Table 3 appear to arise from an
excited state dissociating into V + 5P2. Only one progression
is observed in the VKr+ spectrum, presumably it corresponds to
the most intense transition in VAr+, which is a level
dissociating into V+ 5P2. This is the limit used in the
analysis; misassignment of which could lead to a maximum error
of 147 cm'1, the 5P3-5P2 fine structure interval. The adiabatic
dissociation energy of the ground state of VAr+ or VKr+ is
simply the difference between any experimentally determined
excited state dissociation limit, D, and the isolated V+
promotion energy to the state corresponding to that limit.
From Table 4 and the above assignment of the dissociation
limits (V+ 5P2 <- 5D0 = 13594.7311), the adiabatic dissociation
energy for the ground state of VAr+ and VKr+ is found to be
2986 cm-1 and 3811 cm-1, respectively.
After D has been determined for a particular excited
electronic state, the vibrational binding energy, (D — E(v)),
is used to derive the number of bound vibrational levels in
the potential via the application of Eq. (19) to yield vD.
The number of bound levels in each potential surface is the
largest integer less than vD. These values, included in
Table 3, are 48.7 and 68.8 for VAr+ and VKr+respectively.
According to this, one observes approximately 76% and 69% of
the bound vibronic transitions in the potential surface for
VAr+ and VKr+, respectively.

73
Figure 19. Vibrational Binding Energy for VAr+ and VKr+.
The Figure displays a plot of the vibrational binding energy
to the 1/4 power versus the vibrational index (vD - v) for the
observed excited state of VKr+ (triangles) and VAr+ (circles).
The quantity vD is the hypothetical vibrational index of the
dissociation limit of the potential, i.e., E(vD) = D. The
solid lines are the vibrational binding energies predicted for
VAr+ and VKr+ from Eq. (19) and the literature values of the
rare-gas polarizabilities.

74
Figure 19 shows a plot of the vibrational binding
energies to the 1/4 power versus vibrational quantum number
for the excited states of VKr+ and VAr+. Also shown in the
figure is the predicted dependence (lines) of vibrational
binding energy for VAr+ and VKr+ using Eq. (15) and literature
values50 for the rare-gas polarizabilities (1.66 x 10—24 cm3 for
Ar and 2.52 x 10—24 cm3 for Kr) . One can see that the
theoretical values closely match the experimentally derived
points. The predictive power of this simple model of
vibrational structure implies that inductive forces dominate
the binding in these systems. One may then postulate, that
the attractive part of a potential surface, and for many
Lennard-Jones analytic potentials, the dissociation energy
(see Appendix C), is proportional the a/r4. An increase in
binding energy between the systems VAr+ and VKr+ may therefore
be attributed to the change in polarizability of the rare-gas
partner.
Photodissociation of CoAr* and CoKr+
The second group of metal-cation rare-gas systems to be
presented in this Chapter, CoAr+ and CoKr+, also displays
resonant bound-bound transitions in the visible region. These
systems, unlike VAr+(Kr), each have three prominent
vibrational progressions in their photoexcitation-dissociation

75
spectrum. The congestion perturbs the spectrum slightly but
it is nevertheless experimentally tractable. Similar
vibrational analysis found in the VAr+(Kr) section is applied
here as well.
Figure 20 displays a portion of the resonant
photodissociation spectrum of CoAr+ -*• Co+ + Ar over the region
of 14 800 to 16 300 cm'1. Bound quasi-bound transitions for
three progressions are easily observed in this region.
Approximately eleven transitions of one progression, ca.
150 cm'1 in interval, account for the largest peaks in the
figure. Several transitions belonging to another excited
state, within the region 14 800 to 15 450 cm'1, are seen to
converge to a diabatic dissociation limit. This portion of
the spectrum is similar in appearance the photodissociation
spectrum of VAr+ found the in previous section. Dwarfed
remnants of a third progression may also be observed in the
region of 15 4 60 to 15 710 cm'1. The curved appearance of the
peak intensities, i.e. a drop off in intensity near either end
of this spectrum is a result of the laser dye emission
spectrum (the dye tuning curve, see experimental Chapter) and
does not represent a change in the dissociation cross-section.
The photofragmentation spectrum of CoKr+ is similar to
that of CoAr+. This system also displays three prominent
vibronic progressions. Fortunately, isotopic variants of Kr
are naturally occurring and may be used to help assign the
vibrational spectra of these systems. Figure 21 shows the

76
14800 15000 15200 15400 15600 15800 16000 16200
Laser Frequency (wavenumber)
Figure 20. Resonant Photodissociation of CoAr+.
This figure displays a portion of the CoAr+ resonant
dissociation spectrum in the visible region. Plotted is the
observed Co+ fragment current arising from the one-photon
dissociation of isolated CoAr+ as a function of incident laser
frequency. The relatively smaller dissociation at the low-
and high-frequency sides of the plot represents a drop-off in
the dissociation laser output intensity and not a systematic
change in the peak dissociation cross-section. Each peak in
the spectrum corresponds to an entire vibronic band, which,
because of the 2 K rotational temperature of the ions has
collapsed to less than 3 cm'1 FWHM (Full Width Half Maximum) .
Three upper-state vibrational progressions corresponding to
three different electronic states are evident in the figure.

77
photofragmentation of CoKr+ -+ Co+ + Kr as a function of
dissociation laser frequency in the interval from 15 420 to
15 62 0 cm'1. The top trace shows the photofragmentation of all
naturally occurring Kr isotopic variants of the CoKr+ molecule
and the bottom trace shows the photofragmentation of 59Co86Kr+
only (17.37% natural abundance12) on an increased vertical
scale. The ability to acquire the signal of selected isotopic
variants of a molecular ion considerably simplifies the
spectrum (note the region near 15540 cm-1 in Figure 21) and
facilitates vibrational assignment.
A similar set of experimental conditions applies to the
spectra of CoAr+(Kr) as discussed for the previous rare-gas
containing diatomics. At these photon energies Kr+ is not
observed as a photoproduct of CoKr+ (similarly Ar+ is not
observed from CoAr+) as expected from the large disparity in
the ionization potential of the atoms (IP(Kr) = 13.996 eV;
IP(Ar) = 15.755 eV; IP (Co) =7.86 eV)13. Under the normal
operating conditions of the mass spectrometer, a trace amount
of Co+ from CoKr+ (CoAr+) is observed from collision-induced
dissociative processes with residual He gas in the flight tube
of the TOFMS. In the present experiment, collision-induced
dissociation produces a small background to our laser-induced
dissociation yield that is constant and may be easily
nullified. The bottom of the abscissa axis on the
photodissociation spectra of CoAr+ and CoKr+ therefore
represents zero photodissociation intensity.

78
15425 15475 15525 15575 15625
Dissociation Laser Frequency (wavenumber)
Figure 21. Photodissociation Spectrum of CoKr+ Isotopes.
The figure displays a portion of the photoexcitation spectrum
over the region of 15 420 to 15 620 cm'1 for CoKr+. The top
half of the figure shows the photodissociation, Co+ relative
photocurrent as a function of laser frequency, of all
naturally occurring isotopes of CoKr+. In the lower panel,
only the photodissociation of 59Co86Kr+ is displayed. Isotopic
shift information is necessary to assign the absolute
vibrational numbering of the observed bands. This region of
the spectrum displays peaks from three prominent progression
that are listed in Table 6.

79
Dissociation laser fluence dependence of the resonant
photodissociation indicates a one-photon absorption event.
Poor temporal/spatial quality of the excitation source
prevents accurate absolute cross section measurements, but the
strongest photodissociation transitions have cross sections of
ca. of 10~17 cm2. Partially resolved rotational structure on
the vibronic transitions place a lower limit on the lifetime
of the upper levels of the transition at 10 ps. The upper
limit to the excited state lifetime is placed by the time
between excitation and kinetic energy analysis, about
5 /isec. The features in Figure 21 are representative of the
over 100 sharp vibronic bands found in the photodissociation
spectrum of CoKr+ in the region of 18 000 cm-1 to below
13 500 cm-1. Most (>95%) of these vibronic transitions fall
into three simple upper state progressions from, presumably,
the same lower vibronic state. We identify these three
progressions as distinct electronic band systems.
Vibrational Analysis
The assigned vibronic positions for the photodissociation
excitation spectra, over the frequency interval of 13 500 to
18 000 cm'1, of CoAr+ and CoKr+ are listed in Table 5 and
Table 6, respectively. In each case the positions of the
assigned transitions are grouped into three band systems

80
Table 5. Line positions of assigned 59Co40Ar+transitions in
wavenumbers.
A-X
B-X
C-X
V'
observ.
o-ca
V'
observ.
o-c“
v'
observ.
o-c*
6
14026.3
0.87
6
14076.8
1.01
0
14544.7
-0.71
7
14149.0
0.37
7
14167.2
-0.09
1
14714.3
-0.36
8
14265.4
-0.71
8
14254.4
-0.56
2
14878.6
1.11
9
14375.7
-2.48
9
14338.0
-0.68
3
15034.7
0.69
10
14488.3
3.59
10
14418.7
-0.01
4
15184.7
0.40
11
14577.6
-8.39
11
14494.6
-0.32
5
15328.2
-0.26
*11
14589.7
3.75
12
14567.6
0.12
6
15466.1
-0.48
12
14677.0
-5.02
13
14636.6
0.04
7
15598.6
-0.16
*12
14688.0
6.02
14
14701.9
-0.12
8
15725.0
0.00
13
14767.1
-5.85
15
14763.8
-0.22
9
15845.1
-0.48
*13
14773.7
0.77
16
14822.5
-0.14
10
15960.1
-0.31
*13
14780.3
7.39
17
14877.7
-0.13
11
16069.5
-0.17
25
15502.2
-0.22
18
14930.1
0.23
12
16173.8
0.33
26
15536.3
0.01
19
14979.3
0.58
13
16272.0
0.11
27
15565.9
-0.50
20
15025.6
1.25
14
16364.9
-0.03
28
15592.6
-0.35
21
15067.6
0.57
15
16453.0
0.11
29
15616.7
0.76
22
15106.7
0.08
16
16535.4
-0.26
30
15637.5
1.83
23
15142.9
-0.38
17
16614.1
0.67
31
15656.7
4.55
24
15176.9
-0.19
18
16686.0
-0.30
32
15672.9
7.53
25
15207.7
-0.40
19
16754.9
0.54
33
15687.3
11.65
26
15236.1
-0.29
20
16817.8
0.19
34
15699.5
16.63
27
15261.3
-0.72
21
16875.9
-0.34
35
15710.7
23.35
28
15284.9
-0.16
22
16930.4
-0.04
29
15305.3
-0.27
23
16979.8
-0.31
30
15323.3
-0.22
24
17025.0
-0.44
31
15340.2
1.02
25
17066.9
0.48
32
15354.9
2.50
26
17104.4
1.04
33
15368.2
4.74
27
17138.8
2.67
34
15378.9
6.68
28
17169.4
4.36
35
15388.3
9.45
29
17197.0
7.02
36
15396.6
13.08
30
17221.8
10.66
37
15403.6
17.52
31
17243.2
14.58
38
15409.3
22.59
32
17262.5
20.00
39
15414.3
28.83
33
17279.6
26.81
40
15418.5
36.07
34
17294.6
34.84
41
15421.8
44.05
35
17307.3
43.97
36
17318.3
54.52
37
17327.8
66.79
38
17336.1
80.80
39
17343.1
96.55
40
17348.9
113.94
41
17353.9
133.28
42
17358.0
154.28
43
17361.3
177.15
44
17363.9
201.78
45
17366.1
228.39
46
17367.6
256.59
(a) Observed minus calculated
(*) Extra bands due to perturbation.

81
Table 6. Line positions of assigned 59Co40Kr+ vibronic transitions
in wavenumbers.
A-X
B-X
C-X
v'
observ.
o-ca
V'
observ.
o-ca
v'
observ.
o-ca
2
13696.5
0.14
2
14161.4
1.03
4
15354.4
0.35
3
13835.4
-0.12
3
14270.7
0.61
5
15495.9
0.21
4
13970.8
-0.91
4
14377.4
0.26
6
15633.5
-0.41
4
13981.0
9.32
5
14481.4
-0.26
7
15768.4
-0.21
5
14098.3
-6.53
6
14583.5
0.07
8
15899.8
-0.22
*5
14110.1
5.20
7
14679.6
-3.01
9
16027.4
-0.66
6
14219.7
-15.3
8
14779.6
0.44
10
16152.4
-0.23
*6
14233.8
-1.22
9
14873.2
0.05
11
16273.3
-0.67
7
14356.9
-5.34
10
14964.9
0.44
*11
16276.0
2.04
8
14489.0
2.59
11
15051.0
-2.33
12
16390.5
-1.38
9
14605.0
-2.50
12
15138.9
-0.75
*12
16393.3
1.43
*9
14625.2
17.67
13
15223.2
-0.25
13
16506.3
-0.18
10
14728.6
2.98
14
15305.2
0.45
14
16618.4
0.51
11
14840.1
-0.63
15
15384.7
1.25
15
16725.5
-0.44
13
15061.0
-0.67
16
15462.7
2.93
16
16830.4
-0.33
*13
15063.3
1.64
17
15532.5
-1.05
17
16932.3
0.02
14
15167.0
-0.49
18
15604.7
-0.28
18
17030.4
-0.21
15
15268.0
-2.23
19
15674.1
0.23
19
17126.1
0.36
16
15368.0
-1.99
20
15743.3
2.96
20
17218.2
0.52
17
15455.4
-11.1
21
15803.9
-0.63
21
17306.3
-0.07
*17
15471.5
4.98
22
15864.9
-1.33
22
17392.0
0.01
18
15553.0
-7.02
23
15925.5
-0.05
23
17474.1
-0.29
*18
15566.8
6.83
24
15984.9
2.38
24
17553.4
-0.37
19
15640.9
-9.46
25
16036.9
-0.26
25
17630.0
0.06
*19
15655.8
5.49
26
16088.3
-1.18
26
17702.9
-0.14
21
15818.2
-3.43
27
16139.3
-0.18
27
17773.2
0.12
*21
15837.7
16.04
28
16187.7
0.61
28
17840.1
0.04
24
16048.2
-6.67
29
16231.3
-1.24
29
17904.2
0.18
*24
16057.8
2.86
30
16273.3
-2.42
30
17964.8
-0.06
*30
16276.0
0.29
31
16315.8
-0.74
32
16355.0
-0.23
33
16390.5
-1.12
*33
16393.3
1.69
34
16426.1
0.31
35
16459.2
1.32
(a) Observed minus calculated
(*) Extra lines due to perturbation.

82
labeled C-X, B-X, and A-X. The current labeling is a matter
of convenience; the ground and three observed excited states
are labeled X, A, B, and C, in order of increasing electronic
origin energy. This choice by no means indicates that the 'A'
state observed in this study is the first excited state nor
that no other electronic states lie between the A, B, and C
states. However, the chosen nomenclature is such that the A
(B,C) state of CoAr+ and CoKr+ correspond to the same Co+
atomic ion state at the dissociation limit. The most intense
point of the vibronic band (typical width 2-3 cm-1; see
Figure 21) is taken to be the vibronic band origin for the
present analysis. Table 5 and Table 6 also list the
residuals to the least squares fit of the vibronic bands to
the standard14 formula given previously in Eq. (6) from which
the constants T^, we, wexe, wcye are derived. As in the analysis
of VAr+ and VKr+, the zero of energy for this fit and all the
following discussion is taken as the zero-point level of the
ground electronic state of the molecule. The accuracy with
which Eq. (6) describes the observed vibronic structure
depends on the degree of anharmonicity of the molecular forces
and the existence of any local perturbations between the
electronic states. The best fit in this study is obtained for
the lowest vibrational levels (v' = 0 -*â–  25) of the C state of
CoAr+ which shows no apparent anomalous behavior. Even for
this state, however, the transition frequencies involving the
highest vibrational levels (v' = 30 -* 46) are severely

83
Figure 22. Vibration Fit to Band Origins for CoKr+ States.
This figure displays a least-squares fit to Eq. (6) (solid
curves) of the observed vibrational band origins of the C-X
(solid squares), B-X (triangles) and A-X (open squares)
systems of CoKr+. Absolute vibrational numbering is obtained
from isotopic shift information. The molecular constants
obtained from this fit are listed in Table 7.

84
underestimated by Eq (6) . and so are not included in the fit.
Complications arise, however, from the local perturbations
that all band systems other than CoAr+ C-X exhibit to some
extent.
Figure 22 shows the vibrational structure of CoKr+ in a
plot of transition energy of the C-X, B-X, and A-X systems
versus excited state quantum number, (v'+l/2) . The solid
curves represent the fit to Eq. (6) and the symbols are the
experimental band origins. Despite the evidence of
perturbation from the missing and extra lines apparent in this
plot the overall fit is quite good. Absolute vibrational
numbering of the transitions shown in Figure 22 and listed in
Table 6 are made from the measurement of the spectral shift
among the 86Kr, 84Kr, 83Kr, and 82Kr isotopomers of CoKr+. This
yields a unique absolute vibrational numbering for the C and
B states but the extensive perturbations in the A state make
its vibrational numbering uncertain by + 1 quantum.
Figure 22 clearly shows that the three excited electronic
states observed in photodissociation have similar but not
identical vibrational structure. Also from Figure 22, it is
evident that the electronic origin of the A state is lower
than the B state, but the dissociation limit of the A state is
higher than the B state which means that the A and B state
potential curves cross.
The nature and extent of the perturbations present in
this spectrum are varied. A perturbation between the C and B

85
states of CoKr+ occurs at an accidental degeneracy between the
v' = 11 of the C state and v' = 30 of the B state and again at
v' = 12 and v' = 33 of those states. This perturbation
appears to involve only these two electronic states with an
estimated interaction matrix element of about 3 cm-1. The A
state of this molecule is more severely and ubiquitously
perturbed than the B or C states as is evidenced by the
diminished quality of the fit to Eq. (6) (see Table 6). Extra
lines in this band system arise from perturbations with at
least one otherwise undetected state. The perturbation shifts
in the A-X system indicate a much stronger coupling between
interacting electronic states than is seen in the C-B
perturbation of the same molecule.
At present, neither the spectrum of 59Co36Ar+ nor 59Co38Ar+
(0.34% and 0.07% natural abundance12, respectively) have been
obtained. Without isotopic substitution, the firm assignment
of absolute vibrational quantum numbers to the CoAr+
transitions listed in Table 5 is impossible. Thus, the upper
state vibrational quantum number listed in Table 5 is merely
an effective vibrational index, chosen to be close to the
absolute value.
All of the transitions observed in this study appear to
originate from the ground electronic and vibrational state of
the molecule, i.e. no hot bands have been identified. This is
understandable due to the extensive cooling these ions suffer
in the supersonic expansion. From a conservative estimate of

86
the sensitivity of the experiment (1% of a strong transition)
and a guess of the ground state vibrational frequency
(200 cm-1; see discussion below), we infer the vibrational
temperature of these ions to be less that 65 K. This is
significantly lower than the vibrational temperatures of
transition metal dimer neutrals16 supersonically expanded under
similar conditions. It is possible that ion-molecule
vibrational relaxation collisions are longer ranged or more
efficient than neutral-neutral V-T collisions, leading to a
lower final vibrational temperature for ions relative to that
of neutrals in the beam. Nonetheless, the low internal
temperature of the ions simplifies the spectrum greatly but
prevents direct determination of the ground state vibrational
frequency by photodissociation excitation spectroscopy.
Determination of dissociation limits
Similar treatment of the vibrational levels near the
dissociation limit is done here as in the treatment of
vibrational levels for the systems of VAr+ and VKr+.
Figure 2 3 shows the dependence of the derivative of the
vibrational energy with respect to the transition frequency
for the C-X, B-X, and A-X band systems of CoAr+. The plot
shows that (AG)4/3 is indeed linearly dependent on transition
frequency near the dissociation and a linear least squares
extrapolation may be used to estimate the dissociation limits,

87
Transition Frequency (wavenumber)
Figure 23. Dissociation Limits of CoAr+.
The Figure displays a plot of the derivative of the
vibrational energy with respect to vibrational index to the
4/3 power versus transition frequency (LeRoy-Bernstein plot)
for the A (open squares), B(triangles), and C(solid squares)
states of CoAr+. For molecules which dissociated under the
influence of a -C/r4 attractive force (charge-induced dipole)
these data may be linearly extrapolated (lines) to the
abscissa to obtain the dissociation limit of the respective
excited states. These limits, D, are listed in Table 7 for
both CoAr+ and CoKr+.

88
D. These extrapolated values are listed in Table 7. We must
emphasize that the values of D are not dependent on the
absolute vibrational numbering. Subsequently, the accuracy to
which the ground state binding energy is known is a function
of the LeRoy-Bernstein extrapolation and the correct
assignment of the separated atomic limits. The accuracy of
the excited state vibrational frequency and binding energy
will depend on the correct vibrational assignment.
The dissociation energies, D, listed in Table 7
correspond to the difference in energy between the zero point
level of the molecule and a particular excited state of the
Co+ + Ar(Kr) separated atoms. It is not possible for these
Table 7. Experimental Molecular Constants for 59Co40Ar+ and
59Co84Kr+ in cm1.
CoAr+
CoKr+
State
A
B
C
A
B
C
Teo
13081
13380
14458
13336
13874
14674
165.4
120.9
175.8
148
117.8
159.0
wexe'
3.20
2.21
3.28
1.47
1.36
1.76
WeYe'
0.017
0.011
0.016
-0.002
0.003
0.003
K (N/m)
38.5
20.6
40.1
44.8
28.4
51.7
55.3
55.6
88.9
93.5
Db
15758
15433
17370
17395
16840
18911
D/(c)
2595
1993
2825
3985
2886
4158
De'(d)
2677
2053
2912
4059
2945
4237
“Number of bound vibrational levels.
bDiabatic threshold.
cExcited state binding energy;D0/=Dc/-l/2ü)e/+l/4ojcxx/-l/8a)eyc/.
dExcited state equilibrium dissociation energy; De' = D - T^.

89
dissociation limits to correspond to excited argon(krypton)
atoms. Comparison of the observed D values in CoAr+ and CoKr+
with the Co+ atomic energy levels37 suggests the assignment of
the C state dissociation limit as 3d8 3P2 Co+ + 's Ar(Kr) and
the B state limit as 3d74s 3F2 Co+ + 's Ar(Kr) at 13 261.1 cm-1
and 11 321.5 cm-1 above separated 3d8 3F4 Co+ + *S Ar(Kr)
(ground state) atoms, respectively. This places the A state
dissociation at 11 645 cm-1 above ground state atoms where no
Co+ electronic states presently are assigned. This
observation does not, at present, invalidate the assignment of
the C and B state limits because a number of predicted Co+
atomic terms are still undetected in this energy region.
The adiabatic dissociation energy of the ground state of
CoAr+ or CoKr+ is simply the difference between any
experimentally determined excited state dissociation limit, D,
and the isolated Co+ promotion energy to the state
corresponding to that limit. From Table 7 and the above
assignment of the B and C state limits, the adiabatic
dissociation energies of the X states of CoAr+ and CoKr+ are
found to be 4110 cm-1 and 5585 cm-1, respectively.
Once D has been determined for a particular excited
electronic state, the vibrational binding energy, (D — E(v)),
is used to derive the number of bound vibrational levels in
the potential via the application of Eq.(3) to yield vD. The
number of bound levels in each potential is the largest
integer less than vD. These values are listed in Table 7.

90
(VD -V)
Figure 24. Vibrational Binding Energy for CoAr+ and CoKr+
States.
The Figure displays a plot of the vibrational binding energy
to the 1/4 power versus the vibrational index, (vD - v), for
the C (open squares) and B (crosses) states of CoAr+ and the
C (triangles) and B (solid squares) state of CoKr+. The
quantity vD is the hypothetical vibrational index of the
dissociation limit of the potential, i.e., E(vD) = D. The
solid lines are the predicted vibrational binding energy from
Eq. (19) using the literature values for the polarizability of
argon or krypton.

91
The number of bound levels for the A state of either CoAr+
or CoKr+ have not been determined due to the perturbations and
limited number of observed vibronic levels. However a
significant number of the total vibrational levels are
observed for many of the other states; over 80% for C state of
CoAr+.
Figure 24 shows a plot of the vibrational binding
energies to the 1/4 power versus vibrational quantum number
for the B and C states of CoKr+ and CoAr+. Also shown in the
figure is the predicted dependence (lines) of vibrational
binding energy for CoAr+ and CoKr+ using Eq. (19) and
literature values for the rare-gas polarizabilities
(1.66 x 10~24 cm3 for Ar and 2.52 x 10”24 cm3 for Kr) . Again, as
was the case for VAr+(Kr) systems, the agreement between this
simple model for the vibrational structure of these systems is
extremely good.
Resonant Photodissociation of ZrAr4
The following discussion will look at the results for a
second row transition metal cation, Zr+, with a physisorbed
rare-gas atom, Ar. The photodissociation spectrum for this
system also displays several vibronic progressions.
Unfortunately, the spectroscopic information does not lend
itself to the rigorous analysis found in the cobalt and
vanadium systems discussed previously. We will see that only

92
15400 15600 15800 16000
Laser Frequency (wavenumber)
Figure 25. Resonant Photodissociation of ZrAr+.
The figure displays the resonant photodissociation spectrum
for the process of ZrAr+ -* Zr+ + Ar in the visible region of
15400 to 16500 cm'1. Three prominent vibronic progressions are
annotated with the vibrational index determined from isotopic
analysis. All observed transitions are red degraded.

93
ca. 30% of the vibrational levels for a given electronic
state are observed compared to 80% of CoAr+ A and B states.
A portion of the photoexcitation spectrum for the one-
photon dissociation process of 90Zr40Ar+ -» 90Zr+ + Ar over the
visible region of 15 400 to 16 100 cm’1 is displayed in
Figure 25. A vibrational index marks the band positions for
each of three prominent vibronic progressions. Under current
laser linewidth (ca. 0.1 cm'1) the bands are only partially
rotationally resolved. Thus, insufficient for complete
rotational analysis but nonetheless revealing a distinctive
red degraded peak shape for all observed bands. For
convenience the states giving rise to these three progressions
have been labelled A, B, and C in accordance with increasing
energy of the electronic term. Lower lying states will
undoubtedly be discovered in the future and will necessitate
the revisal of this labelling.
Line positions, corrected to vacuum, for the three
progressions are listed in Table 8. Several other bands
belonging to fragmented progressions are also observed in the
same region. These bands, grouped by progression, are listed
in Table 9 for completeness but are currently unassigned with
regard to vibrational index (see following text).
The vibrational frequencies (co/) and anharmonicities
(coexe,) of each of the progressions are found by fitting the
observed transition to (v' + 1/2) and (v' + 1/2)2 in the
following well known equation, resubmitted here;

94
Table 8. Line Positions for assigned vibronic transitions of
90Zr40Ar+ in wavenumbers.
A-X
B-X
C-X
V /
observed
o-ca
v'
observed
o-ca
v'
observed
o-ca
1
14987.72
0.18
2
15646.20
0.67
2
15723.83
0.17
2
15051.75
0.36
3
15709.54
-0.42
3
15793.61
0.95
3
15113.10
-0.30
4
15772.30
-0.75
4
15858.46
-0.68
4
15173.31
-0.25
5
15834.46
-0.36
5
15922.72
-0.37
5
15231.66
-0.22
6
15895.63
0.40
6
15984.83
0.30
6
15288.09
-0.26
7
15955.04
0.75
7
16045.83
2.38
7
15343.07
0.09
8
16012.36
0.34
8
16097.28
-2.56
8
15395.31
-0.47
9
16067.78
-0.63
9
16152.19
-1.52
9
15447.05
0.32
10
16203.50
-1.57
10
15496.80
0.97
11
16253.69
-0.21
11
15543.25
0.15
12
16300.33
0.12
12
15588.89
0.38
13
16345.79
1.78
13
15630.70
-1.39
14
16387.59
2.31
14
15674.26
0.43
15
16425.70
1.68
16
16460.05
-0.21
17
16491.40
-2.57
(a) Observed minus calculated from vibrational fit.
Table 9. Unassigned line positions (cm1) for 90Zr40Ar+ grouped
by progression.
Progression 1
Progression 2'
Progression 3
15662.04
16169.95
15527.0
15738.23
16220.07
15554.6
15813.84
16266.17
16110.0
15893.41
16310.52
15969.59
*
*
16431.57
16469.89
(*) Absent transition in progression.

95
E(v) = Teo+Je(v'+l/2) +G)exle (v'+\/2) 2 . (20)
Due to the cooling nature of the adiabatic expansion, hot
bands are absent from the photodissociation spectra and all
assigned peaks correspond to transitions originating in the
ground state vibrationless level. The zero of energy for this
fit, and all following discussion, is then conveniently taken
as the zero-point level of the ground electronic state. The
quantity T^, which is directly determined from a fit of the
observed bound-bound transitions, is therefore, 1/2ojc" smaller
than the electronic term commonly denoted45,89 as Te/ . An
accurate determination of the vibrational frequency, however,
depends on the correct assignment of the upper state
vibrational index, v'.
Simultaneous photodissociation of zirconium isotopic
variants in the diatomic (90Zr40Ar+, 92Zr40Ar+, and 94Zr40Ar+ in
51.4, 17.1 and 17.5% natural abundance respectively)33 provide
isotopic shifts necessary to assign the vibrational index for
these excited states. For vibronic bands, the isotopic shift
is a function of the spectroscopic parameters and vibrational
index of both the ground and excited states. One may
eliminate terms involving second and higher anharmonic terms
for regions of low v' in the standard expression:45,89

96
Avisotopic = (1-p) [co/e(v/+l/2) -u"(v"+l/2)
- (1 -p2) [i0eXe(v/+l/2)2-(0eXe(^//+l/2)2 + ’ • ’
Here p is a constant equal to the square root of the ratio of
reduced masses of the two isotopes. In practice, the
determination of the vibrational numbering begins with a
guess. The spectroscopic parameters of the upper state are
then established from Eq. (20) . The ground state we" is then
adjusted in Eq. (21) to minimize the root-mean-square (rms)
deviation of the isotope shifts while approximating wexe'
= o)exe"* Since Eq. (21) is quantized in v', only a few
possible numbering schemes provide a reasonable ground state
vibrational frequency.
The A state isotopic shifts, Av , for 90Zr40Ar+ minus
^Zr^Ar (squares) and 90Zr4UAr+ minus 92Zr40Ar (triangles) as a
function of upper state vibrational index are displayed in
Figure 26. The solid lines represent the calculated isotopic
shift with the vibrational numbering scheme listed in Table 8.
The dotted curves are calculated by shifting the vibrational
assignment plus and minus one quanta. Similar isotopic
analysis was performed for the B and C state. The vibrational
index determined by this method accompanies the bands listed
in Table 8. Equation (20) accurately describes the observed
vibrational levels with less than 1.5 cm'1 residual error for
all transitions listed in the A and B state. The C state is

97
Figure 26. Isotopic Shifts for ZrAr+.
The figure displays the isotopic shifts for 90Zr40Ar+ minus
94Zr40Ar+ (squares) and 90Zr40Ar+ minus ^Zr^Ar4 (triangles)
versus the vibrational index (v# + 1/2) for A <- X. Centrally
located solid lines for both sets of isotopic data represents
the best fit of cje" for vibrational data with the vibrational
index given in Table 8. Curves above and below the central
curve are calculated by shifting the vibrational assignment by
plus and minus one quanta, respectively.

98
Table 10. Spectroscopic Parameters of Excited State in ZrAr+.
State
Tec
(cm1)
«e#
(cm1)
UeXe'
(cm1)
a Bound
Levels3
(cm1)
A—X
14 888.3
67.5
0.92
686.6
B-X
15 478.6
68.5
0.67
421.6
C-X
15 540.1
76.6
1.26
767.6
aThe difference of the bluest and reddest assigned vibronic
bands.
slightly perturbed and does not fit as well with some
residual errors being ca. 2.5 cm'1. Nonetheless, the
vibrational fits for all states are quite good for overall
experimental accuracy of 1.5 cm'1. The residual (observed
minus calculated) values are also listed in Table 8.
Figure 27 displays the vibrational fit of the three
vibrational progressions. Symbols mark the experimental
values and the solid lines represent the calculated values.
The curves for each of states are roughly parallel over the
observed region with a separation of ca. 85 and 750 cm'1
between B and C, and between A and C respectively. The
vibrational frequencies and anharmonicities for each of these
state are listed in Table 10.
Dissociation Limits
Since the Franck-Condon factors reveal only the
vibrational levels near the bottom of the excited state

99
Figure 27. Vibrational Fit of ZrAr+.
The figure displays the vibrational fit for the three vibronic
progressions of ZrAr+ annotated in Figure 25. Observed
transitions for each state are plotted versus vibrational
index with symbols (A = pluses, B = triangles, and C =
squares) . The solid line represents the fit to a second order
polynomial in (v' + 1/2) . The curves for all three states are
roughly parallel. A lower limit to the upper state binding
energies of ca. 686, 829 and 768 cm'1 for the A, B, and C
state, respectively, is determined by the range of bound-bound
transitions.

100
potential energy surface, determination of an upper state
dissociation limit is a moderate extrapolation. In the C
state, and to a lesser degree the A state, vibrational levels
are sufficiently close to the dissociation limit to attempt
the procedure pioneered by LeRoy and Bernstein. The
vibrational information of the B state is insufficient and may
be estimated with the less rigorous Birge-Sponer
extrapolation. An experimental lower limit for each of the
excited states however, may be set by the range of observed
bound-bound transitions. These are 686, 422, and 767cm"1 for
states A, B, and C respectively. Applying, the Birge-Sponer
extrapolation, De = we/4wexe, the dissociation energies for
A, B, and C state are 1238, 1750, 1164 cm'1, respectively.
Calculations of this type typically underestimate the
dissociation energy because of failure to account for long-
range forces. In first-row transition-metal rare-gas (Ar, Kr)
diatomic systems, they are known to be 10 to 20% too low. The
Birge-Sponer extrapolation for the B state is suspiciously
high and may be inaccurate due to a vibrational fit on a
limited number of vibronic levels (v7 = 2 -*â–  9) .
The LeRoy and Bernstein method provides a more accurate
method for determining the dissociation energy by accounting
for long-range attractive forces. The application of this
procedure has been discussed previously.
Figure 28 displays a plot of AG4/3 as a function of
incident laser-frequency for the C state. The solid squares

101
correspond to experimental points. The solid line represents
the calculated slope from a least-squares fit of the lower
four data points, while the dotted line is the theoretical
slope, determined from Eq. (15), intersecting the last
available data point. The intercept of the abscissa
corresponds to the diabatic dissociation limit of the excited
state. The dissociation limit of the excited state is simply
the difference of the diabatic limit and the electronic term
De ~ T^.
Since vibrational data is sufficiently far away from the
diabatic limit (only ca. 30% of vibrational levels are
observed in the C state) it must be treated with caution. The
inclusion of one more data point in the fit would bring the
slope in line with the predicted value. The perturbations of
the C state are reflected in the undulating AG4/3 values with
transition frequency. It is for these reasons that no
significance is attached to the small but apparent deviation
(ca. 13% relative deviation) of the calculated and predicted
slope. Nonetheless, the intercepts of the two lines are
Table 11. Dissociation Energy for ZrAr+ Excited States.
State
Birdge-
Sponer
(cm1)
L J [ 8,4 ]
(cm1)
Born-Meyer
[exp,4]
De:wc (cm’1)
LeRoy-
Berstein
(cm1)
A-X
1238
871
1333:67.6
12861150
B-X
1750
888
-
-
C-X
1164
1031
1306:76.8
1185125

102
believed to roughly bracket De' at 1185 ± 25 cm'1. A similar
treatment was used to determine the dissociation energy of the
A state as 1286 ± 150 cm"1. Unfortunately, the limited
vibrational information of the B state is not sufficient to
warrant a similar procedure. However, the initial premise,
that the attractive force of the system is governed by charge-
induced dipole forces, is apparently valid.
Adiabatic Energy
In order to determine the adiabatic binding energy one
must know the separated atomic limits. Unfortunately, the
dissociated atomic configurations, in addition to the
molecular term symbols, that correspond to the observed
progressions are not known unequivocally. An energy range,
however, may be intelligently set to suggest likely candidates
for the atomic configurations of the dissociation limits.
Photodissociation into an ionic or excited state of Ar is
energetically impossible since the first metastable state and
ionization potential for Ar is 13.5 and 27.6 eV respectively.
This is well above the first ionization potential of
zirconium at 6.74 eV.
Fortunately, the atomic energy levels are relatively
sparse as well as complete in the visible region for zirconium
cation. Since the ground state binding energy is larger than
any excited state, Tm > AEatomic (separated atomic limit) . The

103
Figure 28. ZrAr+ C State Dissociation Limit.
The figure displays the LeRoy-Bernstein plot of the derivative
of the vibrational energy to the 4/3 power versus the
transition frequency. The solid line is determined from a
least squares fit of the last four experimental points
(squares). The dotted line, which intersects the last
available data point, has a theoretical slope predicted from
Eq. (15) using the polarizability of the rare gas atom and an
-C/r4 attractive potential. The linear extrapolation of these
lines is believed to bracket the diabatic threshold of the C
state.

104
upper limit is therefore determined by the largest electronic
term, TM = 15542 cm'1 (C state) . For the lower limit to our
energy window, recall
D0" “ De' = Teo - AEatomic.
As the lower limit to the energy window drops the difference
between the binding energy of the upper and lower states
increases. For an energy difference as high as 0.55eV, EJtomic
> ca. 10000 cm'1, using this time the smallest of the three
progressions for the calculation. An energy difference of
0.55eV corresponds the adiabatic dissociation energy of NiAr+,
a first row transition metal cation.
Within this energy window of 10,000 to 15542 cm'1 one
finds eight energy levels corresponding to four terms symbols
for Zr+. These are, in increasing energy: 2H (4d3) , 2D (4d3) ,
2G (4d25s) , and 2D (4d 5s2) . The separated atomic limits for
the ground state diatomic correspond to the respective atomic
ground states, 4F3/2 (4d25s) Zr+ and !S Ar. The difference in
vibronic transitions for a given v' between the A and C state
is 752 + 7 cm'1 (over the range v' =2 - 14) and is suggestive
of the j spacing interval in the 2Dj = 734.4 cm'1 (2D3/2 =
13 428.50, 2D5/2 = 14162.90). This would appropriately assign
the B state to 2G7/2 = 14 059.7 6 cm'1. These assignments are
tentative at best and should be considered with caution. The
corresponding molecular term symbols constructed from the
above atomic terms suggest the observed bound-bound transition
in photoexcitation spectra of ZrAr+ involve a change in spin

105
state, 2A <- 4A. This would be considered strictly forbidden
if both ground and excited state were either Hund's coupling
case A or Hund's coupling case B.
Using the tentative assignment of the separated atomic
limits and the dissociation limit of the C state derived from
the LeRoy-Bernstein method the ground state dissociation
energy would be ca. 0.3 eV. One may determine a lower limit
to the adiabatic binding energy by subtracting the largest
possible separated atomic limit for Zr+ from the sum of the
energy range of bound-bound states and the electronic term;
De' > ABound + TM - AEalomic. This yields a lower limit to the
adiabatic binding energy of ca. 0.2eV. The adiabatic binding
energy of first-row transition metal argon diatomics has been
shown to be ca. 0.3 to 0.55 eV.
Photodissociation of CaKr*
This final section of metal-cation rare-gas systems will
discuss some preliminary data for the photodissociation of
CaKr+.
In light of the reactive nature of pure calcium special
care must be taken to minimize ambient air contact. Calcium
will quickly oxidize in moist air to form CaO with the
liberation of hydrogen gas. Additionally, the vaporization
laser power typically used for refractory transition metals
will virtually cut the sample rod in half. The heat of

106
sublimation is approximately half that of cobalt.51
Nonetheless, atomic cations are easily made after some surface
cleaning with the vaporization laser.
Figure 29 shows the photofragmentation process for
CaKr+ -» Ca+ + Kr. Three prominent bands along with a small
but perceptible fourth band are observed in this region
corresponding to an excited state of CaKr+. Isotopic analysis
of the krypton substituted system reveals that the reddest
transition at ca 14 216 cm'1 corresponds to the origin band.
Vibrational analysis determines the vibrational frequency at
52 cm'1 with an electronic origin of 14 192 cm'1. The bands are
distinctly red degraded and imply a ground state of smaller
internuclear distance.
Even though this data is meager compared with the
vibrational information of previously discussed systems it is
still revealing. Due to the simple electronic nature of the
calcium cation the separated atomic limits are known without
dispute. Excitation or charge transfer to the rare-gas atom
is impossible at the photointerrogation wavelength.
Consultation of atomic energy levels tables reveal that only
one separated atomic scheme is possible, CaKr+ -+ 2D Ca+ + 's Kr
which correspond to an s to d transition in the calcium
cation. Two j components exist for the calcium cation at 2D3/2
(13 650 cm'1) and 2°5/2 (13 710 cm'1).37 These separated atomic
limits for the cation of calcium are the only ones available
within 4 eV of the ground state.

107
The figure displays the photodissociation spectrum for the
process CaKr+ -+ Ca+ + Kr in the visible region of 14 150 to
14 400 cm'1. Three red degraded bands of an excited state
progression are observed in this region. Isotopic analysis
confirms the transition at ca. 14 220 cm'1 corresponds to the
origin band.

108
Unfortunately, the vibrational information is not
sufficient to estimate the dissociation energy of the excited
state. However, one may speculate on the term symbol
corresponding to the observed excited state. The angular
momentum coupling of a 2D with a lS will result in 2E, 2I1, and
2A molecular term symbols. Considering the nature of
inductive forces, the binding energy will increase with
smaller internuclear separation. Since the ground state
valence electron configuration of the cation corresponds to a
diffuse 4s orbital, it should be bound less than a cation
containing a 3d electron. This is opposite to what the
presence of red-degraded bands suggest. The sigma molecular
state may however limit the approach of the rare-gas atom
since the valence electron of the cation lies along the
internuclear axis.
Discussion
The spectroscopic parameters for the excited and ground
states of the metal rare-gas diatomic systems (MRg+) studied
in this chapter are collected in Table 12 and Table 13,
respectively. Several observations are worth mentioning
concerning this data.

109
Table 12. Spectroscopic Parameters for Excited States.
Ion
config.3
°0 ,
[cm'1]
Teo
[ cm'1 ]
We'
[ cm"1 ]
Ue*e'
[ cm'1 ]
VAr+
3d34s
1368
15166
94
1.95
CoAr+
(A)
2594
13081
165
3.20
CoAr+
(B)
3d7 4 s
1993
13380
121
2.21
CoAr+
(C)
3d8
2824
14458
176
3.28
ZrAr+
(A)
14888
68
0.92
ZrAr+
(B)
15479
69
0.67
ZrAr+
(C)
15540
77
1.26
CaKr+
3d
14192
52
0.08
VKr+
3d34s
2047
15310
99
1.40
CoKr+
(A)
3985
13336
148
1.47
CoKr+
(B)
3d74s
2907
13874
118
1.36
CoKr+
(C)
3d8
4158
14674
159
1.76
Metal ion atomic configuration in separated atom limit.
Table 13. Ground State Adiabatic Bond Strength.
Ion
conf ig.a
D0
D0
obs-cal
%err.
Expt.
Theory
[eV]
[eV]
[eV]
VAr+
3d4
0.370
0.291b
0.079
-21%
CrAr+
3d5
0.29
0.246°
0.04
-15%
CoAr+
3d8
0.510
0.392b
0.118
-23%
NiAr+
3d9
0.55
0.450d
0.10
-18%
VKr+
3d4
0.473
CoKr+
3d8
0.69
aMetal ion atomic configuration in separated atom limit.
bRef [62],cRef [63], dRef[61]

110
Application of the LeRoy-Bernstein procedure to the
vibronic data of this Chapter has determined that the
attractive force is governed by charge induced-dipole forces.
Recall from the introductory Chapter that attractive chemical
forces may be described as consisting of four types of
interaction: covalent, electrostatic, inductive, and
dispersive. In order to provide some perspective, it is
helpful to compare the binding energy of systems that exhibit
other types of bonding. We have shown that metal cations will
be bound to a rare-gas atom by ca. 0.3 to 0.5 eV. As
expected, a MRg+ diatomic is bound considerably less than a
covalent diatomic such as H2 at 4.7 eV(1) or N2 at 9.9 eV.(1)
However the binding energy of a MRg+ is considerably
larger than a van der Waals (dispersive interaction) bound
dimer, such as Ar2 (0.0105 eV)1, NaAr (0.004 eV)52 or AlAr
(0.02 eV)53 for example. The neutral diatomic system, CdAr,
which is perhaps more relevant to transition-metal containing
MRg+systems, is also expected to be bound by van der waals
forces and has a bond energy of ca. 0.012 eV.54
The binding energy of the ground states for the systems
of CoAr+, VAr+, CrAr+, and NiAr+ determined in this study may
be compared to enthalpies of other MRg+ diatomics. The
enthalpies for several alkali metal rare-gas diatomics have
been determined by ion mobility studies: LiAr+ (0.276 eV(55),
0.550 eV(56)) , NaAr+ (0.211 eV)56, KAr+ (0.119 eV)56, LiKr+

Ill
(0.710 eV)56, NaKr+ (0.285 eV)56, and KKr+ (0.161 eV)56. These
alkali containing diatomic systems are generally less bound
than the transition-metal containing diatomic systems. This
may be explained by the larger orbital radius predicted for
the alkali metal cations over a transition-metal cation in a
given row of the periodic table.
One may also compare our finding directly to the mobility
studies of CrAr+ which predicts the dissociation energy as
0.284 ± 0.018 eV(57), and the collision-induced-dissociation
data58 of VRg+; Rg = Ar (0.2 ± 0.2 eV), and Kr (0.4 ± 0.2 eV) .
These determinations are in excellent agreement with our
findings. The binding energy of HgAr+ has been determined
spectroscopically to 0.23 eV with a ground state vibrational
frequency of 99 cm‘.(59) This also compares favorably with the
data presented here.
A number of ab initio calculations have been carried out
on the systems described in this paper60,61,62 and are listed in
the table of ground state adiabatic binding energies for
comparison. Although the calculations predict, qualitatively,
the trend experimentally observed for the binding energies
they are typically low by ca. 20%.
One may understand the contribution of inductive forces
in the bond energy of an electrostatically bound metal cation
and a water molecule. The enthalpies of the following systems
have been determined from high pressure mass spectrometer
technique: Li(H20)+ (1.47 eV)63, Na(H20)+ (1.04 eV)63, K(H20) +

112
(0.78 eV)63, and Ag(H20)+ (1.43 eV)64. Additionally, we may
compare directly to the following data:65 Ca(H20)+ (1.26 eV) ,
V(H20)+ (1.57 eV) , Cr(H20)+ (1.26 eV) Co(H20)+ (1.61 eV) and
Ni(H20)+ (1.52 eV). Here one observes a significant increase
in bond dissociation energy, ca. a factor of 3-4, from the
metal cation argon systems to the metal cation water systems
by the presence of a permanent dipole. One may speculate that
inductive forces play a significant role in the total enthalpy
of solvation for cations in agueous solution, as much as 25%.
As a first approximation, these systems may be thought of
as simple inductively bound complexes. All attractive forces
are electrostatic and depend only on the overall charge and
the polarizability of the neutral partner. Under such an
assumption the ion and neutral are taken as covalently inert
and behave as closed shell atoms. In this sense the only
difference in behavior, for systems containing the same rare
atom, depends on the state of the charged atom and the
repulsive interaction it has with the neutral partner.
One may consider a simple analytic potential surface (in
which the attractive part of the potential is governed by
inductive forces) at this point to help understand the
differences in binding energy of the various systems. A more
detailed description of analytic potentials and their
parameterization will be given in the next chapter.
Presently, for the Lennard-Jones type potential the
equilibrium dissociation energy (De) is proportional to a/r4

113
where a in the polarizability of the rare-gas atom and r is
the internuclear distance. For VAr+ versus VKr+ or CoAr+
versus CoKr+ (ground states), considering the change in
polarizabilities, krypton-containing molecules should be bound
ca. 52% more than the argon-containing molecules. A 30%
increase is observed experimentally. This discrepancy may be
accounted for by the smaller atomic radii66 of Ar (0.659 x 10'
8 cm) in comparison to that of Kr (0.795 x 10'8 cm). A smaller
radii will be favorable for a larger binding energy.
Nonetheless, it is apparent that an increase in the
polarizability of the neutral partner will typically increase
the binding energy of a cation rare-gas system.
It is interesting to note, that both theoretical67 and
experimental68 findings suggest that many transition-metal
helides (helium) are bound more strongly than their neide
(neon) counterparts even though the polarizability of the
latter in greater. Thus, from a simplistic notion, the
shorter internuclear distance of the helide will win out over
the larger polarizability of the neide in determining the
final dissociation energy.
In comparing systems that contain the same rare-gas atom
one would expect the binding energy to be governed solely by
the internuclear distance. In consulting the table of ground
state adiabatic bond strengths one notices that an increase in
bond strength occurs due to the radial contraction of the 3d
orbital for the diatomics CrAr+, CoAr+, and NiAr+. The only

114
anomalous behavior is observed for VAr+. This system has a
larger binding energy than CrAr+ but a smaller metal cation
atomic number.
One may account for this discrepancy by considering the
bonding nature of the 3d orbitals in V+. For transition
metals that have less than a half-filled 3d subshell, vacant
molecular orbitals along the metal rare-gas internuclear axis
are possible, i.e., there is zero valence electron density on
the axis. Of course, core electron density derived from the
cation is still present. The unspherical nature of the d
valence configuration allows a closer approach of the rare-gas
atom to the cation than systems containing a half-filled 3d
subshell. Thus, VAr+ (3d4) is bound by more than CrAr+ (3d5).
However, it is apparent that the 3d orbital contraction will
at some point across the transition-metal row in the periodic
table provide a metal cation of smaller radii than the
effective radii derived from a vacant 3d orbital. An
ab initio calculation provides support for our interpretation
of the bonding found in VAr+.69
In all spectra generated in this chapter the vibronic
bands were decidedly red-degraded (implying a shorter ground
state internuclear distance). This is consistent with our
assignment of the separated atomic limits. Upon promotion of
the electron from a 3d to a 4s, one would expect the binding
energy to decrease due the larger radial extent of the 4s
electron. This is observed between the VAr+ (3d4) ground

115
state and VAr+ (3d34s) excited binding energy of 0.37 to
0.17 eV, and in CoAr+ (3d8) ground and CoAr+ (3d74s) excited
state of 0.51 to 0.25 eV. Basically, the binding energy is
halved for a 4s containing atom. For hydrogenlike orbitals
the radial extent of a 4s orbital is ca. 3 times larger than
the radial extent of a 3d orbital.70

DIATOMIC POTENTIAL ENERGY SURFACES
Analytic Potentials
One of the most important and powerful concepts in
chemistry is that of a potential energy surface (PES). For a
diatomic system under the Born-Oppenheimer approximation, a
potential surface will completely describe the force of
interaction between the atom pair. Recall, the interatomic
force is derived from the gradient, with respect to
internuclear distance, of the potential energy function. In
this chapter we will look at the ability of several simple
analytic potential energy surfaces (PES) to describe the
spectroscopic information determined from metal rare-gas
diatomics of the previous chapter.
The extensive vibrational information of many of the
metal rare-gas diatomic systems discussed in the preceding
chapter provides a unique opportunity for the construction of
an accurate analytic potential energy surface. We have
already seen that the attractive part of the potential for
inductively bound systems is proportional to 1/r4. With the
experimental knowledge of either the vibrational frequency or
116

117
dissociation energy one may easily parameterize a Lennard-
Jones type potential. This potential has the form
where n and m determine the internuclear dependence on the
repulsive and attractive wall respectively. One may use a
shorthand notation in which a Lennard-Jones potential is
symbolized by [n,m]. The constant C may be determined from
the polarizabilty of the neutral partner and is equal to
(ae2)/2. The Lennard-Jones potential then becomes a one-
adjustable function in j8. This parameter may be determined
from either the dissociation energy or the vibration
frequency. Once /3 is known, the three most important
characteristics of a diatomic systems are determined, i.e.,
the vibration frequency, the dissociation energy, and the
internuclear distance.
Equations relating j3 to the vibrational frequency and the
dissociation energy have been derived for three Lennard-Jones
potentials: [6,4], [8,4] and [12,4] and are listed Appendix C.
In cases where the experimental information is limited to
either a knowledge of the vibrational frequency or the
dissociation energy, but not both, one may estimate the
internuclear distance and the unknown parameter. This
analysis has been performed before on VAr+/VKr+(43),
CoAr+/CoKr+(38), and NiAr+(71).

118
For the systems of CoAr/Kr+ and VAr/Kr+ both the
dissociation energy and the vibrational frequency have been
determined by other means (see Chapter on inductively-bound
diatomics). The Lennard-Jones potential is then
overdetermined and we may compare the dissociation energy
derived from the LeRoy-Bernstein method with the dissociation
energy derived from adjusting 0 to the vibrational frequency.
It must be noted that fitting to the dissociation energy
results in an overestimation of vibrational frequency with
respect to fitting the vibrational levels to Eq. (6). The
parameterization of a PES with a Lennard-Jones potential
apparently provides only a moderately accurate estimate of the
behavior of an inductively-bound system.
In cases where both the vibrational frequency and
dissociation energy are known, a two adjustable potential may
be parameterized. The Born-Meyer potential is of the form
U(r) = be~z/p - C/r4 (23)
where b and p are determined from the experimentally
determined vibrational frequency and dissociation energy.
Consequently, one may relate the internuclear distance to the
vibrational frequency and the dissociation energy (see
Appendix C) . Again, the constant C may be determined from the
polarizability of the rare-gas atom. But how may we test the
accuracy of the Born-Meyer PES? A rigorous inversion of
vibrational data to a potential surface is possible through

119
the Rydberg, Klein, and Rees (RKR) procedure72 but only if at
least partial rotational information is available.
Unfortunately, rotational analysis has been limited and is
therefore insufficient for a RKR analysis.
Vibrational Eigenvalues from the WKB Approximation
The utility of some of these analytical potentials may be
rigorously tested by applying a numerical procedure for the
determination of the vibrational eigenvalues. The numerical
calculation that shows particular promise for such a task is
the Wentzel, Kramers and Brillouin (WKB)73 approximation. This
method is a semiclassical quantization of the molecular
vibration.
Under the Born-Oppenheimer approximation the motion of
the nuclei in a diatomic system is governed by a potential
U(r). Presently, we will ignore the rotation of the system.
We may now describe the vibrational bound states, E(v), of a
given potential with a one-dimensional Schroedinger equation.
h d2
8^:2)i dr2
+ U(r)
(24)
Following a classical formalism, as the nuclei oscillate
periodically between the turning points r^ and r^ , kinetic
and potential energy are exchanged with the total energy
remaining a constant. This oscillation may be thought of a

120
trajectory in phase space. Since the total energy is given by
the following equation,
(25)
the momentum trajectory as a function of internuclear distance
will be given by
p[z) = ±[2\l{E-U[i))1'2.
(26)
Invoking the quantization rules postulated by Bohr and
Sommerfeld74 ('old' quantum theory) one may quantize the action
over one complete period as a half integer multiple of h;
(27)
Substitution of Eq. (26) into Eq. (27) results in a expression
relating the potential surface, U(r), of a diatomic system to
a vibrational index, v;
(28)
These results can also be obtained by considering a classical
approximation to the wave function.75,76
To lend some credence to the effectiveness of the WKB
approximation, one may show that the vibrational eigenvalues
for a harmonic potential are described exactly. The harmonic
potential is given by, U(r) = l/2kr2, where k is the force
constant for a diatomic system. The action integral may be

121
described conveniently by noting that harmonic potential is a
symmetric function with zero potential energy at r = 0. The
boundary conditions of the closed loop integral of Eq. (27)
may then be then expressed as,
4 (2H)1/2
Í7(r) ]1/2di = h(v + 1/2) .
(8)
Substitution of the harmonic oscillator eigenvalues for E(v)
and consultation of integration relations33 results in an
expression for the integrand of the above equation,
r
r[2(v+l/2) ^-r2]1/2 +
k
2i (v+l/2) hojsin 1
k[2 (v+l/2)
k
(9)
The boundary r for a harmonic oscillator may be expressed as
a function of the vibrational index. Since,
U(r) = 1ki2 = (v + 1/2) hm (10)
the variable r is easily expressed as,
r = [2 (v + 1/2) ho]1/2.
Applying the bounds to the integrand of Eq. (30) and combining
with the prefactor of the righthand side of Eq. (27) results
in the relation
(v ♦ i/2).

122
Recall that the force constant k is defined as (27rod)2/¿, thus
lefthand side of Eq. (27) is h(v + 1/2) and the WKB
approximation is exact for a harmonic oscillator.
Unfortunately, real diatomic systems are not accurately
described by a harmonic potential surface. However the WKB
approximation will allow one to predict the vibrational bound
levels of more realistic potential surfaces numerically. For
a given potential energy surface, U(r), one may determine the
vibrational energy levels, E(v), that quantize the action
integral with vibrational index, v. These numerically derived
vibrational eigenvalues may be compared to the observed
vibrational levels. Indeed, one may parameterize an analytic
potential function by minimizing the root-mean-square (rms)
deviation of observed and calculated vibrational levels.
Clearly, this is easily accomplished with the one-adjustable
Lennard-Jones potential mentioned early in this Chapter.
One may extend this procedure to a two-adjustable
potential. Consider the Born-Meyer potential, Eq. (23) . The
parameter b and p will be uniquely determined from a given ue,
Dc pair. It is possible to independently vary coe and Dc over
a range and note the rms value.
An rms contour plot for the CoKr+ C state versus the we,
De grid is shown in Figure 30. A minimum for the fit is
observed within a small range near a vibrational frequency of

123
Figure 30. RMS Contour Plot of CoKr+ C state.
The figure displays the root-mean-square (rms) contour for the
observed vibrational levels versus the WKB predicted values
for the C state of CoKr+. The two adjustable parameters for
a Born-Meyer potential are uniquely determined by the
dissociation energy and the vibrational frequency. The
central contour corresponds to an rms of 1.6 cm'1 with each
successively larger ring increasing by 0.2 cm'1. The minimum
rms suggests that the dissociation energy is 4263 cm'1 with
vibrational frequency of 159.4 cm"1. This is in good agreement
with the experimentally determined value of 4158 cm'1 and
159 cm'1 for the dissociation energy and vibrational frequency
respectively.

124
159 cm'1 and a dissociation energy of 4263 cm'1. The central
contour is the minimum rms contour and corresponds to 1.6 cm'1
within each adjacent contour increasing by 0.2 cm'1. Over the
27 observed vibrational levels that encompass an energy range
of 2600 cm'1 the fit is guite good. The vibrational frequency
determined from Eq. (6) of 159 cm'1 and the dissociation energy
of 4237 cm'1 are in superb agreement.
The vibrational levels for many of the systems discussed
in the previous chapter have been used to parameterize the
Born-Meyer potential using the WKB approximation. The
adjustable parameters corresponding to a minimum in the root-
mean-square deviation are listed in Table 14 along with
corresponding diatomic characteristics, rc, oe, and De. The WKB
parameterization of the Born-Meyer potential results in a
potential energy surface that describes the observed
vibrational levels for most systems with small rms deviation.
The largest deviation occurs for the C state of CoAr+. In
this system, all but 9 bound vibrational levels encompassing
99% of the binding energy are observed experimentally.
Further refinement of the analytic potential may be necessary
to reduce the rms.
Notice that the vibrational frequency and dissociation
energy agrees extremely well with previously determined values
listed in Table 12 of excited state parameters. In most cases
the vibrational frequency, within a wavenumber, is exactly
matched. For those molecules in which the dissociation energy

125
Table 14. WKB Parameterization of Born-Meyer Potential with
Experimental Eigenvalues.
MRg+
v/vD*
%Eb
P
&
RMSC
re
De
Á
cm'1/106
cm"1
Á
cm'1
cm"1
VAr+
37/49
43
0.302
4.26
0.2
2.4
1420
94
VKr+
41/69
48
0.291
8.65
2.7
2.4
2130
99
CoAr+
A
19/
0.216
37.43
6.9
2.1
2720
166
CoAr+
B
36/55
65
0.276
6.03
3.1
2.2
2065
120
o
o
o >
d
+
47/56
99
0.205
58.48
10.9
2.1
2930
179
CoKr +
A
19/
0.259
11.38
7.4
2.5
4080
149
CoKr +
B
34/89
80
0.281
8.15
3.3
2.2
3000
118
CoKr +
C
27/94
63
0.245
17.35
1.5
2.1
4263
159
ZrAr+
A
14/
0.359
1.29
0.6
2.3
1333
68
ZrAr+
C
16/
0.318
3.09
1.8
2.4
1297
77
bPercentage of potential well depth observed over vibrational
bound states.
cRoot-mean-sguare deviation of WKB calculated versus
experimental vibrational eigenvalues.

126
have been determined via the LeRoy-Bernstein method, the
comparison to WKB determined dissociation energy is also quite
good, the relative error is less than 2% in each case. In the
worst case, the WKB procedure overestimated the experimental
value by a mere 1.87%.
Figure 31 displays the rms-minimized potential surface
and vibrational eigenvalues determined from the WKB
approximation and the Born-Meyer PES for the three observed
excited states of CoKr+. In the figure, it is easy to see
where perturbations of vibrational levels may occur. Also
notice that since the A state has a larger binding energy than
that of the B state and happens to corresponds to a larger
promotion energy in the cobalt cation. The Born-Meyer
potential surface suggests a internuclear distance of ca. 2.1
Á.
With the WKB technique it is possible to parameterize the
one-adjustable Lennard-Jones type potentials. This becomes
important when the experimental information is limited. Here
we may compare the ability of a Lennard-Jones [6,4] and [8,4]
with that of the Born-Meyer to describe the spectroscopic
parameters. Figure 33 displays the residual error for
vibrational eigenvalues of VKr+ determined by the WKB
approximation for several analytic potential functions. In
each case the adjustable parameter(s) was optimized by
minimizing the rms value. From the figure it is apparent that
only the Born-Meyer ([exp,4]) potential adequately describes

127
19000
13000
5 6 7
Internuclear Distance [Á]
Figure 31. Potential Energy Curves of CoKr+ Excited States,
The figure displays the potential energy curves of the excited
states, A, B, and C using the best fit parameters via the WKB
approximation. The A state curve crosses the B state such
that the A state has a higher dissociation energy and a lower
potential minimum. Note the extremely short predicted
equilibrium separation of ca. 2 Á.

128
the observed vibrational levels. For the system VKr+, the
Lennard-Jones [6,4] potential provides a better fit than the
[8,4] potential. However, assuming that the Born-Meyer
potential accurately predicts the internuclear bond distance,
the [8,4] provides a closer match (see Figure 34).
One immediate question that arises for this procedure is
how accurate is the approximation, and how accurate is the
computer code. The code is included in the Appendix B. Two
iterative procedures along with an integration will introduce
some inaccuracy in the determination of the vibrational
eigenvalues. One may test the accuracy of the program against
the known eigenvalue of the harmonic oscillator. A variety
criteria for the root finder procedure and minimizing routine,
along with varying the step size of the integrator have been
tried. A set of conditions that have been found in which the
computer calculated eigenvalues are within a 0.2 cm'1 of the
known harmonic eigenvalues over a range of 4000 cm'1.
As has been shown previously in this Chapter, the WKB
approximation applied to a harmonic potential is exact.
Comparison of WKB generated vibrational eigenvalues using the
harmonic PES will provide a good test of the computer code.
For such a calculation the rms was found to ca. 0.05 cm'1 for
40 vibrational levels spanning a well depth of ca 4000 cm'1.
On may further test the source code on non-harmonic
potential surfaces. A small change in potential energy near

129
vibrational index
Figure 32. WKB Error for Morse Potential.
The figure displays the error for the WKB-generated
vibrational eigenvalues for the Morse potential. The Morse
potential was parameterized by using the vibrational frequency
and dissociation energy of CoKr+ B state. The rigorously
determined vibrational eigenvalues using Eq. (34) are compared
to the semi-classical WKB method. Over the range of bound
levels 0 -> 52, an rms value of 0.068 cm'1 is observed with a
1000 step integration (squares). Increasing the number of
integration steps to 2000 (crosses) or 3000 (triangles)
results in an rms value of 0.024 cm'1 and 0.013 cm'1,
respectively.

130
the attractive portion of the surface will result in a large
change in internuclear distance. A convenient non-harmonic
PES one may easily test with the WKB approximation is a Morse
potential. For a Morse potential the vibrational eigenvalues
may be determined rigorously.77
E{v) = -)1/2 {v + 1/2) - AP2 (v + 1/2)2 (34)
\2 n2c\il 87t2cp
Here p and De are in cm'1, p is the reduced mass in grams and
h and c are the usual in cgs units.
Figure 32 displays the relative error of the Morse
vibration eigenvalue minus the WKB determined eigenvalue. The
dissociation energy of the potential was adjusted to
correspond to the rms minimized CoKr+ C state data. The
number of integration steps were increased from 1000, to 2000,
and finally 3000. Obviously, as the number of integration
steps increase the accuracy improves. However calculation
time is directly proportional to the number of integration
steps. We see that the results for a 1000 step integrator are
still significantly less than one wavenumber and therefore
more than adequate in modelling vibrational eigenvalues
determined in our experiment. The generation of an rms
contour plot requires ca. 9 hrs. of 486 33 Mhz computer
processor time.

â–  [exp, 4] A [8, 4] a [6, 4] x [Morse]
Figure 33. Residuals to WKB.
The figure displays the residual error (observed minus
calculated) for several analytic potentials parameterized via
the WKB approximation. The best fit of the vibrational levels
is achieved for the Born-Meyer potential,' annotated in the
graph legend as [exp, 4] which corresponds to Eq. 118. The
Lennard-Jones potentials, [8,4] and [6,4] along with the Morse
potential, poorly describe the experimental vibrational
levels.

132
Internuclear Distance (Angstoms)
Figure 34. Potential Energy Surfaces for VKr+.
The figure displays the potential energy surfaces used in
modelling the vibrational levels via the WKB approximation.
The internuclear distance of the Morse potential has been
arbitrarily adjusted to approximately agree with the other
potentials. Notice that the internuclear distance is ca.
2.4 A for both the [exp,4] and [8,4] potentials

METAL RARE-GAS CLUSTERS
One normally thinks of a dissolved ion as strongly
associated with a small number of polarized solvent molecules.
The solvent molecules very close to or 'touching' the ion,
which comprise the primary solvation sphere, will
significantly affect the solute ions' diffusivity and chemical
reactivity. Solvent molecules further away than this first
'shell' are much more loosely associated with ion position and
have a subsequently smaller effect on the ion's solvated
properties. Simple electronically closed shell ions, for
instance alkali ions, will attract the solvent almost
exclusively with charge dipole or charge induced-dipole
electrostatic forces. The number of molecules in the first
solvation shell will largely depend on the ability of the
solvent to pack around the ion. Open shell ions (in
particular transition metals) would be expected to have
interactions above and beyond the simple electrostatic,
ranging from mild preference for a particular coordination
number to covalent interactions so strong that the ion-plus-
solvation shell is best thought of as a single molecule
(coordination complex).
133

134
The experimental apparatus has been demonstrated to be
capable of generating a variety of transition-metal rare-gas
diatomics. The cluster properties of the expansion may
additionally 'solvate' a ionic species with several rare-gas
atoms. Here, we will define solvation to include all types of
ligands, and not just water molecules. Aqueously solvated
ions represent only one special case of complex. As will soon
be apparent, a unique stability is often associated with a
specific number of rare-gas atoms.
Figure 35 suchs a TOFMS of cobalt argon clusters obtained
under three different ion source expansion conditions. The
top trace in Figure 35 shows the observed positive ion mass
spectrum with p0d (the product of stagnation pressure in Torr
and the nozzle diameter in cm) of about 1 Torr-cm. The
pressure of the Co+-containing plasma upstream of the
expansion orifice is only a few Torr under these conditions
and is insufficient to promote homogeneous cobalt clustering
beyond the dimer or trimer. With the same laser fluence and
five times the stagnation pressure, Con+ (2 < n < 10) clusters
are observed in quantity. The top panel of Figure 35 shows
that Co+ clustering with the Ar in the carrier gas to form
CoArn+ is a dominant process under these conditions. The
middle panel and bottom panels of Figure 35 show the TOFMS
resulting from still lower stagnation pressure (p0d
0.7 Torr-cm and 0.3 Torr-cm, respectively). The vertical
scale in this figure has been reduced by a factor of

Relative Ion Current
135
50 150 250 350 450 550 650
AMU
Figure 35. Mass Spectra for the Uniquely Stable CoAr6+.

136
three from the top to the middle (= bottom) panels. The
absolute as well as the relative abundance of CoAr6+ ions
detected increases with decreasing stagnation pressure over
this pressure interval. We interpret this as an indication of
a kinetic or thermodynamic significance to the CoAr6+ molecule.
Kinetics and energetics play complicated roles in
determining the observed ion abundance in this experiment.
The average size of the cobalt argon clusters may be reduced
by a reduction in backing pressure for two reasons: 1) the
average number of Co+ - Ar collisions has been reduced
(nucleation is restricted) or 2) the final temperature of the
ion ensemble is higher (unimolecular dissociation is
enhanced). Effect 1) can be demonstrated by operating at very
low Ar concentrations but moderate total stagnation pressure,
at which point the only cobalt argon cluster represented in
the mass spectrometer is the CoAr+ ion because the probability
of a CoAr+ encountering and capturing another Ar atom is too
small. In this case the cobalt argon cluster abundance is
simply and completely nucleation rate limited. At higher Ar
concentrations at the same total pressure, multiple Ar
encounters will be the rule rather than the exception and
nucleation rates for any particular cluster will depend on the
lifetime of the ion-argon encounter complex and the rate of
collisional energy removal from the ion. The survival of any
ion thus formed will further depend on its unimolecular
decomposition rate at the final temperature of the molecular

137
beam for the duration of the 1 ms transit to the mass
spectrometer. At present, we cannot uniquely separate the
individual influence of these distinct processes. Conditions
of high Ar concentrations but low total pressure as in
Figure 35 would first promote nucleation to large sized
clusters followed by attrition by unimolecular dissociation
due to unquenched internal energy. Thus, small CoArn+ clusters
with fast nucleation rates would be small in number and large
clusters with small per atom binding energies would
'thermally' dissociate. One might expect rather rapid
nucleation of the unshielded central ion until the first
'solvation' shell is complete and closed.
Figure 36 shows the relative abundance for transition
metal-argon complex ions as a function of the number of rare-
gas atoms in the molecule for two different metals, V+ and Co+.
The relative abundance is derived for source conditions
similar to that giving rise to the bottom panel of figure
Figure 35. The total pressure is insufficient to effectively
cool their total binding energy. Thus, metastable decay
mediates the size of the complexes detected in the mass
spectrometer. Presumably, larger clusters have undergone
unimolecular decomposition in the ca. 1 ms between ion
formation and mass analysis leaving by attrition only the most
kinetically and/or energetically stable species, i.e. VAr/ and
CoAr6+.

138
Number of Argon Atoms (n)
Figure 36. Relative Abundance of VArn+ and CoArn+.
The figure displays the relative abundance of transition-
metal-argon complex ions as a function of the number of argon
atoms in the molecule. The horizontal axis (bottom of the
figure) indicates zero relative abundance. These data are
derived from mass spectra obtained under ion source conditions
such that extensive metastable decay due to the excess
internal energy of the ions occurs in the ca. 1 ms between in
creation and mass analysis. The anomalous abundance of VAr4+
and CoAr6+ indicates an unusual kinetic and or thermodynamic
stability of these species. This behavior is taken to imply
a preferred coordination of V+ and Co+ with argon of 4 and 6,
respectively.

139
As further proof of the unique stability of a given metal
rare-gas system, one may observe the collision-induced
dissociation (CID) of larger MRgn+ systems. Figure 37 shows
the fragment ion distribution following CID of CoArn+. The
loss of a single Ar atom for the cluster is a large channel
but cannot be quantified with the present apparatus.
Otherwise the major fragment is always the formation of CoAr6+.
Similar experimental manipulations have been applied to
other transition-metal containing systems. Below is a
complete list of transition-metal rare-gas magic clusters
observed: TiAr6+, VAr4+, NbAr4+, CoAr6+, NiAr+4<6r8, CuAr6+, AgAr10+
and FeAr6+.
An additional factor contributing to the enhanced
stability of the CoAr6+ molecule is the ligand field
stabilization of transition metal ions in the coordination
complex. However, the 'ligands' surrounding the central atom
are not point charges or dipoles in this case but point
induced dipoles, leading to a much weaker ligand (crystal)
field splitting than is normally observed in strongly bound
covalent or ionic d-orbital complexes. Nonetheless, cobalt
argon complexes, with their central d8 Co(I), would be
expected to favor the octahedral symmetry in CoAr6+ as the
isoelectronic species Ni(II)F6"4, Ni (II) (H20) 6+2, and
Cu(III) (H20)6+3 do. The energy realized by the ligand field

140
100 150 200 250 300 350 400 450
AMU
Figure 37. Collision Induced Dissociation of CoAru+.
The figure displays the collision-induced dissociation of
mass-selected CoArn+. Aside for the CoArn+ - CoArn_1+ + Ar
channel, the production of CoAr6+ is always observed to be a
dominant channel for parent ions with n * 8. This behavior
indicates a greater relative stability for the CoAr6+ ion.

141
breaking of the degeneracy of the d-orbitals on the Co+ and
thus lowering its energy is in addition to the net charge-
induced dipole binding energy of bringing up the Ar atoms to
the ion. However, the per atom binding energy based on simple
electrostatic forces does not seem to be a very sharp function
of Ar atom count unlike the very structure dependent ligand
field stabilization. Thus, the ligand field stabilization of
octahedral CoAr6+ might play a key role in making CoAr6+
uniquely stable.
Using the vibrational structure of metal rare-gas
diatomic systems, we have seen that it is possible to
parameterize simple analytic potentials. Because the nature
of the binding between the metal ion and the rare-gas ligand
is simply inductive in nature, one would expect the forces in
systems containing multiple rare-gas atoms to be pairwise
additive as a first level of approximation. Molecular
dynamics calculations that incorporate a Lennard-Jones [8,4]
potential for the metal cation rare-gas pair and a Lennard-
Jones [12,6] potential for the rare-gas interactions have been
carried out on VArn+ complexes.78 The lowest energy geometries
for VArn+ were found to be as follows: n = 2, bent with bond
angle 147°; n = 3, planar equilateral triangle; n = 4,
tetrahedral; n = 5, face-capped tetrahedral; n = 6,
octahedral; n = 7-8, face-capped tetrahedral; n = 9-14, edge-
and face-capped tetrahedral.

142
The molecular dynamic calculations also support the
unique stability of VAr4+ observed experimentally. The
calculations reveal a significant drop in per atom binding
energy after the fourth physisorbed argon atom. Additionally,
the heat of solvation of a V+ in liquid Ar was determined as
ca. 28.5 kcal/mol. This suggests, in comparison to the
aqueous solvation energy for Rb+ of 81.5 kcal/mol, that
inductive forces make a significant contribution to the total
binding energy of an ion in an aqueous media.
Monte Carlo calculation have also been carried out on
several metal-cation rare-gas containing systems via a
simulated annealing procedure.79 Some of these calculations
considered three body terms arising from the interaction of
the charge-induced dipoles in neighboring argon atoms. The
inclusion of the three body term was found to lower the total
binding energy and lower the symmetry of a given cluster.

METAL CATIONS WITH PHYSISORBED POLYATOMICS
Predissociation of V(OCO)*
Transition metal-containing molecules and surfaces are
known to be important in the catalysis of many types of
chemical reactions both at interfaces80 and in solution81.
Therefore, the role of partially filled d orbitals in the
lowering of activation barriers for bond cleavage, for
example, is of fundamental importance in organic and inorganic
chemistry. The structure and dynamics of simple gas-phase
transition-metal-containing species may be useful in modelling
such processes if sufficient detail may be deduced.
Most catalytic reactions proceed through a weakly bound
or 'physisorbed' state of the reactants complexed by
non-covalent forces. This precursor state is a stable but
weakly bound species which is a local minimum in the reaction
coordinate. If these complexes can be formed and isolated,
the reaction between two species may be photochemically
studied as a unimolecular process and thus without the
intrinsic averaging over impact parameters and collision
energies as in a scattering experiment. In principle,
spectroscopic methods could reveal the shape of the potential
143

144
energy surface for the reaction, and, in particular, elucidate
the nature of the reaction barrier.
If a chemical transformation can be studied from an
isolated, weakly-bound reactant 'cluster', great control is
possible in the choice of the initial conditions of the
reaction. In particular, specific vibrational motions in the
cluster can be photoexcited and any chemistry dependent on
this motion revealed. Such non-statistical behavior monitored
on a molecular level will allow the refinement of absolute
reaction rate theories and have consequence in the
understanding of extended systems. This section reports the
results of the photodissociation of V(OCO)+ which demonstrates
partial vibrational mode-specificity.
When a laser-induced plasma of solid vanadium is expanded
supersonically in a carrier gas of He and 0.2 % C02, a variety
of Vx+(C02) cluster ions are formed, but, under typical
experimental conditions, no VC+ or VCO+ ions are detected. The
ion VO+ is present but in the same amount regardless of
whether a He/C02 mixture or pure He is used in the ion source.
This implies that' the ensemble of ions spectroscopically
probed in this work is comprised of electrostatic complexes
and not high-temperature ion-molecule reaction products.
Additional evidence for an electrostatically bound V(OCO)+ may
be derived from collision induced dissociation; only V+ is
detected as a CID fragment of V(OCO)+.

145
Figure 38. Stick Plot of V(OCO)+ Photodissociation.
Stick plot of the photodissociation of V(OCO)+ fragmenting
into V+ and 0C0 as a function of laser frequency. The
relative intensities depicted are normalized to laser power
and parent ion current to about 20%. The three prominent
vibrational progressions annotated in the spectrum correspond
to a pure stretching motion (marked stretch), a stretching
progression in combination with a rocking of the C02 relative
to the V+ atom (marked rock+stretch) , and a stretching
progression in combination with a C02 bend (marked bend-
stretch) .

146
Photofragmentation of the V(OCO)+ molecular ion in the
visible shows sharp resonant absorption features and two
distinct dissociation pathways: V(OCO)+ - V+ + C02 and
V(OCO)+ -* V0+ + CO. The excitation spectrum of this molecule
appears quite similar to that of the electrostatically bound
VAr+, VKr+ and V(H20)+ molecules which result from
predissociation of a long-lived excited electronic state. The
spectral breadth of the transitions observed in V(OCO)+ places
a lower limit to the lifetime of the photoexcited level at
about 1 ps.
Figure 38 shows a stick plot representing the positions
and intensities of the peaks in the photodissociation
excitation spectrum of V+(OCO) - V+ + 0C0 in the range of
15 500 to 17 500 cm-1. The relative peak intensities have been
normalized to incident laser power and parent ion intensity
and should be representative of the actual photodissociation
cross section to about 20%. A progression in an excited state
vibration is evident indicating a frequency of 196 cm-1 and an
anharmonicity of 4.7 cm-1. In addition, vibrational
progressions of this mode in combination with two other modes
(frequencies of 105 and 600 cm-1) are seen.
The intensity distribution in the spectrum indicates only
a moderate change in geometry of the molecule upon excitation,
and, in comparison to the previously studied systems (VAr+,
VKr+ and V(H20)+) both upper and lower states of V(OCO)+ are

147
electrostatically bound. If this is the case, the vibrational
modes of the C02 moiety might be considered separable from
(two) modes arising entirely from the new electrostatic
'bond'. In accord with this idea, preliminary assignment of
this spectrum places the origin at the reddest peak
(15 800 cm-1)/ the V+—(OCO) stretching mode at 196 cm-1 and the
V+-(OCO) 'rocking' motion at 105 cm-1. The bending motion of
the OCO moiety is observed then at 600 cm-1 which is reduced
by 66 cm-1 from the gas phase value82. Estimation of the
geometry of the system from classical electrostatics suggests
that a distorted T-shape (Cs not C2v) is the global minimum
structure.
Unfortunately, spectral information is insufficient for
rigorous determination of the geometry. The vibrational
assignment of the V(OCO)+ spectrum is also tentative and will
be checked by spectroscopic shifts induced by isotopic
substitution of the C02 and subsequent normal mode analysis.
Figure 39 shows that the photofragmentation excitation
spectra of V(OCO)+ to produce VO+ or V+ are identical in
structure (to within our signal to noise). Thus, the V+ and
VO+ photofragments not only arise from the same isomeric form
of V(OCO)+ but are the result of the unimolecular
decomposition of the same excited electronic state. Moreover,
the branching ratio for VO+/V+ production is dependent on the

148
16200 16250 16300 16350 16400 16450
Figure 39. Photoexcitation Spectrum of V(0C0)+.
The figure displays the photodissociation excitation spectrum
of V(OCO)+ in the visible region. The relative photofragment
current (vertical axis) is plotted versus the incident photon
frequency (horizontal axis) for the V(OCO)+ - V+ + C02 (bottom
curve) and V(OCO)+ - VO+ + CO (top curve) photofragmentation
processes. The VO+ product ion intensity has been multiplied
by a factor of two to elucidate comparison of the spectra.
Power dependence of these signals show that both fragmentation
events follow a one-photon absorption by V(OCO)+ and thus the
two fragmentation processes proceed via the same photoexcited
intermediate.

149
photoexcitation transition (note the bands at 16330 cm1 and
16390 cm-1) .
Figure 40 shows this VO+/V+ branching ratio at fixed laser
frequencies which correspond to strong transitions in the
spectrum. The experimental data are shown as symbols with
vertical error bars corresponding to two standard deviations
of the mean. Each data point corresponds to 25 separate
experimental trials.
The dissociation limit of V(OCO)+ - VO+ + CO may be shown
thermochemically to be 0.45 eV lower than that of
V(OCO)+ - V+ + OCO through the accurately known V-0+ and O-CO
bond energies.83'1 The upward trend in the VO+ production as a
function of the internal energy of the parent molecule
(Figure 40) indicates an energetic barrier for the production
of VO+ over that of V+. This barrier is not unexpected
considering that strong covalent bonds must be made and broken
to form the products. In analogy84 with N20, the adiabatic
dissociation of C02 to form ground state fragments is spin
forbidden (the spin allowed dissociation is 2 eV higher than
the adiabatic limit) which also may contribute to the
existence of this barrier.
The non-monotonic increase of VO+ production with energy
indicates mode specificity in the fragmentation of V(OCO)+.
Using the tentative vibrational assignment of the
photodissociation spectrum above, it is suggestive to compare
the branching ratio for VO+/V+ production for the origin band

150
Laser Frequency (wavenumber)
Figure 40. [VO+]/[V+] Branching Ratio.
The figure displays the [VO+]/[V+] branching ratio for
absorption transitions of V(OCO)+as a function of excitation
frequency. The branching ratio is measured by fixing the
excitation source to the desired transitions and alternately
determining V+ and VO+ product ion intensities. The symbols
in the figure represent the experimental data with vertical
error bars representing two standard deviations of the mean.
The solid line is a RRK model of the data yielding an
activation energy for the formation of VO+ of 1.6 eV.

151
and the bands corresponding to one quanta of stretch, rock,
and C02 bend. To within experimental error, the branching
ratios corresponding to no vibrational excitation in the
initially excited V(OCO)+ and excitation of one quanta of
stretch or C02 bend are identical. However, excitation of one
quanta of the rocking motion increases the relative V0+
production by 50% as might be expected because this motion
would force the V+ and O atoms closer together. Excitation of
more vibrational quanta in the initial state leads to a
greater relative VO+ yield but with less obvious
mode-specificity.
Nonetheless, the overall trend in the branching ratios
seems to be describable by simple RRK85,86 theory (the solid
curve in Figure 40) . The chemical equation for the two
photodissociation pathways are described as follows:
V (OCO) * — V* + oco
V(OCO) * — VO* + CO.
For two parallel and competing reactions one may equate the
ratio of the rate constants to the ratio of cationic products,
K m [VO*]
k2 [V*]
The ratio of products is easily measured from the
fragmentation spectra of the parent ion. RRK theory states
that for a systems of classical oscillators, s, the rate

152
constant is related the relative percentage of a system's
total energy, E above some critical energy, E0:
For our treatment s is determined by the vibrational degrees
of freedom. One may easily show that the branching ratio
[VO+]/[V+] is related to critical energy of each dissociation
pathway,
(38)
The variables E, and E2 refer to the critical energy barrier
for the two dissociation pathways. The total system energy is
given by the transition frequency.
Under the assumption that the system V(OCO)+ is
electrostatically bound, there should be no reaction barrier
to form the products of V+ and C02. The barrier is at the
adiabatic dissociation limit which is estimated to be about
1 eV. One may adjust E, to minimize the error of the
branching ratio. The calculated curve in Figure 40 places an
estimate for the barrier in the process V(OCO)+ -*• VO+ + CO at
1.6 eV (37 kcal/mol). This determination is insensitive to
the dissociation energy estimate of the electrostatically
bound complex; a binding energy change of 25% corresponds to
less than 5% change in derived activation energy.

153
V++ CO + o
The figure displays the relative energy for isomers involved
in the photodissociation of VC02+. The figure does not
represent a reaction coordinate. Photoexcitation to quasi¬
bound vibrational levels of an excited state will subsequently
dissociate along two distinct pathways; VC02+ -*• V+ + C02 and
VC02+ - V0+ + CO.

154
Figure 41 displays the energetics in the
photodissociation of VC02+. The initial state of species is
not the global minimum. Presumably the VO+-CO species is
energetically more stable than V+-OCO, since the binding
forces in the former system include permanent dipole
interactions. Photoexcitation the V+-OCO isomeric form leads
to a metastable electronic state which dissociates by two
pathways.
The relative fragmentation rates of two dissociation
pathways in the predissociation of electrostatically bound
V(0C0)+ have been measured as a function of vibronic state.
The overall trend in this branching ratio places an estimate
on the barrier to C02 bond activation in the presence of a
transition metal but the predissociation does not appear to be
entirely statistical.
Vibration Structure of Electrostatically Bound
A natural progression from metal-cation rare-gas
diatomics is the study of metal cations with polyatomic
ligands. The gas-phase analysis of molecular clusters
provides a unique and powerful way to study the intermolecular
interactions commonly found in condensed phases. Moreover,
such model systems may be chosen judiciously to be of chemical
interest and yet simple enough to be tractable, both in theory

155
and experiment. Recent research has successfully
characterized inductive binding in the absence of covalent
interactions in transition-metal rare-gas complexes. The
analysis of these prototypical systems has motivated the study
of more complex species exemplifying polyatomic intermolecular
forces. In this section, we begin an analysis of the
potential surface of a vanadium ion electrostatically bound to
a H20 molecule.
Vanadium atomic and cluster ions are generated by laser
vaporization of the target metal under a high pressure (ca.
1 atm) of helium carrier gas. This flow is then
supersonically and adiabatically expanded in a vacuum. When
the carrier gas is spiked with ca. 0.3 mole percent water,
aggregates of Vx(H20)y+form in the supersonic expansion. Source
conditions determine the range of x and y and are optimized
for the ion of interest, namely the ion-water pair.
Resonant one-photon dissociation of VH20+ and its
isotopic variants is observed to occur over the range of
15 200 to 18 500 cm'1. Figure 42a shows a portion of the
spectrum of VH20+. A series of nine prominent features with
an interval of ca. 340 cm-1, immediately suggests a single
upper state vibrational progression with approximately this
vibrational frequency. This progression begins with the
reddest and most intense feature at 15 880 cm-1 and shows a
monotonically decreasing intensity with increasing photon
energy. The abrupt onset of the progression is indicative of

Relative V HPhotodissodation Intensity
156
Transition Frequency (wavenumbers)
Figure 42. Resonant Photofragmentation Spectrum of V(H20)+.

157
the origin of the electronic transition at this energy
(isotopic analysis has confirmed this). No hot band
transitions have been observed due to the extensive
vibrational (and rotational) cooling the parent molecules
suffer in the supersonic expansion. Furthermore, no high
frequency vibrational intervals indicative of V—H stretching
or H20 normal modes are evident in this spectrum.
The spectrum of V(H20)+ may be casually compared to the
resonant photodissociation spectra of VAr+ and VKr+, which
also occur in a similar spectral region. These diatomics show
a single predominant electronic transition in the visible
which arises from a parity forbidden (5P [3d34s] ♦- 5D [3d4])
transition in isolated V+. Due to the significant change in
ionic radius of the V+3d34s excited state relative to the 3d4
ground state, a long upper state vibrational progression is
observed in the VAr+ and VKr+ spectrum. Both theoretical87 and
experimental evidence indicate little covalent nature in the
binding of these ions.
Analysis of the V(H2160)+, V(D2160)+, V(HD160)+, and V(H2180) +
isotopic species is used to determine the identity of the
upper state vibrational progression and confirm the nature and
structure of the carrier of the spectrum in Figure 42. Two
plausible structures of the V(H20)+ ion exist: the
electrostatically bound V+(OH2) and the chemically bound
inserted H—V—OH+ structure. The existence of the inserted
structure has been suggested from analysis of guided ion beam

158
data. 88,89 The insertion process has been asserted to have a
small or zero activation barrier.
Several observations make it impossible for the H—V—OH+
molecule to be the carrier of the spectrum reported here.
First, the VHDO+ spectrum should contain contributions from
two distinct isomers, H—V—0D+ and D—V—OH+. Only a single
progression is observed in the VHDO+ spectrum. Moreover, if
the upper state progression is in fact a symmetric stretch or
bending mode (the H—V—OH+ is treated as a quasitriatomic here,
i.e. the OH a quasiatom) a large isotope shift (ca. 25% of the
fundamental) should be observed between the H—V—0H+, H—V—OD+,
and H—V—180H+ species; and between the D—V—OH+ and D—V—OD+
species. This is not observed. The only mode of the inserted
structure which could exhibit a small enough isotope shift
upon deuterium substitution of the lone proton to be
consistent with experimental observation is the asymmetric
stretch. A very small V-0 stretching force constant (ca. 15%
of a typical single bond) would have to be assumed to be
consistent with a 34 0 cm-1 vibrational frequency for this mode
which is inconsistent with the existence of a true covalent
interaction. Thus, the H—V—OH+ inserted structure is ruled
out.
If the V(H20)+ ion spectrum in fact arises from the
electrostatically bound structure, then the upper state
vibrational progression should represent the V+—(OH2) stretch,
in analogy with the VAr+ and VKr+ spectra. V+(OH2) is treated

159
Figure 43. Isotope Shifts of V+(,8OH2) minus V+(16OH2).
Isotope Shift of V+(18OH2) minus V+(16OH2). The observed
(symbols) and calculated (curves) isotopic shifts versus upper
state stretching quantum number for the first six bands of the
spectrum in the previous figure. The solid curve is derived
from the fit vibrational constants (w/ = 339 cm1, a)e" = 42 0 cm'
^eXc/ = ^eXe” = 4.5 cm1) assuming the electronic origin at
15 880 cm'1. Dotted curves are calculated by shifting the
vibrational assignment by plus and minus one quanta.

160
as a quasi-diatomic and the masses of the V+ and H20 moieties
are used to calculate45,89 the V+(18OH2) - V+(16OH2) isotope shift.
These two species have the most similar band contours (see
Figure 42b) and provide the most accurate isotope shift data.
Figure 43 shows the observed (symbols) and calculated
(curves) isotope shift: v[V+(16OH2) ] — v[V+(18OH2)] versus
excited state vibrational quantum number. The solid curve
assumes a vibrational numbering which assigns the reddest
observed band as the electronic origin and the dotted curves
change this vibrational assignment by plus or minus one
quanta. The upper state constants were derived from a fit to
the standard form45,89 of the V+(OH2) band positions and yields
w/ = 339 ± 5 and wcxe' =4.5 + 2 cm-1, respectively with a root
mean square deviation of 0.6 cm-1. The ground state wc" was
adjusted to fit the isotope shift data fixing wexeM = wexe' to
yield we" = 420 + 75 cm-1. The excellent agreement between
observed and calculated shifts confirm the identity of the
vibrational progression as the V+—(OH2) stretching motion and
the assignment of the origin band at 15 880 cm-1.
Figure 44 displays the photodissociation spectra for the
v' = 0, and v' = 1 stretching bands of deuterated V+(water)
systems. The bands have been normalized to the largest
feature in each case. The band substructure is apparently more
sensitive to deuterium substitution than the isotopic
substitution of oxygen (see Figure 42b). However, the
photodissociation

Photocurrent
161
4
o
II
•>
I
I—I—I—I—1
j V(DOD)+
A
: ii
1 A J
1 . V(HOD)+
\ Xu... A.
X
—\—i—i—i—
V(HOH)+
p^ -
T— “r“ i
16100 16140 16180 16220 16260 16300 16340
Figure 44. Photodissociation Spectra of Deuterated Isotopes
of V(Water)+

162
spectrum for V+(HOD) -*• V+ + HOD indicates only one structure
is present in the beam.
The electronic origin of the one-photon dissociation
transition places an upper limit to the ground state adiabatic
dissociation energy of 1.97eV. This is consistent with
theoretical90 and experimental estimates of this dissociation
limit of ca. 1.5 eV.
The spectroscopic characterization of an
electrostatically bound ion-water complex has been
demonstrated. The V+-OH2 stretching frequency has been
determined in two different electronic configurations of the
ion. These results represents a significant step toward the
elucidation of electrostatic charge-solvent potential energy
surfaces necessary to model condensed phase chemical
reactions.
Resonant Photodissociation of V(NH,) +
The study of physisorbed molecules on a vanadium cation
nucleation center have been very congenial with regard to
photodissociation spectra. The separated atomic limit for the
vanadium cation are believed to be same as in the rare-gas and
previous polyatomic ligand cases. Figure 45 displays the
photodissociation spectrum of V(NH3)+ dissociating to a cation
with mass of approximately V+. However, the secondary mass
resolution is not sufficient enough to distinguish between a

Photocurrent
163
Laser Frequency (wavenumber)
Figure 45. Resonant Photodissociation of V(NH3)+.

164
hydrated and bare cation. Nonetheless, a sector scan of
the photofragments reveals an isolated peak center on 51 amu
corresponding to the naked V+ cation.
The spectrum consists of three bands of a progression
which provide a vibrational frequency of ca. 318 cm'1. The
structure is not known unequivocally but is believed to be
determined by the orientation of the permanent dipole in the
ligand with the charge on the vanadium cation. This
electrostatic reasoning would therefore place the nitrogen
nearest the cation. Several smaller bands are seen to the red
of the major progression and have a spacing of about 3 0 cm'1.
In an electrostatically bound system one would expect the
vibrational modes of the uncomplexed ammonium ligand to not be
significantly shifted. The vibrational frequency of the
normal modes found in ammonia have been determined previous.
The two symmetric modes are ca. 3300 cm'1 and ca. 930 cm'1. The
other modes are ca. 1600 cm"1 and ca. 3000 cm'1.
This system has the smallest difference in ionization
potential between the transition metal and the ligands of all
the systems studied thus far and therefore significant
covalent character may be found in the bonding forces.
Currently, we have not looked for charge transfer.

165
Resonant Photodissociation of CríN-J*
The photodissociation spectrum of Cr(N2)+ displays a
threshold to a diabatic threshold. This spectrum is similar
in appearance to the threshold spectra of NiAr+ -*• Ni+ + Ar and
CrAr+ -» Cr+ + Ar discussed in the chapter on inductively
bound diatomics.
Figure 46 displays the photodissociation spectrum for
Cr(N2)+-> Cr+ + N2 in the region of 16 900 to 17 300 cm'1. This
particular spectrum has a signal-to-noise level of ca. 2 to 1
due to the poor stability of the parent system. However a
large and dramatic change is observed by the significant
increase in Cr+ photocurrent near 17 100 cm'1.
As in the case of metal rare-gas diatomic molecules, one
would not expect photodissociation into charged nitrogen
molecules. The difference in IP is Cr[6.763]37 - NjflS.SSl]1 =
8.818 eV. We confirmed this experimentally by looking for
photodissociation into charged N2+; there was no production.
The onset to photodissociation presumably corresponds to
some promotion of Cr+ plus the adiabatic binding energy. We
find that the only spin allowed transition in the cation
within 5.8 eV of the ground state is 6D at 12 14 8.0 cm"1. Thus,
the adiabatic dissociation energy is given by the difference
of diabatic threshold and the separated atomic limit as 0.61
±0.4 eV. The uncertainty in the adiabatic dissociation limit

Cr+ Relative Photocurrent
166
Laser Frequency (wavenumber)
Figure 46. Photodissociation Threshold for Cr(N2) + -*â–  Cr+ + N2.

167
is a consequence not knowing the exact J state of the Cr+ ion
in promotion.
Dissociation into a vibrationally excited state of N2 is
a possibility. The molecular vibrational frequency is
2359 cm'1 or 0.292 eV.(1) Excitation of one quanta of the
nitrogen stretch would lower the predicted dissociation energy
to ca. 0.318 eV. These values may be compared to the
theoretically determined equilibrium dissociation energy of
0.53 eV. The theoretical number agrees well with the
experimental binding energy of 0.61 eV. Recall that the ab
initio calculations of binding energies for metal rare-gas
diatomics are consistently 20% lower than experimental.
Unfortunately, the experimental information is not
sufficient to determine the electrostatic vibrational
frequencies or the configuration of the electrostatically
bound system. However, the results of ab initio calculations
predict that the predominant interaction is charge-induced
quadrupole; CrN2+ is expected to be linear due to the negative
quadrupole moment.
Resonant Photodissociation of Ca(lM +
Another nitrogen containing system that we have studied
is Ca(N2)+. The photodissociation spectrum for this molecule
is displayed in Figure 47. The production of Ca+ is monitored
as a function of incident laser frequency. A very

Ca++N ¿v"=0)
168
_ i i . Aa m
14000
Figure 47.
2650 cm’1;(cOg (N^=2359 cm1)
14400 14800 15200 15600
wavenumber
Vibrationally Excited Photofragments of Ca(N2)+.

169
complicated photoexcitation spectrum is observed in the
region of 14 400 to 15 400 cm'1. A vibrational progression
ends abruptly going toward the red at ca. 14 570 cm'1. This
has been assigned to the origin band.
For the cation of calcium there is only one possible
atomic state in the vicinity of the spectroscopic region; 2D
which has two J components corresponding to 13 650 and
13 710 cm'1. The 60 cm'1 spin orbit splitting is similar to the
vibrational spacing dominant in the progression. The
complicated nature of the spectrum may be due to this spin-
orbit component. Also, the molecule will have more than one
low frequency vibrational mode which may be seen as a separate
vibrational progression or a series of combination bands.
This particular molecule displays a progression built
upon an excited state of the nitrogen molecule in the
wavelength region of 17 100 to 17 700 cm'1 (see inset of the
figure). The nitrogen excited progression is shifted from the
primary progression by 2 650 cm'1 which may be compared to the
molecular nitrogen stretch of 2359 cm'1. In both regions of
the spectrum only Ca+ is observed as a photodissociation
product.
We may speculate as to the configuration of system. The
author believes the system is linear. A T-shaped system would
probably not account for the increase in vibrational
frequency. If anything, the vibrational frequency should go
down due to the electron withdrawal along the nitrogen bond

170
axis. A linear configuration would however account for the
increase in frequency. Here, the observed vibrational
frequency would correspond to an approximate symmetric mode
localized in the nitrogen stretch. The added electrostatic
bond would require additional energy to excite the approximate
nitrogen mode.
The electronic origin is to the blue of the separate atom
limit and implies that the ground state is bound by more than
the excited state. One may set as a lower limit the
dissociation energy of the ground state by the range of
observed vibrational transitions of 0.1 eV. This will set a
lower limit to the adiabatic binding energy of 0.217 eV.

METAL-METAL SYSTEMS
Ni2+
Transition metal clusters have drawn the interest of many
theorists and experimentalists because of the central role
these species play in the expansion of predictive chemistry
beyond the main group elements. Transition metal-containing
systems are also of significant importance as catalysts. At
present, however, the nature of metal-metal bonding is poorly
understood. Experiment has provided insufficient conclusive
detail about the nature of transition metal clusters (or their
ions) to significantly affect theory, and ab initio theory
seems to be taxed to its limits in the description of even the
simplest transition metal dimers.
Perhaps the single most important characteristic of a
diatomic system is its bond energy. High temperature
equilibrium studies have provided thermodynamically derived
metal-metal bonds strength in several transition-metal
systems.91,92 For a recent review of neutral transition metal
diatomics, see Morse.® Unfortunately, no such extensive
literature exists for transition-metal diatomics in non-zero
171

172
charge states. The bonding in charged species is at least as
interesting as the neutrals and comparison of the nature of
different charge states should provide insight into orbital
contraction and its effect upon s-d hybridization. In this
Chapter will present the spectroscopic data for three cationic
metal dimers, Ni2+, Cr2+, and Ca2+.
Recent results from collision-induced dissociation of
Ni2+ have determined the bond dissociation energy at
2.08 ± 0.07 eV.93 The neutral diatomic binding energy has been
spectroscopically established at 2.07 ± 0.01 eV.94 Coupling
this information with the appearance potential of Ni2+ in a
mass spectrometer predicts the binding energy as
3.3 ± 0.2 eV,95 a > 1 eV difference in these two experiments.
Theoretical determinations are no less incongruous. The
theoretical calculation of Upton and Goddard96 predict a bond
dissociation energy of 4 eV. While Bauschlicher et al97
predict a dissociation energy, D0 of 1.82 eV. In this section
we will look at photodissociation spectra of Ni2+ and also
introduce a novel technique for determining the bond
dissociation energy of Ni2+ through the photodissociation of
its van der Waals adduct.
Figure 48 shows the low mass portion of the TOF mass
spectrum obtained with the energy analyzer set to transmit
1.45 keV (single positive charge) ions. This figure
represents the stable (lifetime > 1ms) positive ion
distribution emanating from the source operating with 'pure'

173
30 80 130 180 230
AMU
Figure 48. Mass Spectrum of Argon Seeded Nickel Beam.
The figure displays time-of-flight mass spectrum of the
positive ion distribution generated in a laser-driven nickel
plasma seeded in a supersonic expansion. The top panel
corresponds to an expansion in a pure He carrier gas. The
bottom panel corresponds to an expansion in ca. 2% Ar/He gas
mixture. Note the appearance of NixAry+ with this carrier gas.

174
He as a carrier gas (Figure 48a) and ca. 2% Ar/He
(Figure 48b). Negatively charged ions are observed under the
same source conditions, but at no time has any evidence for
stable multiply charged species been discerned. Due to the
chemical reactivity of small transition metal clusters and
their positive ions, unavoidable contamination of the ion
source with H20, C02, hydrocarbons, etc. leads to the
production of partially ligated metal cluster ions such as
Mx0+ which are clearly evident in the mass spectra in
Figure 48a. Figure 48b reveals that presence of argon in the
source produces Ar+ and Ar2+ as well as species of the series
MxAr+ and MxAr2+.
The MxAry+ ions are particularly interesting because they
provide a spectroscopically important analog to the bare Mx+
cluster itself. Since the ionization potential of Ar
(15.755 eV) is much higher than that of the nickel atom
(7.63 3 eV) which in turn is higher than that of the nickel
clusters ( <7 eV) , we expect the nature of MxAry+ to be that of
Mx+(Ar)y, i.e., polarized rare-gas atoms loosely bound to the
electric field of the relatively unperturbed charged metal
cluster. An estimation of the binding energy of the Ar atom
to the metal ion might be made by comparison with the binding
energy of another charge induced-dipole bound complex, H3+.Ar,
which has recently been characterized,98 and its binding energy
has been estimated to be approximately 0.29 eV. We would
therefore expect the binding of Ar to Ni2+, for instance, to

175
be of this order. The binding energy of Ar to larger metal
cluster ions would be expected to be a decreasing function of
cluster size because the electric field at the 'surface' of a
larger cluster is weaker than that of a smaller one. For a
roughly spherical cluster, one would expect the binding energy
to be proportional to x4/3 (where x is the metal atom count) .
The binding energy of additional argon atoms to a fixed size
metal cluster would be expected to decrease only slightly
until the Ar atoms 'cover' the metal ion and thus complete the
first 'solvation shell' at which point the binding energy
should drop drastically. The concept of a solvation shell for
these gas-phase ions has been supported by the observation of
the anomalously large abundance of particular sized clusters
(for example NiAr4+ as can be seen in the figure in the ion
beam under somewhat different source conditions, implying a
special kinetic or energetic stability of these molecules.
Our picture of the nature of the MxAry+ molecule has
another important consequence: The UV-Visible electronic
absorption spectrum of the MxAry+ ion should be almost the same
as the bare Mx+ ion itself. However, all the MxAry+ levels
accessed by visible and UV photoabsorption are above the
dissociation threshold to Mx+ + Ar. This means that the
spectrum of the f^Ar^ ion will be lifetime broadened with
respect to the Mx+ ion, but the former's one-photon absorption
may be detected with near unit efficiency in a tandem mass
spectrometer.

176
How the MxAry+ ion photofragments will depend on exactly
what photon energy is absorbed. Consider the
photodissociation of Ni2Ar+, for example. If the photoexcited
Ni2Ar+ has internal energy above its lowest dissociation
threshold, that into Ni2+ and Ar, and below all other
dissociation limits, then all the Ni2Ar+ will fragment into
Ni2+ + Ar, and no other products will be observed. The rate
at which the unimolecular decomposition occurs may depend
strongly upon the detailed nature of the photoexcited state
but would be expected to be somewhat shorter than the
timescale for secondary mass analysis in this experiment (10'5
s) . However, if the internal energy of the Ni2Ar+ is somewhat
larger than the energy required to break the Ni-Ni bond, then
one would expect facile photodissociation of Ni2Ar+ into
Ni+ + Ni + Ar. Therefore, the observation of the products
formed from the photodissociation of Ni2Ar+ as a function of
photon energy allows the Ni2+ bond dissociation energy to be
estimated.
Figure 49 shows the laboratory kinetic energy spectrum of
Ni2Ar+ which has been photoexcited after initial TOF mass
selection but before entering the energy analyzer. The
entrance and exit apertures of this analyzer have been opened
sufficiently to give maximum detection efficiency for parent
(Ni2Ar+) and daughter (photofragment) ions and maintain an
energy resolution of approximately 8 (mean energy/energy
FWHM). Since the greatest possible center of mass kinetic

177
*4* ^* *■*■**■"’ "■» ~*Mm, ^ , , 7«n*—
40 60 80 100 120 140
AMU
Figure 49. Photofragmentation of Ni2Ar+.
The figure displays the kinetic energy analysis of
photoexcited Ni2Ar+. For a photoexcitation energy of 3.49 eV,
Ni+is the dominant fragment. At 2.98 eV, Ni2+ is the dominant
fragment. The reversal of the major photofragment channel
indicates that the bond energy of Ni2+ is between 2.98 and
3.49 eV.

178
energy release in the photofragmentation of our parent ion
would be entirely veiled by the energy analyzer resolution,
the lab kinetic energy spectrum may be considered a secondary
mass spectrum where the ratio of parent to daughter kinetic
energies is equal to the ratio of parent to daughter masses.
Taking these considerations and the parent ion beam energy of
1.45 keV into account, the ordinate axis has been converted
from lab energy into a mass axis. The feature in Figure 49
have been labeled as to their identities as Ni+ and Ni2+ 58 amu
and 116 amu, respectively.
The relative abundance of the photoproduct channels shown
in the figure may be interpreted as follows: At 3.0 eV photon
energy (416 nm generated by Stokes shifting the Nd:YAG third
harmonic in H2; 5 mJ/cm2; bottom panel of Figure 49) , one-
photon excitation of the parent Ni2Ar+ molecule does not
provide sufficient internal energy to break the Ni-Ni bond.
However, a small but almost unavoidable fraction of the parent
ensemble absorbs two or more laser photons ( >6.0 eV) and
photofragments into Ni+ + Ni + Ar. At 3.5 eV (355 nm Nd:YAG
third harmonic, 5mJ/cm2; top panel in Figure 49) , most of the
Ni2Ar+ photofragments into Ni+ + Ni + Ar, indicating one laser
photon is sufficient to cleave the metal ion itself. However,
a small fraction of the Ni2Ar+ ensemble fragments into
Ni2+ + Ar at this photon energy. The dissociation limit of
Ni2+ might lie slightly above 3.5 eV, but most of the
molecules in the ensemble have enough thermal excitation to

179
photodissociate anyway. Or, the optically excited (Ni2+)*.Ar
is 'caged' by collision of an outgoing Ni or Ni+ colliding
with the Ar atom, resulting in a translationally hot Ar atom
and a bound Ni2+ ion. The latter caging effect is presently
being investigated in our laboratory by the use of increased
kinetic energy resolution in the photofragmentation detection.
Either explanation, however, would indicate 3.5 eV to be
rather close to the dissociation threshold of Ni2+.
Measurement of the Ni2+ bond dissociation threshold by
this method yields a reasonable result,
3.0 < D0(Ni2+) < 3.5 eV. As discussed in the beginning of this
section, our determination is in agreement with the previous
estimates of Kant of D0(Ni2+) = 3.3 ± 0.2 eV. However, it is
at odds with that determined by Armentrout et al of
2.08 ± 0.07 eV.
Further insight into the nature of the bonding
interaction of Ni2+ may be found by direct spectroscopic
probing of the uncomplexed ion. Figure 50 shows the Ni+ ion
current arising from the laser photodissociation of
Ni2+ -* Ni+ + Ni as a function of frequency on the interval from
16 940 to 16 980 cm"1. The top trace of this figure is the
spectrum arising from 58Ni2+ and the bottom trace is the
simultaneously acquired 60Ni58Ni+ spectrum. These data were
recorded in a single sweep of 0.08 cm'/s at a laser fluence of
ca. 3 mJ/cm2. A small continuous photodissociation is evident
between the sharp features which is attributable to non

180
16940 16950 16960 16970 16980
Laser Frequency (wavenumber)
Figure 50. Resonant Two-Photon Dissociation of Ni2+.
The figure displays the resonant 2-photon dissociation
spectrum of Ni2+ over the region 16 940 to 16 980 cm'1. The
upper panel of this figure is the spectrum arising from the
58Ni2+ isotope and the bottom panel is the simultaneous
acquired 58Ni60Ni+ spectrum. The vertical scale in the lower
spectrum has been multiplied by 2.6 to account for the
naturally less abundant 58Ni60Ni+ isotope. The spectrum
displays a partially rotationally resolved band for the B «- X
state.

181
Table 15. Line Positions for R2PD of Ni2+ (cm1).
A-X
58Ni2+
58Ni60Ni +
V'
freq.
o-c
freq.
o-c
18
16346
-0.4
16321
•
o
i
19
16506
0.5
16479
-0.3
20
16664
0.1
16637
0.3
21
16821
0.3
16793
0.0
22
16976
-0.7
16947
-0.5
23
17101
o
•
o
24
17285
0.2
17253
0.0
B-X
58Ni2+
58Ni60Ni +
V'
freq.
o-c
freq.
o-c
8
16317
-0.2
9
16484
-0.2
16469
-2.0
10
16649
0.4
16633
-1.0
11
16812
0.6
16796
-0.5
12
16973
-0.2
16955
l
I-*
•
o
13
17132
o
•
o
17114
VO
•
o
1
14
17289
•
o
l
17270
-0.2
15
17444
in
•
o
i
17425
0.4
16
17599
0.6
17581
3.8
C-X
58Ni2+
58Ni60Ni +
V'
freq.
o-c
freq.
o-c
8
16424
0.4
9
16581
-0.7
16568
10
16740
•
o
16726

182
-resonant multiphoton absorption. The peak of the resonant
features correspond to less than 1% depletion of the parent
ensemble at this laser fluence. The vertical scale in the
panel has been multiplied by 2.6 to allow comparison of the
spectrum of the naturally less abundant 60Ni58Ni+ to that of
58Ni2+.
The sharp photodissociation features in Figure 50 exhibit
a non-linear laser fluence dependence indicating that a two-
photon absorption leads to the production of Ni+ from Ni2+.
This is consistent with the recent determination of the
binding energy of Ni2+ from the photodissociation of Ni2Ar+ of
3.0 < DQ(Ni2+) < 3.5 eV, i.e. the absorption of two photons at
this frequency deposits 4.21 eV of energy into the molecule
which is sufficient to dissociate the Ni-Ni+ bond. Sharp R2PD
features have been observed in this study up to photon
energies of 2.95 eV confirming the lower limit to the
dissociation of Ni2+ at ca. 3.0 eV.
Figure 50 represents only a small portion of the
frequency range that resonant dissociation occurs in the Ni2+
ion, but this plot is representative of the nature of the data
recorded. Vibrational progressions in several (at least six)
different electronic transitions have been observed in the
visible region of which vibronic bands from two such
transitions are displayed in the figure. Below 17 450 cra-1
(2.16 eV) , the Ni2+ spectrum is relatively simple and
unperturbed in appearance. However, the R2PD spectrum becomes

183
more congested and less amenable to analysis above this
energy. The change in the nature of the spectrum is not
accompanied by a change in absorption cross section nor a
discernable change in the linewidth of the spectral features.
This figure displays two vibronic bands (with partially
resolved rotational structure) belonging to two different
electronic transitions in the Ni2+ ion. Note that the 60Ni58Ni+
spectral features are shifted to lower energy with respect to
the corresponding features in 58Ni2+ indicating a large upper
state vibrational quantum number. These isotope shifts are
used to assign an absolute vibrational numbering to the
vibronic bands in Ni2+. The two prominent bands in Figure 50
have been assigned by this method to the (18,0) band of the
A-X transition and the (8,0) band transition of the B-X
transition. Positions of other bands belonging to these
electronic transitions and one other (the C-X system) are
listed in the table. The nomenclature for the three assigned
excited states in this study as the A, B, and C states
reflects only the order of their electronic origins and is not
meant to imply that the so called A state is the lowest lying
excited state nor that no undetected states lie between the
origins of the assigned states. For the table, the frequency
of the most intense feature in the vibronic band is taken as
the vibronic band origin.
All the bands observed in this study are red degraded
indicating a longer equilibrium internuclear distance in the

184
excited states than the ground state. The rotational
structure of these bands is only partially resolved at the
current resolution and firm assignment of the ground and
excited state electronic symmetries has not yet been made. No
vibrational or electronic hot band spectra have yet been
obtained due to the low internal excitation of the parent Ni2+
ion prior to photoabsorption.
The table also lists the residuals to the least squares
fit of the vibronic bands to the standard formula
E(v) = Tw + we(v+l/2) - wexe(v+l/2)2
from which the constants Tro, we, wexe/ weye are derived. The
zero of energy for this fit and all the following discussion
is taken as the zero-point level of the ground electronic
state of the molecule.
The table lists the molecular constants of 58Ni2+ derived
from the fit of the data in the table to the above equation.
No ground state molecular constants have yet been obtained due
to the absence of any apparent hot bands.
The discussion of the bonding character of Ni2+ focuses
on the comparison to its neutral variant, Ni2. The
interaction of two ground state 3d84s2 Ni atoms is not expected
to form a chemical bound Ni2 as the radial extent of the 3d
orbitals is significantly smaller than that of the 4s and the
overlap of the 4s2 closed subshells will be repulsive.
However, promotion of both Ni atoms to a 3d94s configuration
(promotion energy 0.03 eV) will lead to a favorable overlap of

185
the half filled 4s shells leading to a single 4s sigma bond
similar to that of in the alkali metals or H2. The weakly
interacting 3d holes will lead to a manifold of 100 electronic
states, all essentially of the same bonding character and
nearly isoenergetic. This picture of exclusively s-s bonding
in the low-lying states of Ni2 is supported by ab initio
calculation" and experimental data100101. Resonant two-photon
ionization spectroscopy has placed the ground state
dissociation energy of Ni2 at 2.07 eV and the equilibrium bond
length at 2.20 Angstroms.
In contrast, the R2PD spectrum of Ni2+ shows that this
species has a much more sparse electronic state density than
Ni2 at similar excitation energies. Moreover, the ground
state of Ni2+ seems to have a uniquely short internuclear
separation relative to the excited states accessed by optical
probes. These excited electronic states exhibit a much
smaller vibrational frequency (see the table) than the low
lying excited states102 of Ni2 (ca. 180 cm'1 for Ni2+ relative to
ca. 330 cm'1 for Ni2) . A large increase in bond length and a
reduction in vibrational frequency upon excitation might be
explained by the description of the ground state as arising
from 3d94s Ni + 3d84s Ni+ atomic configurations with a full 4s
sigma bond and the excited states arising from 3d94s Ni +
3d9 Ni+ separated atoms with only a 1/2 order sigma bond.
This explanation does not seem consistent with the sparse
electronic state density of Ni2+ or the large (over 1 eV)

186
difference in ground state bond energy of Ni2+ over Ni2. Ab
initio calculations do suggest however a shortening of the
bond length and an increase in bond energy of Ni2+ as compared
to Ni2.
Resonant two-photon dissociation (R2PD) has been
demonstrated as a method for the spectroscopic interrogation
of small transition metal molecular ions cations. Only by
virtue of the reduced internal temperature of the ion target
is the complex nature of the spectrum simplified enough for
interpretation. Preliminary analysis of the Ni2+ electronic
spectrum has revealed significant differences in the bonding
of Ni2+ in comparison with Ni2.
The accuracy of the appearance potential is somewhat
surprising since we now know through rotational analysis of
the Ni2+ R2PD spectrum that the ionization of Ni2 is not
vertical but involves a significant bond length change.
Threshold Photodissociation of Cr2+
Chromium dimer represents a particularly interesting
chemical bond. The ground electronic state chromium dimer is
*2 whereas the ground state of the Cr atom is 7S. This
represents a change from the lowest to the highest spin state
of the valence electrons upon dissociation of the system into
separated atoms. Indeed, a sextuplet bond is suggested to be

187
16700 16900 17100 17300 17500 17700
Dissociation Laser Frequency (wavenumber)
Figure 51. Photodissociation Threshold of Cr2+ -♦ Cr+ + Cr.
The figure displays a portion of photodissociation spectrum
for the process Cr2+ -> Cr+ + Cr. Relative photocurrent for
production of Cr+ is monitored as a function of dissociation
laser frequency. The onset of one-photon predissociation is
indicated by an arrow at 2.13 eV.

188
formed in Cr2 originating from all the 4s3d5 valence atomic
orbitals on each nuclei. 103,104 105 The high bond order is in
accord with the experimental determination of the equilibrium
internuclear distance of ca. 1.7 a(106,107,108) and the vibrational
frequency of ca. 450 cm"1(109,110) in the ground state of Cr2. The
dissociation energy of this sextuple bond has been determined
by high-pressure mass spectrometry to be a surprisingly low
1.47 ± 0.05 eV (111). This section outlines the investigation
of the dissociation energy of Cr2+ through a non-equilibrium
method (photodissociation) which will place an upper limit to
the binding energy of neutral chromium dimer at 1.77 eV.
Figure 51 shows the relative photodissociation cross-
section for the process Cr2+ -*â–  Cr + Cr+ as a function of
dissociation laser frequency. For laser energies of greater
than 2.13 eV, the spectrum appears as a lumpy but apparently
continuous one-photon dissociation. At energies lower than
2.13 eV, relatively sharp and sparse vibrational progressions
become discernable at high laser fluence (>5 mJ/cm2). These
features appear to the red of 14300 cm"1 (1.77eV).
The figure shows hypothetical potential energy curves as
a function of internuclear separation for the Cr2+ ion and a
cartoon of the processes that give rise to the spectrum in
Figure 51. For photon energies above 2.13 eV, one-photon
absorption populates states of similar internuclear separation
to that of the ground state but above the adiabatic
dissociation limit (shown with the dashed line) of the

.189
Intemuclear Separation
Figure 52. Cr2+ Photodissociation Mechanisms.
The figure displays hypothetical potential energy curves which
explain the photodissociation features in the spectrum of
Cr2+. The upper diagram displays the phenomenon of
predissociation leading to the vibrationally modulated slope
observed in Figure 51 for energies above 2.13 eV. The lower
diagram represents the mechanism of R2PD. Two photons are
required to dissociate Cr2+ and will result in sharp vibronic
features seen below 2.13 eV.

190
molecule. Small isotope shifts of the 'lumps' on the
dissociation spectrum indicate only moderate vibrational
excitation in the initially prepared upper level. This level
is non-radiatively coupled to levels that are truly unbound at
this energy and may rapidly predissociate. The
photodissociation action spectrum obtained from this process
contains only 'smeared out' remnants of vibrational structure
of the state initially populated by photoabsorption. The top
panel of the figure indicates this predissociation mechanism.
Below 2.13 eV the photoabsorption event populates a truly
bound vibronic state and no dissociation can occur unless a
second photon populates an unbound or quasi-bound level at
higher energy. This incoherent Resonant 2-Photon Dissociation
(R2PD) is diagrammed in the bottom panel of the figure. The
R2PD signal is modulated by the bound-bound transition
probability and gives a sharp spectrum. Predissociation may
only occur above the adiabatic dissociation energy (bond
strength) of the target molecule whereas R2PD may occur to as
far red as half this energy.
Chromium dimer specifically, and transition metal
clusters in general, present some experimental difficulty
because of the facile competition between one-photon
predissociation and R2PD. The large transition probabilities
and high density of electronic states in transition metal
complexes make multi-photon processes competitive or even
overwhelming under moderate conditions of dissociation laser

191
CD
C .
13900 14100 14300 14500
Laser Frequency (wavenumber)
Figure 53. R2PD of Cr2+.
The figure displays a portion of the resonant 2-photon
dissociation spectrum of Cr2+ -*• Cr+ + Cr over the region of
13 900 to 14 600 cm'1. Six vibronic bands of a common excited
state are separated by ca. 120 cm'1. The identity of the state
is currently unknown.

192
fluence. Suppose Cr2+ has a small one-photon absorption
cross section at energies near 2 eV, but also, a very large
probability of absorbing a second photon from the initially
photoexcited level. R2PD might mask the one-photon
predissociation threshold in this case. With this under
consideration, an upper limit to the bond strength of Cr2+ may
be assigned at 2.13 eV, the apparent one-photon fragmentation
threshold in Figure 51.
It is unlikely that the observed threshold corresponds to
the production of any excited fragment. The smallest possible
promotion energy in either Cr+ (11962 cm-1) or Cr (7593 cm-1)
would make the derived bond strength of Cr2+ improbably small.
The application of the literature values for the
ionization potential of Cr2 (6.4 ± 0.2 eV) and Cr (6.763 eV)37
places an upper limit to the bond strength of Cr2 neutral as
1.77 eV. This is in accord with experimental determinations
of the dissociation limit by Kant and Strauss112 of
1.78 + 0.35 eV and a more recent measurement by Hilpert and
Ruthardt of 1.47 + 0.05 eV.
The bond energy of the neutral dimer, at < 1.77 eV, seems
weak for a sextuple bond of a 1.7 Á bond length and 450 cm'1
vibrational frequency. The resemblance of theory to
experiment has been discussed before.113 Good agreement with
experiment is shown by the ab initio calculation of Goodgame
and Goddard.114 This calculation indicates the ground state
potential energy surface has a double minimum. A global

193
minimum has a well depth of 1.86 eV at 1.61 Á and is dominated
by the interaction of the valence d orbitals. At larger
internuclear separation, a second but smaller minimum exists
due to the interaction of s orbitals alone. There is
experimental evidence for this double minimum ground state.115
A strict upper limit to dissociation for Cr2+ has been
determined spectroscopically for the first time as 2.13 eV.
From this, the neutral dimer adiabatic dissociation limit is
determined to be < 1.77eV confirming the surprisingly weak
binding energy of this molecule.
189 shows possible mechanisms leading to
photodissociation of Cr2+ with reference to hypothetical
potential surfaces. The upper diagram displays
predissociation giving rise to the vibrational progression
displayed in Figure 51. Excitation to a level in the excited
state which lies above the dissociation limit of the ground
state (dashed line) results in coupled predissociation. The
lower diagram displays Resonant 2-Photon Dissociation (R2PD).
Here the transition of the first photon lies below, in energy,
of the adiabatic dissociation energy. A second photon is
required to photodissociate Cr2+, resulting in sharp vibronic
features in the photodissociation spectrum.

194
Photodissociation of Ca?+
The photodissociation spectrum of Ca2+ is displayed in
the Figure 54. Several blue degraded bands are observed
through resonant photodissociation. The progression is seen
to end abruptly with the reddest transition at 19 021 cm'1.
This transition is believed to correspond to the electronic
origin band. Currently, this assignment has not been
confirmed with isotopic analysis. A vibrational fit to Eq.
(6) with the reddest transition assigned to v' = 0 determines
a vibrational frequency of 67 cm1.
This is the first blue degraded spectrum that has been
observed in this laboratory and implies a shortening of the
internuclear distance upon excitation. For the neutral
diatomic, the ground state has been spectroscopically
determined as a 'Zg+ characterized by a ag2au2 valence electron
configuration.116 Thus, molecular orbital theory would predict
a zero bond order. Nonetheless the ground state has binding
energy of 1075 ± 150 cm'1 with a vibrational frequency of
64.93 cm'1. The bond energy is surprising large considering
the dominant interactions are presumed to be van der Waals.
One would speculate that the cation analogue of the
neutral calcium dimer would be bound more strongly. Under the
convention of molecular orbital theory the bond order would
increase from zero to 1/2. In addition, simple classical
electrostatics would suggest that the presence of a charge may

Ca Relative Photodissociation
195
Laser Frequency (wavenumbers)
Figure 54. Resonant Photodissociation of Ca2+.

196
increase the bonding energy via the addition of inductive
forces. This implies the ionization potential of the neutral
dimer is smaller than that of the atom which is often the case
for transition metals, see for example, the systems of Ni2+
and Cr2+ discussed previously in this Chapter.
With this in mind, one would also assume that the binding
energy of the cation would be bound by more than the neutral
dimer. Intuitively, the vibrational frequency should increase
in the following sequence: cje" (Ca2) < we" (Ca2+) < ue' (Ca2+) .
The vibrational analysis of the excited state of Ca2+
determines cje' as 67 cm'1 while the we" of Ca2 is ca. 65 cm'1.
Thus, the possibility exists that the cation dimer is bound by
less than the neutral dimer in spite of the prediction of
molecular orbital theory and classical electrostatics.

CONCLUSIONS
A variety of small clusters systems have been
spectroscopically probed in the visible region by
photodissociation of mass-selected ions. The spectra allow
the accurate determination of ground and excited state
dissociation limits of many of these ions, as well as their
vibrational structure. The ground and excited state
parameters for the inductive and electrostatically bound
metal-ligand species presented in this work are included in
Table 16 and Table 17, respectively.
For an inductively bound system the only influence the
identity or state of the charged atom has upon the binding
energy is through the repulsive interaction it has with the
neutral partner. Due to the disparity of the ionization
potential between the metal atom and the rare-gas atom, both
the ion and neutral partner are considered covalently inert.
Thus, the binding energy of a metal-cation rare-gas diatomic
will be determined by the polarizability of the rare-gas atom
and its limiting approach to the cation. An increase in
polarizability is always accompanied by an increase in binding
energy. Naturally, the internuclear distance is governed by
the radial extent of the interacting atoms. This is displayed
199

200
Table 16. Excited State Parameters for Metal-Ligands.
Ion
conf ig*
D0
[cm'1]
Teo
[cm'1]
We'
[cm1]
weXe'
[cm'1]
VAr+
3d34s
1368
15166
94
1.95
CoAr+ (A)
2594
13081
165
3.20
CoAr+ (B)
3d74s
1993
13380
121
2.21
CoAr+ (C)
3d8
2824
14458
176
3.28
ZrAr+ (A)
14888
68
0.92
ZrAr+ (B)
15479
69
0.67
ZrAr+ (C)
15540
77
1.26
CaKr+
3d
14192
52
VKr+
3d34s
2047
15310
99
1.40
CoKr+ (A)
3985
13336
148
1.47
CoKr+ (B)
3d74s
2907
13874
118
1.36
CoKr+ (C)
3d8
4158
14674
159
1.76
V(H16OH) +
3d34s
6200
15712
339
4.5
V(H180H) +
3d34s
6300
15719
326
4.1
V(OCO)+
3d34s
15703
196
4.7
105
600
V(NH3) +
17342
370
17.5
Metal ion atomic configuration in separated atom limit.

201
Table 17. Ground State Adiabatic Bond Strength.
System
conf iga
“e
cm'1
D0
Expt.
[eV]
D0
Theory
[eV]
obs-cal
1
%err.
VAr+
3d4
0.370
0.291b
0.079
-21%
CrAr+
3d5
0.29
0.24 6c
0.04
-15%
CoAr+
3d8
0.510
0.392b
0.118
-23%
NiAr+
3d9
235
0.55
0.450d
0.10
-18%
VKr+
3d4
0.473
CoKr*
3d8
0.69
V(HOH)+
3d4
420
1 Cr (N2)+
3d5
0.61
aMetal ion atomic configuration in separated atom limit.
bRef [61],cRef [62], dRef[60]
in the progression across the transition-metal row with the
an increase in binding energy due to the d orbital contraction
for the following systems; CrAr+, CoAr+, NiAr+. However, the
radial extent of the metal cation may not always be
spherically symmetric. In the case of V+(3d4) ground state the
neutral rare-gas atom will minimize the internuclear distance
by forming an molecular orbital along an empty metal d
orbital. This explains the anomalously larger binding energy
of VAr+ compared to CrAr+.
The comparison of binding energy of VAr+(Kr) with V(H20) +
suggest that inductive forces will contribute significantly to
the enthalpy of solvation for a given monovalent cation. The
photodissociation of electrostatically bound V(HOH)+ provides,
for the first time, details for a cation-water pair potential.

202
The spectroscopic data has demonstrated that the system of
V(0H2)+ is electrostatically bound. Although an inserted
isomer may also exist for this system, there is certainly a
barrier to isomerization.
Metal-cation ligated clusters may be thought of as
molecular 'models' ideal for the study of the non-covalently
bound systems. Insight into the nature of this type of
bonding has been revealed through the vibrational structure of
many inductively and electostatically bound systems. Optical
interrogation has been shown to provide the ultimate technique
for direct measurement of the quantal details in these
systems. In some cases, the vibrational information for a
metal rare-gas diatomic is so extensive that an accurate
potential surfaces may be parameterized using the WKB
approximation.

APPENDIX A
ELECTRICAL CIRCUITS
+150V
O
Figure 55. Valve Driver Circuit.
203

204
A.
MCP
B.
MCP
_ To
Pre-Amp
METAL
COLLECTOR
ANODE
I / \
1.4 MO 500
COLLECTOR
ANODE
3MÍ1 1.4MO 100KÍ2
Figure 56. Bias Conditions for MicroChannel Plate Detector.
The figure displays the electrical connections for detecting
cations (part A) and anions (part B) . In each case, the
interaction of the charged species with the first MCP results
in the emission of secondary electrons which in turn strike a
second MCP. This electron cascade is accelerated with the
appropriate field to the anode.

APPENDIX B
COMPUTER CODE
WKB Grid Program
#include
#include
#include
#include
/include
/include






/define BANNER " GRID Version DANO 1.1 7/21/92
/pjb/del\n"
/define HCONST 12.899226 /* for u(r) in cnT-1 used> */
/*************** FUNDAMENTAL CONSTANTS *******************/
/define PI 3.14159265359 /* dimensionless */
/define CSPEED 2.997925el0 /* cm/sec */
/define NAVAGADRO 6.02217e23 /* dimensionless */
/define ECHARGE 4.80298e-10 /* esu */
/define HPLANCK 6.6256e-27 /* erg.sec */
/define GRID_STEP 20
/********************* GLOBAL VARIABLES ******************/
FILE *dfile;
char fnam[80];
int v, z=0, v_index[50], num_pts,isteps=1000;
float trans[50];
double (*u)(double);
double rms,
e,
rmin,
rin,
rout,
rinstart,routstart,
rstep = le-3,
recrit = le-6,
205

206
estart,
estep = 10.0,
ecrit = le-4,
emincrit = le-15,
emin,
hcon,
/*mu=31.7333333,re=2.1,De=-2047.0,we=99.0,
VKr excited state*/
mu =23.83838383, re=2.0,De=-2594.0,we=165.0,
/* CoAr+ A state */
k,
alpha=l.66,
aeon,
bcon=3e5,
ccon,
dcon,
rho;
/**********************************************************/
double igrator(double (*funcnam)(double),double a,double
b,int steps) /* integrator */
{
double aa,bb,inc,sum=0.0,x,val;
int i ;
if (a==b) return(O.O);
aa=(b>a)?a:b;
bb=(b>a)?b:a;
inc=(bb-aa)/(double)steps;
for(x=aa+inc;x sum += (*funcnam)(x);
sum += ((*funcnam)(bb)+(*funcnam)(aa))/2.0;
sum *= inc;
return(sum);
}
/********************Root Finder**************************/
double rootfinder(double (*funcnam)(double),double
start,double inc,double crit)
{
double guess=start,oldvalue,value,abscrit;
int oposflag,posflag;
abscrit=fabs(crit);
oldvalue = (*funcnam)(guess);
oposflag = (oldvalue>0.0)?1:0;
do
{
guess += inc;
value = (*funcnam)(guess);
posflag = (value>0.0)?1:0;
if(posflag!=oposflag) /* value has changed sign */
{

207
if (fabs(value) /* good enough? */
inc /= -2.001; /* step slower and change
direction */
}
else /* value has same sign */
{
if (fabs(value) > fabs(oldvalue))
/* change direction? */
{
inc = -inc;
guess += inc; /* restore guess */
value = oldvalue;
posflag = oposflag; /* restore results
*/
}
}
oldvalue = value;
oposflag = posflag;
} while (value != 0.0);
return(guess); /* got lucky */
}
/**********************************************************/
double minimizer(double (*funcnam)(double),double
start,double step,double crit)
{
double guess,oldvalue,value,abscrit,test;
guess=start;
abscrit = fabs(crit);
oldvalue = (*funcnam)(guess);
do
{
guess += step;
value = (*funcnam)(guess);
if (value > oldvalue)
step /= -2.001;
test = value-oldvalue;
test = fabs(test/step);
if (test < abscrit) return(guess);
oldvalue=value;
} while (1);
}
/*********************************************************/
/* BORN MAYER POTENTIAL */
double uBM(double r)
{
double ret,r4;
r4 = r*r;

208
r4 *= r4;
ret = -r/rho;
ret = exp(ret);
ret *= bcon;
ret -= (ccon/r4);
return(ret);
}
/*********************************************************/
double BM_pot(double r)
{
double ret,dum;
ret=bcon*exp(-r/rho);
dum=r*r*r*r;
ret-=ccon/dum;
return(ret);
}
double tp(double r)
{
double ret;
ret = e - u(r);
return(ret);
}
double momentum(double r)
{
double ret;
ret = e - u(r);
if (ret<=0.0) return(O.O);
ret = sqrt(ret);
return(ret);
}
double doit(double energy)
{
double ret;
e=energy;
ret= -rstep;
rin=rootfinder(tp,rinstart,ret,recrit);
rout=rootfinder(tp,routstart,rstep,recrit);
rinstart=rin;
routstart=rout;
•ret = 2.0*igrator(momentum,rin,rout,isteps);
ret -= hcon*((double)v + 0.5);
/*printf("%18.lllf\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b",e);*
/
return(ret);
}
/*********************************************************/

209
double rhol(double r)
{
double ret;
ret = r*r*r*r*r;
ret *= De/ccon;
ret += r;
ret /= 4.0;
return(ret);
}
double rho2(double r)
{
double ret,dum;
dum = r*r*r*r*r;
dum *= k;
dum += (20.0*ccon/r);
ret = 4.0*ccon/dum;
return(ret);
}
double bBM(double r)
{
double ret;
ret = exp(r/rho);
ret *= 4.0*rho*ccon;
ret /= (r*r*r*r*r);
return(ret);
}
double rrootBM(double r)
{
double ret;
ret = rhol(r)-rho2(r);
return(ret);
}
/**********************************************************/
void BM_menu()
{
int i;
double temp,rcalc,dum_rms,energy,dum_k;
emin=De;
rms=0.0;
rmin = rootfinder(rrootBM,re,0.001,le-10);
re=rmin;
rho=rhol(rmin);
bcon=bBM(rmin);
routstart = rinstart = rmin;
printf(”\nDe = %5.41fcm-l\twe = %3.21fcm-l\tre =
%2.6If[A]”,emin,we,rmin);
estart = emin + (v_index[0]+0.5)*we;

210
u=uBM;
estart = (estart>0.0)?(-2.0*estep):estart;
printf("\nrho = %lf[A]\tbcon = %lfcm-l",rho,bcon);
printf("\n\nCalculating Vibrational Levels,
working...\n\n");
printf("\nIndex\tObserved\tCalculated\tDev.\n");
for(i=0;i {
v=v_index[i];
while ((estart+estep)>0.0) estep /= 2.0001;
energy=rootfinder(doit,estart,estep,ecrit);
estart = energy;
dum_rms=trans[i]-(energy-emin);
rms+= (dum_rms*dum_rms) ;
cprintf("%3d %12.41f %12.4lf %12.41f
%10.4lf\r\n",
v,trans[i],energy,(energy-emin),dum_rms);
}
rms/=num_pts;
rms=sqrt(rms);
z+=l;
/**********************************************************/
void input()
{
char fnam[20],dum[80];
int i,j;
dfile=fopen(fnam,"r");
printf("\n File to Fit ? ");
gets(fnam);
if((dfile = fopen(fnam,"r")) == NULL)
{
printf("<%s> NOT FOUND\n",fnam);
exit(0);
}
fscanf(dfile,”%d \n",&num_pts);
for(i=0;i {
fscanf(dfile,"%d”,(v_index+i));fscanf(dfile,"%f
\n",(trans+i));
}
fclose(dfile);
printf(”\n The number of points is %d”,num_pts);
for(i=0;i
211
printf("\n v = %d Transition = %f",v_index[i],
trans[i]);
getch();
}
void root_finder_parms()
{
printf("\nUse default accuracy criteria (*/n)?: ");
if('n'==getche())
{
printf("\ninput recrit (%20.21e): M,recrit);
cin » recrit;
printf("\ninput ecrit (%20.2le): ",ecrit);
cin » ecrit;
printf("\ninput isteps (%d): ",isteps);
cin » isteps;
}
}
/ **********************************************************/
void main()
{
char c;
int i=0,j,n;
double x,w;
double we_beg=118.0,
we_end=122.0,
De_beg=-2050.0,
De_end=-2200.0,
we_step,
De_step;
textcolor(YELLOW);
we_step=(we_end-we_beg)/GRID_STEP;
De_step=(De_end-De_beg)/GRID_STEP;
clrscr();
printf("\n");
printf(BANNER);
printf("filename for output: ");
gets(fnam);
printf("\nGrid program for Born Mayer with l/r4
attraction");
printf("\nReduced Mass is %lf",mu);
printf("\nPolarizability of neutral atom = %lf",alpha);
hcon=(HPLANCK*NAVAGADRO)/(2.0*CSPEED);
hcon=le8*sgrt(hcon/mu);
ccon =alpha*5.0e7*ECHARGE*ECHARGE/(HPLANCK*CSPEED);
input();
dfile=fopen(fnam,"a");
fprintf(dfile,BANNER);

212
fprintf(dfile,"\n\n");
fprintf (dfile, ,,rho\t\tbcon\t\trms\t\tDe\t\twe\tre\n,,) ;
fflush(dfile);
fclose(dfile);
for(j=0;j {
for(n=0;n {
we=we_beg+(double)j*we_step;
k=(2.0*PI*we*CSPEED);
k *= k;
k *= mu/(NAVAGADRO); /* Force constant in Dynes/cm
*/
k /= HPLANCK*CSPEED*1.0E16; /*Force constant in
cm-l/A~2*/
De=De_beg+(double)n*De_step;
clrscr();
cprintf("\nOutput Data in file %s",fnam);
printf("\nCalculating Grid point %d of
%d",(i+1),(GRID_STEP*GRID_STEP));
printf("\nPrevious rms value = %lf",rms);
BM_menu();
dfile=fopen(fnam,"a");
fprintf(dfile,”%2.7If\t%10.4If\t%12.4If\t%6.2If\t%4.2If\t%2.
51f\n”,
rho,bcon,rms,De,we,rmin);
fflush(dfile);
fclose(dfile);
i+=i;
}
}
}

213
CAMAC Low Level Routines
FILENAME CAMAC.C
/define LINT_ARGS
/include /* for crate setup */
/define
IBMC 0x24F
/*
CAMAC
crate control register
*/
/define
WH
0x240
/*
CAMAC
high write port
*/
/define
WM
0x241
/*
CAMAC
middle write port
*/
/define
WL
0x242
/*
CAMAC
low write port
*/
/define
AC ,
0X243
/*
CAMAC
subaddress register
*/
/define
FC
0X244
/*
CAMAC
function code register
*/
/define
NC
0x245
/*
CAMAC
station / register
*/
/define
ZC
0x246
/*
CAMAC
Z,C,I register
*/
/define
CC
0x247
/*
CAMAC
start cycle register
*/
/define
LL
0x248
/*
CAMAC
LAM,X,Q register
*/
/define
RH
0x249
/*
CAMAC
high byte read register
*/
/define
RM
0x24A
/*
CAMAC
middle byte read register*/
/define
RL
0x24B
/*
CAMAC
low byte read register
*/
/define
DMA
EN OxOA
/*
DMA controller enable register
*/
/define
DMA"
MODE 0x0B/*
DMA controller mode register
*/
/define
DMA"
CLR 0x0C/*
DMA controller clear register
*/
/define
DMA"
"RD 0x45/*
DMA mode for read
*/
/define
DMA"
WRT 0x49/*
DMA mode setting for write
*/
/define
DMA"
ADX 2
/*
DMA address register
*/
/define
DMA"
CNT 3
/*
DMA count register
*/
/define
DMA
PAGE 0x83/*
DMA page register (top 4 bits
of
address) */
/*********************************************************/
camac_z() /* clears all modules in the camac crate */
{
outp(ZC,1) ;
outp(WL,0);
outp(WM,0);
outp(WH,0);
outp(IBMC,0);
outp(CC,0); /* sends Z and initiates CAMAC cycle */
outp(ZC,2);
outp(CC,0); /* send a C as well (why not) */
}
/**********************************************************/
camac_c() /* initializes all modules in the camac crate */

214
{
outp(ZC,2); outp(CC,0); /*sends C and initiates CAMAC
cycle */
}
/**********************************************************/
unsigned camac in(n,f,a)
/* inputs 16 bit word data from camac crate */
unsigned n,f,a;
{
unsigned lowbyte,highbyte;
outp(NC,n); outp(FC,f); outp(AC,a); outp(CC,0);
lowbyte = inp(RL); highbyte = inp(RM);
return (lowbyte + (highbyte « 8));
}
/**********************************************************/
unsigned long camac_lin(n,f,a)
/* inputs 24 bit word from crate */
unsigned n,f,a;
{
unsigned lowbyte,highbyte,midbyte;
unsigned long ret=0;
outp(NC,n); outp(FC,f); outp(AC,a); outp(CC,0);
lowbyte = inp(RL); midbyte = inp(RM); highbyte=inp(RH);
ret = ((unsigned long)lowbyte +
((unsigned long)midbyte << 8)
+ ((unsigned long)highbyte « 16));
return(ret);
}
/**********************************************************/
camac_out(n,f,a,d)
/* outputs 16 bit word to crate (high 8 bits zeroed) */
unsigned n,f,a,d;
{
outp(NC,n); outp(FC,f); outp(AC,a);
outp(WL,(d & OxFF)); outp(WM,(d » 8)); outp(WH,0);
outp(CC,0);
}
/**********************************************************/
camac_lout(n,f,a,d)
/* outputs 24 bit word to crate */
unsigned n,f,a;
unsigned long d;
{
unsigned dl,d2;
outp(NC,n); outp(FC,f); outp(AC,a);
dl = d & OxFFFF; d2 = d»16;
outp(WL,(dl & OxFF)); outp(WM,(dl » 8)); outp(WH,d2);
outp(CC,0);

215
/**********************************************************/
unsigned camac_q()
/* returns 1 if q is set (does NOT cycle crate) */
{
return (0x01 & inp(LL));
/* returns 1 if q is set, 0 otherwise */
/**********************************************************/
unsigned camac_lam()
/* returns station of highest LAM set (0 if none) */
{
/* does NOT cycle the crate */
unsigned dummy;
dummy = inp(LL);
dummy »= 2;
dummy &= 31;
return(dummy);
/**********************************************************/
dmainlq(station,length,page,offset)
/* for retrieving TR8837F data (8 bit) */
unsigned station,length,page,offset;
/* DMA q-stop transfer */
{
int q,i=0x500;
outp(ZC,0x28); /* clear acl and keep camac buss */
outp(NC,station);
outp(FC,2);
outp(AC,0); /* send F(2)A(0) to station */
outp(CC,0); /* cycle crate */
outp(DMA_PAGE,page); /* set DMA page for channel 1 */
outp(DMA_CLR,0x46); /* set first/last flip/flop */
outp(DMA_ADX,(offset & OxFF));
outp(DMA_ADX,(offset » 8));/*Set Address Register */
outp(DMA_CLR,0x46); /* set first/last flip/flop */
outp(DMA_CNT,(length & OxFF));
outp(DMA_CNT,(length » 8));/*set maximum cycle count */
outp(DMA_MODE,DMA_RD); /* set dma mode to read */
outp(DMA_EN,1); /* enable DMA channel 1 */
outp(IBMC,0x44);/*DMA to read 1 byte in q-stop mode */
do {
i—;
q = camac_q();
} while (q && i);
/* wait for q=0 */
outp(IBMC,0);
/* clear IBMC */

216
outp(DMA_EN,5);
/* disable DMA */
outp(ZC,0x10);/*free camac buss for other controllers */
}
/**********************************************************/
dma_in3q(station,length,page,offset)
/* for retrieving SA4100 data (24 bit) */
unsigned station,length,page,offset;
/* DMA q-stop transfer */
{
int q,i=0x2000;
outp(ZC,0x28);/* clear acl and keep camac buss */
outp(NC,station);
outp(FC,2);
outp(AC,0); /* send F(2)A(0) to station */
outp(CC,0); /* cycle crate */
outp(DMA_PAGE,page); /* set DMA page for channel 1 */
outp(DMA_CLR,0x46); /* set first/last flip/flop */
outp(DMA_ADX,(offset & OxFF));
outp(DMA_ADX,(offset >> 8));/*Set Address Register */
outp(DMA_CLR,0x46); /* set first/last flip/flop */
outp(DMA_CNT,(length & OxFF));
outp(DMA_CNT,(length » 8));/*set maximum cycle count*/
outp(DMA_MODE,DMA_RD);/* set dma mode to read */
outp(DMA_EN,1);/* enable DMA channel 1 */
outp(IBMC,0x46);/* DMA to read 3 bytes in q-stop mode */
do {
i—;
q = camac_q();
} while (q && i);
/* wait for q=0 */
outp(IBMC,0);
/* clear IBMC */
outp(DMA_EN,5);
/* disable DMA */
outp(ZC,0x10);/* free camac buss for other controllers
*/
}
/**********************************************************/
setup_sa (nshots, reden, pretrig, period)
/* Setup SA4100 & TR2100S Combo */
signed nshots,reden,pretrig,period;
{
unsigned long outword,dum;
outword = (pretrig%8);
switch (period)
{
case 10: dum = 0; break; /* period in nanoseconds */
case 20: dum = 1; break;
case 50: dum =2; break;

217
case 100: dum = 3; break;
case 200: dum =4; break;
case 500: dum =5; break;
case 1000: dum =6; break;
case 0: dum =7; break; /* external */
default: dum = 0;
}
outword += (dum « 6);
switch (reclen)
{
case 32768: dum =6; break;
case 16384: dum =7; break;
case 8192: dum =0; break;
case 4096: dum = 1; break;
case 2048: dum = 2; break;
case 1024: dum =3; break;
case 512: dum =4; break;
case 256: dum =5; break;
default: dum =0; break;
}
outword += (dum « 3);
/* Load TR2001S */
camac_out(TR2001S,9,0,0);
/* Clear TR */
camac_lout(TR2001S,16,0,outword);
/* set rec_len,pretrig, period */
camac_out(TR2001S,26,0,0);
/* enable LAM */
/* Load SA4100 */
if (dum < 6) outword = (dum « 6);
else outword = 0;
/♦maximum array length in SA4100 is 8k */
camac_out(SA4100,24,1,0); /* disable averaging */
camac_out(SA4100,26,0,0); /* enable LAM */
camac_lout(SA4100,16,0,outword);
/* Set rec_len in SA4100 */
camac_out(SA4100,17,0,(unsigned)(OxlOOOOL - nshots));
/* set shot counter */
camac_out(SA4100,9,0,0); /* clear and enable */
}
/********************************************************** j
setup_td(reclen,pretrig,period)
unsigned reclen,pretrig,period;
{
unsigned long outword,dum;
outword = (pretrig%8);
switch (period)
{
case 32: dum =0; break; /* period in nanoseconds */
case 64: dum =1; break;

218
case 125: dum =2; break;
case 250: dum =3; break;
case 500: dum =4; break;
case 1000: dum =5; break;
case 2000: dum =6; break;
/* case 0: dum = 7; break; */ /* external */
default: dum =0;
}
outword += (dum « 4);
switch (reden)
{
case
8192:
dum
=
7;
break;
case
7168:
dum
=
6;
break;
case
6144:
dum
=
5;
break;
case
5120:
dum
=
4;
break;
case
4096:
dum
=
3 ;
break;
case
3072:
dum
=
2;
break;
case
2048:
dum
=
l;
break;
case
1024:
dum
=
o;
break;
default: dum =3; break;
}
outword += (dum « 8);
camac_out(TR8837F,17,0,0);
/* set CAMAC read Mode */
camac_lout(TR8837F,16,0,outword);
/* set reclen, pretrig, period */
camac_out(TR8837F,24,0,0);
/* disable LAM */
camac_out(TR8837F,9,0,0);/* Clear TR */
}
/**********************************************************/
setup_P3655(station,delays,recycle)
unsigned station,*delays,recycle;
{
unsigned i,outword=0;
if (recycle) outword = 64; /* Set recycle bit */
outword += 62;
/* set clock to 1 MHz and enable all pulses */
camac_out(station,17,0,outword);
camac_out(station,24,9,0);
/* Disable inhibit assert */
camac_out(station,17,13,0); /* Clear LAM mask */
for(i=0;i<8;i++)
camac_out(station,16,i,delays[i]);
}
/**********************************************************/
setup_P4222(station,delays)
unsigned station;

219
unsigned long *delays;
{
unsigned i;
camac_out(station,24,0,0); /* enable access to P4222 */
for(i=0;i<4;i++)
camac_lout(station,16,i,delays[i]);
/* load delays */
camac_out(station,26,0,0);
/* disable access & go! */
/**********************************************************/
read_qadc(values)
unsigned *values;
{
values[0] = (0x07FF & camac_in(QADC2249W,2,0));
/* Get DATA */
camac_out(QADC2 2 4 9W,9,0,0);
/* Clear ADC */
}
/**********************************************************/
read_adc(values)
unsigned *values;
{
unsigned i;
for(i=0;i<5;i++)
values[i] = (OxOFFF & camac_in(ADC1612,0,i));
>
/**********************************************************/
load_dac(values)
unsigned *values;
{
unsigned i;
for(i=0;i<6;i++)
camac_out(DAC3016,16,i,values[i]);
}

220
CAMAC Header File
FILENAME:
CAMAC.H
/define
TR2001S
4
/define
SA4100
8
/define
P3655A
20
/define
P3655B
19
/define
P4222
18
/define
ADC1612
23
/define
DAC3016
21
/define
QADC2249W
13
/define
TR8837F
10
/define
TR2262
12
Control Program
This program is compiled with Microsoft C, version
5.1 software. The complier line options are as follows:
cl=/FPi87 /G2/ Ot/ LINK/ ST:0X4000 pjb
FILENAME: DRGAT03A.EXE
#include
/include
/define HEADLN " Version 3 4/9/91
/pjb/rla/del\n”
/define
ARRLEN
2048
/define
SCANLEN
4096
/define
XRES
512
/define
SCANLENGTH
128
/define
TDARRLEN
1024
/define
TDFREQ
32
/define
TDPERIOD
31.25
/define
GRID
1
/define VMUL0
/define VOFFO
/define VMUL1
/define VOFF1
/define VMUL2
/define VOFF2
/define VMUL_DET
/define VOFF DET
HV Supply Parameter ********************/
7.53815
(0x8000-12)
-7.57578
(0x8000-15)
3.2768
0x8000
-7.46714456
(0x8000-13)
/****************** MEMORY ALLOCATION *********************/
/define PLOTBUF 0x4E00

221
/defineTMPSCRN 0x5700
/define AXSC 0x5300
/define SABUF 0x5000
/define DMAPAGE 5
/define DMAOFF 0x2000
/define TDBUF 0x5200
/define SCANBUF 0x5B00
/define STSCPG 0x6B00
/define SCRNUM 13
/********************* MACRO'S ****************************/
/define set_sa()
setup_sa(iparm.n,iparm.arrien,iparm.pretrig,iparm.period)
/define initiate() camac_out(P3655A,25,0,0)
/****************** FLAGS AND COUNTERS ********************/
unsigned
AVGNUM=16,
AVGNUMD,
toc=0,
scanner=0,
action=16, /* RECYCLE ON */
tddone=0,
alte = 0,
len = ARRLEN,
bin = 0,
didon = 0,
nsave,
didl,did2,iscanid=0,
sachan[3][4],
iscanlen,scannumber=0;
long
bininc=lL, start=0L, send=300L,
vchargelamp=30000L,
/* dchargelamp=48000L, now iparm.scan[9] */
doff1,doff2;
char avgnumid[30] ="Number of shots to average",
avgnumidd[30];
char signal_name[6][40]={"SA Signal One","SA Signal
Two","SA Signal Three",
"TD Signal","Etalon","Diss Power"};
char lab_date_string[10];
/*********************** FLAG MASKS ***********************/
/* for */
/define SAPLOT 0
/define CRATEOK 1
/define READSA 2
/define READADC 4

222
/define
CLEARSA
8
#define
RECYCLE
16
#define
INHIBDMA
32
#define
NEWI
64
/define
INVALID
128
/define
DIDDLE
256
/define
I SCAN
512
/define
ESCAN
1024
/define
ASCAN
2048
/define
TDPLOT
4096
/define
SCANPLOT
8192
/define
TICTOC
16384
/********************** PLOTTING **************************/
unsigned
new_axis,
new_pvec,
s_o=l,
lock_zero=0,
time_axis=0,
scalemod=32,
opage=0,
page=6;
/define SA
(6)
/define TD
(7)
double
yi[8]
={ o,
o,
0,-200,-2000, -10,
256, 256},
ys [ 8 ]
={ 128,
128,
128,1024, 2048,1024,
-255,-255};
/*
={
SAI, SA2,
SA3,
OPTO, ETAL, POW, SA
, TD} */
int
xi [ 8 ]
={ o,
o,
o
o
o
o
o,
0},
xs [ 8 ]
={ 128,
128,
128, 128, 128, 128,
ARRLEN,
128};
struct pvec vec[XRES];
/********************** DATA STRUCTURES *******************/
struct iparms {
char scanid[12][30],
pulseid[20][10];
unsigned n,
arrien,
pretrig,
period,
p3655a[8],
p3 655b[8],
dac3016[16];
long scan[12];
unsigned long p4222[4];

223
};
struct eparms
unsigned
};
{
sweep,
adc[16];
struct sdata {
long sa[6];
};
/************************* file control *******************/
char filnam[80],fnam[80];
FILE *dfile;
struct file_counting_control {
int a, f, i, t, v;
} file_count= {0,0,0,0,0};
/************************* INITIALIZE *********************/
struct sdata sdat = {0L,0L,0L,0L,0L,0L}, zero =
{OL,OL,OL,OL,OL,OL},vdat;
struct
iparms temppar,iparm={
" (00)
Nozzle ->
Vf ire
[us]
"(01)
VFire ->
Accel
[us]
" (02)
Accel ->
SAstop
[ns]
" (03)
SAstop ->
Df ire
[ns]
" (04)
SAstop ->
TDstop
[ns]
" (05)
Dfire ->
Marker
[ns]
"(06)
VLamp ->
VFire
[us]
" (07)
DLamp ->
DFire
[us]
» (08)
Detector |
-) [Volts]
" (09)
Dcharge ->
Lamp
[us]
"(10)
Sector (+)
[Volts]
"(11)
Alternate
Df ire
(03)
"B Trig ",
"Nozzle ",
"Vfire ",
"Accel ",
" "
" "
" "
" "
"Vlamp "
"Dlamp "
" "
"Dcharge "
"Vcharge "
" "
"
II

224
" ",
"Dfire ",
"SAstop ",
"TDstop ",
"Marker ",
0,ARRLEN,0,20,
60000,60001,60002,
60003,
60004,60005
,60006,60007,
60000,60001,60002,
60003,
60004,60005
,60006,60007,
0x8000,
0x8000,0x8000,0x8000,0x8000,
0x8000,0x8000,0x8000
0x8000,
0x8000,0x8000,0x8000,0x8000,
0x8000,0x8000,0x8000
/*"(00)
Nozzle ->
Vf ire
[us]"*/
600L,
/*"(01)
VFire ->
Accel
[us]"*/
620L,
/*"(02)
Accel ->
SAstop
[ns]"*/
35000L,
/*"(03)
SAstop ->
Dfire
[ns]"*/
19900L,
/*"(04)
SAstop ->
TDstop
[ns]"*/
0L,
/*"(05)
Dfire ->
Marker
[ns]"*/
5500L,
/*"(06)
VLamp ->
VFire
[us]"*/
390L,
/*"(07)
DLamp ->
DFire
[us]"*/
340L,
/*"(08)
Detector (
-) [Volts]"*/
0L,
/*"(09)
Dcharge ->
lamp
[us]"*/
44000L,
/*"(10)
Sector (+)
[Volts]"*/
310L,
/*" (ID
Alternate
Dfire
(03)"*/
25000L,
};
0L,0L,0L,0L
struct
eparms
eparm;
/****************
Help Strings ************************
char
hmenu[40][80]={
"FI - internal parameter menu",
"F2 - average shots",
"F3 - diddle internal parameters",
"F4 - diddler off",
"F5 - setup scan parameters",
"F6 - scan off",
"F7 & 8 - this menu",
"F9 - toggle to current scan page",
"F10 - toggle to single shot TD",
"rt arrow - expand-compress-offset",
"It arrow - horozontally",
"up arrow - expand-compress-offset"
t

225
"dn arrow - vertically",
"Ins - toggle Scaling or Origin",
"1 - SA signal 1 screen (F9)",
"2 - SA signal 2 screen (F9)",
"3 - SA signal 3 screen (F9)",
"4 - Opto signal screen (F9)",
"5 - Etalon signal screen (F9)",
"6 - Power signal screen (F9)",
"Esc - quit",
"b - give the big picture",
"c - toggle time and bin number",
"d - dump screen page",
"g - display screen page",
"h - tddone",
"i - input a file",
"k - clear averaging (F2)",
"1 - lock zero",
"n - shots to average (F2)",
"o - output a file 'automatic'",
"0 - output a file 'manual'",
"p - new pvec",
"q - quit",
"r - refresh screen",
"s - save screen page",
"t - set SA channel period",
"x - set x axis scale",
"y - set y axis scale",
"z - set LAB date"
char
h_choice[40] ={
59,
60,
61,
62,
63,
64,
66,
67,
68,
77,
75,
72,
80,
82,
'1',
'2',
'3',
'4',
'5',
'6',

226
27,
'b',
'c',
'd',
'9',
'h',
'i',
'k',
'1
'n',
'o',
'O',
'P',
'q' /
'r',
's',
't',
'x',
'y',
'z'
/*********************************************************/
caldelayO {
iparm.p3655a[0] = 1;
iparm.p3655a[l] = iparm.scan[6] + 1;
iparm.p3655b[0] = iparm.scan[0];
iparm.p3655a[2] = iparm.p3655a[l] + iparm.p3655b[0];
iparm.p3655a[3] = iparm.p3655a[2] + iparm.scan[1];
iparm.p4222[1] = iparm.scan[2];
iparm.p4222[0] = iparm.scan[3] + iparm.p4222[1];
iparm.p4222[2] = iparm.scan[4] + iparm.p4222[1];
iparm.p4222[3] = iparm.scan[5] + iparm.p4222[0];
iparm.p3655b[1] = (iparm.p4222[0]/1000L) +
iparm.p3655a[3] - iparm.scan[7];
iparm.p3655b[2] =1; /* recycle past 64 ms */
iparm.p3655b[4] = 44574 + iparm.p3655b[0]-vchargelamp;
iparm.p3655b[3] = 44574 + iparm.p3655b[l]-
iparm.scan[9];
}
/**********************************************************/
clear_sa() {
int timeout=0xl000;
camac_out(SA4100,9,0,0);
do {
timeout—;
} while ((!camac_q()) && timeout);
if (timeout) tddone = 0;
/**********************************************************/

227
unsigned read_sa() {
/* readout SA4100 to DMAPAGE */
unsigned ret=10;
camac_out(SA4100,24,1,0) ;
/* disable averaging and set LAM */
do {ret—;if(!ret) return(O);} while (camac_lam() 1=
SA4100);
tddone = (0x400 & camac_in(SA4100,0,0)); /* test
for LAM type */
camac_out(SA4100,16,1,0);
camac_out(SA4100,16,1,0);
/*Set readout and first channel to 0 */
ret = camac_in(SA4100,1,0);
/* read shot counter register */
dma_in3q(SA4100,0x2000,DMAPAGE,0);
/* perform array transfer to buffer */
camac_out(SA4100,16,1,0);/* reset to channel 0 */
camac_out(SA4100,10,0,0);/* clear LAM set by f24al*/
if (!tddone)
camac_out(SA4100,26,1,0);
/♦enable if nhots incomplete */
return(ret);
}
/**********************************************************/
read_td() { /* readout TR8837F to DMAPAGE+DMAOFF */
int timeout=10;
camac_out(TR8837F,17,0,0); /* Set readout */
camac_out(TR8837F,27,0,0);
do {timeout—; if(¡timeout) return;}
while (!camac_q());
if (action & CRATEOK)
dma_inlq(TR8837F,0x500,DMAPAGE,DMAOFF);
camac_out(TR8837F,9,0,0);
}
/**********************************************************/
load_i() {
unsigned i;
iparm.dac3016[0] = VMUL0 * iparm.scan[10] + VOFFO;
iparm.dac3016[1] = VMUL1 * iparm.scan[10] + VOFF1;
iparm.dac3016[10]= VMUL_DET * iparm.scan[8] + VOFF_DET;
for (i=0;i<10;i++)
camac_out(DAC3016,16,i,iparm.dac3016[i]);
setup_P3655(P3655A,iparm.p3655a,0);
setup_P3655(P3655B,iparm.p3655b,0);
setup_P4222(P4222,iparm.p4222);
}
/**********************************************************/
lab_date_set() {

228
struct dosdate_t lab_date;
unsigned labmonth, labday, labyear;
unsigned char c;
char si[80], s2[80], s3[80];
_dos_getdate(&lab_date);
do {
printf("\nCurrent date:
%d/%d/%d is this correct (y/*)?",
lab_date.month, lab_date.day, lab_date.year - 1900);
c=getch();
if(c=='y') break;
do {
printf("\n\nEnter date in form MM/DD/YY: ");
scanf("%d/%d/%d",
&labmonth, &labday,&labyear);
labdate.month = labmonth;
lab_date.day = labday;
lab_date.year = labyear + 1900;
} while (_dos_setdate(Slabdate) != 0);
printf("\n%d/%d/%d is this correct (*/n)? ",
lab_date.month, lab_date.day, labdate.year - 1900);
c=getch();
} while(c=='n');
printf("\n");
if (lab_date.month < 10)
sprintf(si,"0%d\0",lab_date.month);
else sprintf(si,"%d\0",lab_date.month);
if (lab_date.day < 10)
sprintf(s2,"0%d\0",lab_date.day);
else sprintf(s2,"%d\0",lab_date.day);
sprintf(s3,"%d", lab_date.year -1900);
sprintf(lab_date_string, "%s%s%s\0", si, s2, s3);
}
init() {
int i;
set_mode(6);
camac_z();
for (i=0;i<0xl000;i++)
wmove(0,(unsigned)&zero,SCANBUF,i*24,12,0);
if ((camac_in(ADC1612,6,0)) == 1612)action ¡= CRATEOK;
setup_td(TDARRLEN,0,TDFREQ);
caldelay();
set_sa();
action ¡= TICTOC;
ticon(); /* and away we go !! */
}
/**********************************************************/
leave() {
ticoff();

set_mode (3);
fcloseall();
camac_z();
229
/**********************************************************/
diddle() {
int reset=0;
if (eparm.adc[0] > 3000) reset =1;
else didon =0;
if (didon) {
reset =0;
iparm.scan[didl] = doffl + (eparm.adc[1] » 2);
iparm.scan[did2] = doff2 + (eparm.adc[2] » 2);
caldelay();
}
if (reset) {
doffl = iparm.scan[didl] “ (eparm.adc[l] >> 2);
doff2 = iparm.scan[did2] ~ (eparm.adc[2] >> 2);
didon =1; reset = 0;
}
/*********************************************************/
escanner() {
unsigned i,signal;
long buf=0;
if (scanner == (AVGNUM-1)) action ¡= READSA;
sdat.sa[4] += (long)eparm.adc[4]-0x800L;
/* etalon markers */
sdat.sa[5] += (long)eparm.adc[3]-0x800L;
/* diss laser pwr */
for (i=0;i move(TDBUF,(sachan(0][3]+i),0,(unsigned)&buf,1,0);
sdat.sa[3] -= (long)buf;
move(TDBUF,(sachan[l][3]+i),0,(unsigned)&buf,1,0);
sdat.sa[3] += (long)buf;
}
if (¡scanner) {
for (signal=0;signal<3;signal++)
for (i=0;i bmove(SABUF,(sachan[0][signal]+i),0,(unsigned)&buf,3,0);
sdat.sa[signal] -= (long)buf;
bmove(SABUF,(sachan[1][signal]+i),0,(unsigned)&buf,3,0);
sdat.sa[signal] += (long)buf;
}
for (signal=0;signal<6;signal++)
iparm.dac3016[2+signal] =
(unsigned)(sdat.sa[signal]) + 0x8000;
wmove(0,(unsigned)&sdat,SCANBUF,(bin*24),12,0);

sdat = zero;
bin++;
230
}
scanner++; scanner %= AVGNUM;
}
/**********************************************************/
iscanner() {
unsigned i, signal;
long buf =0;
if (scanner == (AVGNUM-1)) action ¡= READSA;
sdat.sa[5] += (long)eparm.adc[3]-0x800L;
/* diss laser pwr */
for (i=0;i {
bmove(TDBUF,(sachan[0][3]+i),0,(unsigned)&buf,1,0);
sdat.sa[3] -= (long)buf;
bmove(TDBUF,(sachan[l][3]+i),0,(unsigned)&buf,1,0);
sdat.sa[3] += (long)buf;
}
if (¡scanner) {
wmove(SCANBUF,(bin*24),0,(unsigned)&vdat,12,0);
for (signal=0;signal<3;signal++)
for (i=0;i bmove(SABUF,(sachan[0][signal]+i),0,(unsigned)&buf,3,0);
vdat.sa[signal] -= (long)buf;
bmove(SABUF,(sachan[l][signal]+i),0,(unsigned)&buf,3,0);
vdat.sa[signal] += (long)buf;
}
vdat.sa[3]+=sdat.sa[3];
vdat.sa[4]++; /* the number of passes per bin */
vdat.sa[5]+=sdat.sa[5];
for (signal=0;signal<6;signa1++)
iparm.dac3016[2+signal] =
(unsigned)(sdat.sa[signal]) + 0x8000;
wmove(0,(unsigned)&vdat,SCANBUF,(bin*24),12,0);
sdat = zero;
bin++;
iparm.scan[iscanid] = start + (bininc * bin);
caldelay();
}
scanner++;
scanner %= AVGNUM;
bin %= iscanlen;
}
/*********************************************************/

231
aescanner() {
unsigned i,signal;
long buf=0;
sdat.sa[4] += (long)eparm.adc[4]-0x800L;
/* etalon markers */
sdat.sa[5] += (long)eparm.adc[3]-0x800L;
/* power */
if (scanner == (AVGNUM-1)) {
action ¡= READSA;
if (alte) iparm.p4222[0] = iparm.scan[3]
iparm.p4222[1];
else iparm.p4222[0] = iparm.scan[11] +
iparm.p4222[1];
}
+
for (i=0;i bmove(TDBUF,(sachan[0][3]+i),0,(unsigned)&buf,1,0);
sdat.sa[3] -= (long)buf;
bmove(TDBUF,(sachan[l][3]+i),0,(unsigned)&buf,1,0);
sdat.sa[3] += (long)buf;
}
if (¡scanner) {
for (signal=0;signal<3;signal++)
for (i=0;i bmove(SABUF,(sachan[0][signal]+i),0,(unsigned)&buf,3,0);
sdat.sa[signal] -= (long)buf;
bmove(SABUF,(sachan[1][signal]+i),0,(unsigned)&buf,3,0);
sdat.safsignal] += (long)buf;
}
for (signal=0;signal<6;signal++)
if (¡alte) {
vdat.sa[signal] += sdat.sa[signal];
wmove(0,(unsigned)&vdat,SCANBUF,(bin*24),12,0);
sdat=zero;
} else {
vdat.sa[signal] -= sdat.sa[signal];
iparm.dac3016[2+signal] =
(unsigned)(sdat.sa[signal]) + 0x8000;
vdat.sa[5] = iparm.scan[iscanid];
wmove(0,(unsigned)&vdat,SCANBUF,(bin*24),12,0);
sdat = zero;
bin++;
caldelay();
}
alte ~= 1;

232
}
scanner++;
scanner %= AVGNUM;
bin %= iscanlen;
/**********************************************************
tic() {
if (action & TICTOC) {
if (toe) { /* this is a toe */
read_td();
if (!(action & INHIBDMA))
if (((action & READSA) j{ (camac_lam()==SA4100))
&& ltddone) {
eparm.sweep = read_sa();
if (tddone) eparm.sweep = iparm.n;
else eparm.sweep -= (unsigned)(OxlOOOOL -
/
iparm.n);
}
if (¡(action & CRATEOK)) eparm.sweep=l;
action &= -READSA;
if (action & RECYCLE) action ¡= CLEARSA;
DIDDLE ¡ ESCAN))
if (action & (READADC ¡
read_adc(eparm.adc);
if (action & CLEARSA) {
clear_sa();
action &= “CLEARSA;
}
} else { /* this is a tic */
load_i();
initiate();
if ((action & NEWI) && ¡(action & INVALID)) {
caldelay();
set_sa();
action &= -NEWI;
}
if (action & ESCAN)
if (action & ISCAN)
if (action & ASCAN)
if (action & DIDDLE)
}
toe 1;
} else { /* dummy tictoc */
if (!toc) { initiate();}
toc~=l;
}
}
escanner();
iscanner();
aescanner();
diddle();
/**********************************************************/
plot () {
static int flag; /* if(flag) then pvec
valid! */

233
if (action & TDPLOT) {
wmove(TDBUF,0,PLOTBUF,0,0x200,0);
if(gen(PLOTBUF,(unsigned)(xifpage]),xs[page],l,vec)) {
axis(TDPLOT);
pltvec(vec,yi[page],ys[page]);
} else {
axis(TDPLOT);
Pplot(1,1);
}
} else {
if (action & SCANPLOT) {
axis(SCANPLOT);
scanplot();
} else {
if ((new_pvec) && (eparm.sweep)) {
action ¡= INHIBDMA;
wmove(SABUF,0,PLOTBUF,0,0x1000,0);
nsave = eparm.sweep;
action &= -INHIBDMA;
if(gen(PLOTBUF,(unsigned)(xi[page]*3),xs[page],3,vec)) {
flag =1;
axis(SAPLOT);
if (nsave)
pltvec(vec,yi[page]*nsave,ys[page]*nsave);
} else {
flag =0;
if (nsave) {
axis(SAPLOT);
pplot(3,nsave);
}
}
new_pvec=0;
} else if(nsave) {
if(flag) {
axis(SAPLOT);
pltvec(vec,yi[page]*nsave,ys[page]*nsave);
} else {
axis(SAPLOT);
pplot(3,nsave);
/**********************************************************/
axis(axistype)

234
unsigned axistype;
{
double ix,fx;
if (new_axis) {
cls() ;
switch(axistype) {
case TDPLOT:
if(time_axis) {
ix= ((double)iparm.scan[2] +
(double)iparm.scan[4] +
(double)xi[page]*TDPERIOD)/1000;
fx= ix + (double)xs[page]*TDPERIOD/1000
locate(23,0);printf("time[us]->");
} else {
ix = (double)(xi[page]);
fx = (double)(xi[page]+xs[page]);
locate(23,0);printf("31.3ns/chan");
}
locate(l,35);printf("SINGLE SHOT TR8837F");
break;
case SCANPLOT:
ix = (double)(xi[page]*bininc+start);
fx = (double)((xi[page]+xs[page])*bininc +
start);
locate(1,38);
printf("%s",signal_name[page]);
if (action & (ISCAN ¡ ASCAN)) {
locate(24,30);printf("%s",iparm.scanid[iscanid]);
}
break;
case SAPLOT:
if(time_axis) {
ix= ((double)iparm.scan[2] +
(double)xi[page]*iparm.period)/1000;
fx= ix +
(double)xs[page]*iparm.period/1000;
locate(23,0);printf("time[us]->");
} else {
ix = (double)(xi[page]);
fx = (double)(xi[page]+xs[page]);
locate(23,0);printf("%3uns/chan",iparm.period);
}
break;
}
axies(ix,fx,yi[page],yi[page]+ys[page],GRID);
if (action & DIDDLE) {
locate(3,39); printf("%26s
=",iparm.scanid[didl]);

235
locate(4,39); printf("%26s
=",iparm.scanid[did2]);
}
if (!(action & CRATEOK)) {
locate(2,39);printf("\nCRATE FAILURE");
}
wmove(0xB800,0,AXSC,0,0x2000, 0) ;
if(axistype != SCANPLOT)new_axis =0;
} else wmove(AXSC,0,0xB800,0,0x2000,0);
locate(0,0);
printf((s_o)?" ":" ");
printf((lock_zero)?"":"< >");
locate(l,70); printf("%5u",nsave);
if (action & DIDDLE) {
locate(3,67);
printf("%61d",iparm.scan[didl]);
locate(4,67);
printf("%61d",iparm.scan[did2]);
>
if (action & (ESCAN j ISCAN j ASCAN)) {
locate(1,15); printf("%5u",bin);
}
if (action & (ISCAN j ASCAN)) {
if(bin==0) scannumber++;
locate(1,25); printf("%3u",scannumber);
}
locate(1,0); printf("%-12s",filnam);
}
/**********************************************************/
unsigned gen(arrseg,arroff,len,bytes,vec)
unsigned arrseg,arroff,bytes;
int len;
struct pvec *vec;
unsigned
long
float
n=0,i=0,k=0,mergenum;
ldum=0;
fdum=0;
if (len <= XRES) return(0);
if ((len % XRES) != 0) return(0);
else {
mergenum = (unsigned)(len/XRES);
for (k=0;k bmove(arrseg,arroff+n,0,(unsigned)&ldum,bytes,0);
fdum = (float)ldum;
n += bytes;
vec[k].h = vec[k].l = fdum;
for (i=l;i bmove(arrseg,arroff+n,0,(unsigned)&ldum,bytes,0);

236
fdum = (float)ldum;
n += bytes;
vec[k].h = (fdum >
vec[k].h)?fdum:vec[k].h;
vec[k].l = (fdum <
vec[k].1)?fdum:vec[k].1;
}
if (k) {
if(vec[k].h < vec[k-l].l)
vec[k-l].1;
if(vec[k].l > vec[k-l].h)
vec[k-l]. h;
>
}
}
return (1);
}
vec[k].h=
vec[k].1=
#define TOP
#define BOT
/define LEFT
/define RIGHT
/define TOPBOT
1.0
180.0
110
622
-179.0 /* TOP minus BOT */
/**********************************************************/
void pltvec(vec,yorig,yscale)
struct pvec *vec;
double yorig,yscale;
unsigned
double
x, yl, y2, chan;
dum;
for (chan=0;chan x = chan + LEFT;
dum= BOT + ((TOPBOT) * (vec[chan].h -
yorig))/yscale;
if (dum < TOP) dum = TOP;
if (dum > BOT) dum = BOT;
yl = dum;
if (yl < TOP) yl = TOP;
if (yl > BOT) yl = BOT;
dum = BOT + ((TOPBOT) * (vec[chan].l -
yorig))/yscale;
if (dum < TOP) dum = TOP;
if (dum > BOT) dum = BOT;
y2 = dum;
if (y2 < TOP) y2 = TOP;
if (y2 > BOT) y2 = BOT;
stl6(x,yl,x,y2);
>
}

237
/**********************************************************/
symbol(x,y)
unsigned x, y;
{
unsigned yy;
for (yy=y-i;yy<=y+i;yy++) sti6(x-2,yy,x+2,yy);
}
topsymbol(x)
unsigned x;
{
unsigned yy;
for (yy=T0P;yy<=T0P+3;yy++)
stl6(yy-TOP+x,yy,TOP-yy+x,yy) ;
}
botsymbol(x)
unsigned x;
{
unsigned yy;
for (yy=BOT;yy>=BOT-3;yy—)
st16(yy-BOT+x,yy,BOT-yy+x,yy);
}
scanplot() {
int i, x, yl, y2;
double mul;
struct sdata one;
mul= (XRES/(double)xs[page]);
if(bin) {
for (i=(new_axis)?0:(bin-1);i wmove(SCANBUF,i*24,0,(unsigned)&one,12,0);
x = LEFT + (i-xi[page])*mul;
if ((X>=LEFT) && (x<=RIGHT)) {
yl=BOT +
TOPBOT*((one.sa[page]-yi[page])/ys[page]);
if (yl else if (yl>BOT) botsymbol(x);
else symbol(x,yl);
}
}
wmove(0xB800,0,AXSC,0,0x2000,0);
new_axis=0;
}
}
/**********************************************************/
pplot(bytes,scale)

{
unsigned
unsigned
bytes, scale;
238
double
unsigned
mul, i, xl, yl, x2, y2,
origoff, shiftlimit;
dum;
long one=OL;
mul= (XRES/xs[page]);
origoff = bytes*xi[page];
shiftlimit = (bytes*xs[page])+origoff;
bmove(PLOTBUF,origoff,0,(unsigned)&one,bytes,0);
xl = LEFT;
dum = BOT +
TOPBOT*((((double)one/scale)-yi[page])/ys[page]);
if (dum if (dum>BOT) dum=BOT;
yl = dum;
if (yKTOP) yl=TOP;
if (yl>BOT) yl=BOT;
for (i=origoff;i bmove(PLOTBUF,i,0,(unsigned)&one,bytes,0);
x2 = LEFT + ((i-origoff)/bytes)*mul;
if (X2 if (x2>RIGHT) x2=RIGHT;
dum = BOT +
TOPBOT*((((double)one/scale)-yi[page])/ys[page]);
if (dum if (dum>BOT) dum=BOT;
y2 = dum;
if (y2 if (y2>BOT) y2=B0T;
stl6(xl,yl,x2,y2);
yl=y2;xl=x2;
}
}
#undef TOP
#undef BOT
#undef TOPBOT
#undef LEFT
#undef RIGHT
/**********************************************************/
filo(fnam, c)
char c, *fnam;
{
unsigned temp, seg, off;
int i, signal;
char video[0x400];
unsigned long buf = 0L;

239
temp = action;
action =0;
_fpreset();
if((dfile = fopen(fnam,(c=='v')?"ab":"aM)) == NULL) {
printf("UNABLE TO CREATE FILE <%s>",fnam);
getch();action = temp/return;
}
if (c!='v') {
fprintf(dfile,"%12s\n",fnam);
fprintf(dfile,HEADLN);
fprintf(dfile,Msweeps= %5u\nperiod=
%5u\npretrig=%5u\n",
eparm.sweep,iparm.period,iparm.pretrig);
for (i=0;i<12;i++)
fprintf(dfile,"%30s %101d\n",
iparm.scanidfi],iparm.scan[i]);
}
locate(17,15);
switch(c) {
case 'e':
printf("outputting FREQUENCY SCAN data to diskfile
<%s>",fnam);
for (signal=0;signal<4;signal++)
fprintf(dfile,"signal%2d data=%5d base=%5d
number=%5d\n",
signal,sachan[0][signal],sachan[l][signal],sachan[2][signal]
) ;
fprintf(dfile,"bin=%4u\n",bin);
fprintf(dfile,"%30s %10u\n",avgnumid,AVGNUM);
fprintf(dfile,"\nEXTERNAL SCAN data
follows:\n\n\n");
for (i=0;i wmove(SCANBUF,(unsigned)(i*24),0,(unsigned)&sdat,12,0);
for (signal=0;signal<6;signal++)
fprintf(dfile,"%ld ",sdat.sa[signal]);
fprintf(dfile, "\n") ;
}
break;
case 'i':
printf("outputting INTERNAL SCAN data to diskfile
<%s>",fnam);
for (signal=0;signal<4;signal++)
fprintf(dfile,"signal%2d data=%5d base=%5d
number=%5d\n",
signal,sachan[0][signal],sachan[1][signal],sachan[2][signal]
);

240
fprintf(dfile,"\nstart= %101d\nbininc=
%101d\niscanlen= %4u\n\n",start,bininc,iscanlen);
fprintf(dfile,"%30s %10u\n",avgnumid,AVGNUM);
fprintf(dfile,"\nINTERNAL SCAN data
follows:\n\n\n");
for (i=0;i wmove(SCANBUF,(unsigned)(i*24),0,(unsigned)&sdat,12,0);
for (signal=0;signal<6;signal++)
fprintf(dfile,"%ld ",sdat.sa[signal]);
for (signal=0;signal<3;signal++)
fprintf(dfile,"%12.8lf ”,
((double)sdat.sa[signal]/sdat.sa[4]));
fprintf(dfile,"\n");
}
break;
case 'v':
printf("outputting SCREEN PAGE data to diskfile
<%s>",fnam);
for (i=0;i<(SCRNUM«4) ;i++) {
wmove((STSCPG+(i*0x4 0)),0,0,(unsigned)video,0x200,0);
fwrite(video,1,0x400,dfile);
}
break;
default:
printf("outputting TOFMS data to diskfile
<%s>",fnam);
fprintf(dfile,"\nTOF data follows:\n");
seg = SABUF;
for (i=0;i off = i*3;
bmove(seg,off,0,(unsigned)&buf,3,0);
fprintf(dfile,"%101u\n",buf);
}
}
fclose(dfile);
strcpy(filnam,fnam);
action = temp;
}
filp(testp)
int testp;
{
char aa, bb, c, dummy, filename[80];
locate(5,30);printf("'e' = External scan");
locate(6,30);printf("'i' = Internal scan");
locate(7,30);printf("'w’ = Video dump");
locate(8,30);printf("'*' = TOFMS)");

241
locate(9,30);printf("Enter file type? ");
c = getche();
if (testp) {
locate(12,15);printf("filename please: ");
if (skeyin(filename) == 0) return;
filo(filename,c);
} else {
switch(c) {
case
'e':
aa = file count.f
/
26
+
c;
bb = file count.f
%
26
+
' a
file count.f ++;
break;
case
'i':
aa = file count.i
/
26
+
c;
bb = filecount.i
%
26
+
'a
file count.i ++;
break;
case
'v':
aa = file_count.v
/
26
+
c;
bb = file count.v
%
26
+
' a
file count.v ++;
break;
default :
c = ' t ';
aa = file_count.t
/
26
+
c;
bb = file count.t
%
26
+
'a
file count.t ++;
}
sprintf(filename,"%s%c%c.prn\0", lab_date_string,
aa, bb);
filo(filename,c);
locate(13,15);printf("If you want to save this to
A: or B: drive");
locate(14,15);printf("Enter 'a' or 'b': ");
dummy = getche();
if ((dummy =='a')¡¡(dummy == 'b')) {
sprintf(filename,"%c:\\%s%c%c.prn\0",
dummy, lab_date_string, aa, bb);
filo(filename,c);
}
}
}
fili()
{}
/* {
unsigned temp,seg,off;
int i;
char c,video[0x400],dum[120];
unsigned long buf = 0L;
locate(10,25);printf("filename please: ");
if (skeyin(fnam) == 0) return;
locate(11,30);printf("file type:");
locate(11,42);printf("'e' = External scan");

242
locate(12,42);printf("'i' = Internal scan");
locate(13,42);printf("'v' = Video dump");
locate(14,42);printf("'*' =TOFMS)?: ");
c = getche();
temp = action;
action =0;
_fpreset();
locate(17,30);
if((dfile = fopen(fnam,(c=='v')?"rb":"r")) == NULL)
{
printf("<%s> NOT FOUND",fnam);
getch();action = temp;return;
}
if (c!='v')
{
fscanf(dfile,"%12s\n",fnam);
fscanf(dfile,"%[~\n]\n",dum);
fscanf(dfile,"sweeps= %5u\nperiod=
%5u\npretrig=%5u\n\n",
&eparm.sweep,&iparm.period,&iparm.pretrig);
for (i=0;i<12;i++)
fscanf(dfile,"%29c
%10ld\n",(iparm.scanid+i),(iparm.scan+i));
}
locate(16,15);
switch(c)
{
case 'e':
{
printf("inputting EXTERNAL SCAN data from diskfile
<%s>",fnam);
fscanf(dfile,"\nsasig= %5u\nsabas=
%5u\nsachan= %5u\nsa2sig= %5u\nsa2bas= %5u\nsa2chan=
%5u\n",
Ssasig,&sabas,Ssachan,&sa2sig,&sa2bas,&sa2chan);
fscanf(dfile,"bin=%4u\ntdsig= %5u\ntdbas=
%5u\ntdchan= %5u\n",&bin,Stdsig,&tdbas,Stdchan);
fscanf(dfile,"\n%29c %5u\n",avgnumidd,AVGNUMD);
if (AVGNUMD!=0) AVGNUM=AVGNUMD;
fscanf(dfile,"\nEXTERNAL SCAN data
follows:\n\n\n");
fscanf(dfile,"%[A\n]\n",dum);
for (i=0;i {
fscanf(dfile,"%10ld%10ld%10ld%10ld\n",
&sdat.sal,&sdat.sa2,&sdat.td,&sdat.etalon);
wmove(0,(unsigned)&sdat,SCANBUF,(unsigned)(i<<4),8,0);

243
>
} break;
case 'i':
{
printf("inputting INTERNAL SCAN data from diskfile
<%s>",fnam);
fscanf(dfile,"\nsasig= %5u\nsabas=
%5u\nsachan= %5u\nsa2sig= %5u\nsa2bas= %5u\nsa2chan=
%5u\n",
Ssasig,&sabas,Ssachan,&sa2sig,&sa2bas,&sa2chan);
fscanf(dfile,"\nstart= %101d\nbininc=
%10ld\niscanlen= %4u\n\n",&start,&bininc,&iscanlen);
fscanf(dfile,"\ntdsig= %5u\ntdbas=
%5u\ntdchan= %5u\n",
&tdsig,&tdbas,Stdchan);
fscanf(dfile,"\n%29c %5u\n",avgnumidd,AVGNUMD);
if (AVGNUMD!=0) AVGNUM=AVGNUMD;
fscanf(dfile,"\nINTERNAL SCAN data
follows:\n\n\n");
fscanf(dfile,"%[A\n]\n",dum);
for (i=0;i {
fscanf(dfile,"%101d%101d%101d%101d\n",
&sdat.sal,&sdat.sa2,&sdat.td,&sdat.etalon);
wmove(0,(unsigned)&sdat,SCANBUF,(unsigned)(i«4),8,0);
>
bin = iscanlen;
} break;
case 'v':
{
printf("inputting SCREEN PAGE data from diskfile
<%s>",fnam);
for (i=0;i<(SCRNUM«4) ;i++)
{
fread(video,1,0x400,dfile) ;
wmove(0,(unsigned)video,(STSCPG+(i*0x40)),0,0x200,0);
}
} break;
default:
{
printf("inputting TOFMS data from diskfile
<%s>",fnam);
fscanf(dfile,"\nTOF data follows:\n");
seg = SABUF;
for (i=0;i {
off = i*3;
fscanf(dfile,"%101u\n",&buf);

244
bmove(O,(unsigned)&buf,seg,off,3,0);
}
}
}
fclose(dfile);
strcpy(filnam,fnam);
action = temp;
}
*/
/**********************************************************/
svscrn() {
int nunt, add;
char c, scrnnam[40];
locate(0,0); printf("-> ");
locate(0,2);
num = (int)inf();
locate(2,37); printf("-> ");
skeyin(scrnnam);
if((num < SCRNUM) && (num>=0)) {
add = STSCPG+num*(0x400);
wmove(0xB800,0,(unsigned)add,0,0x2000,0);
} else {
locate(0,2);
printf("INVALID #") ;
getch();
}
}
/**********************************************************/
dump() {
unsigned a[SCRNUM], i, row=5, col;
cls() ;
for (i=0;i set_mode(3);
locate(20,0);
printf("\tto select screens to be printed, move cursor
to screen number\n");
printf("\t\t toggles select\n");
printf("\t\t->this line starts print\n");
printf("\t\t->this line aborts");
do {
for (i=5;i locate(i,10);
printf("[%2d]",i—5);printf((a[i-5])?"
"");
}
locate(row,20);
use_curs(&row,&col,' ');
if((row=5))
A
i;
a[row-5]

245
if(row == 22) {
set_mode(6);
for (i=0;i if(a[i]) {
wmove((STSCPG+i*0x400),0,0xB800,0,0x2000, 0) ;
locate(0,0); printf("->%2d"/i);
prscrn();
bdos(5,12,0);
}
return;
}
} while (row < 23);
set_mode(6);
}
/**********************************************************/
gtscrn() {
int num=0, add;
double inf();
char c, d=0;
wmove(0xB800,0,TMPSCRN,0,0x2000,0);
do {
add = STSCPG+num*(0x400);
wmove(add,0,0xB800,0,0x2000,0); /* retrieve
saved screen */
locate(0,0); printf("->%2d ",num);
c = getch();
if ( c==0 ) d=getch();
else {
d=0;
if (c==/b/) wmove(add,0,AXSC,0,0x2000,0);
}
if(d == 77) num = (num>=(SCRNUM-1)) ? 0:(num+l);
if(d == 75) num = (num<=0) ? (SCRNUM-1):(num-1);
} while ((c != 27) && (d != 117));
wmove(TMPSCRN,0,0xB800,0,0x2000,0) ;
}
/*********************************************************/
dum_data() {
int i, dl=245, d2=210;
long ldl=250, ld2=200;
for (i=0;i bmove(0,(unsigned)&dl,TDBUF,i,1,0);
for (i=0;i bmove(0,(unsigned)&d2,TDBUF,i,1,0);
for (i=0;i bmove(0,(unsigned)&ldl,SABUF,i,3,0);

246
for (i=0;i bmove(0,(unsigned)&ld2,SABUF, i, 3,0);
tddone =1;
eparm.sweep = 1;
}
/*********************** MENU'S **************************/
help_menu() {
unsigned i, j, row=l, col=40, choice;
set_mode(3);
locate(0,30);
printf("DRGATO Help Menu");
for(i=0;i<20;i++) {
locate(i+2,1); printf("%s",hmenu[i]);
locate(i+2,41); printf("%s",hmenu[i+20]);
}
locate(24,0) ;
printf("Use arrow keys to get on command then press
");
do {
locate(row,col);
use_curs(&row,&col,13);
} while (row>21);
if(row<2) {
set_mode(6);
return;
}
if(col<40) choice = row - 2;
else choice = row + 18;
set_mode(6);
new_axis = new_pvec = 1;
plot () ;
if (choice<14) {
ungetch((char)h_choice[choice]);
s_hand(0);
}
else s_hand((char)h_choice[choice]);
>
iparm_menu() {
unsigned i, j, row=17, col=35;
set_mode(3);
locate(4,0); printf("%35s\n",avgnumid);
locate(5,0); for (i=0;i<12;i++)
printf("%35s\n",iparm.scanid[i]);
do {
locate(4,35); printf("%10u",AVGNUM);
for (i=0;i<12;i++) {
locate(5+i,3 5);
printf("%101d",iparm.scan[i]);

247
}
locate(row,col);
use_curs(&row,&col,'c');
if ((row>=4) && (row<17)) {
j = (row-5);
locate(row,35);
printf("-> ");
locate(row,37);
action j= INVALID;
if (row==4) AVGNUM=(long)inf();
else iparm.scan[j] = (long)inf();
action &= -INVALID;
action ¡= NEWI;
temppar=iparm;
}
} while ((row >= 4) && (row < 17));
display_t();
set_mode(6);
}
/**********************************************************/
display_t() {
int i ;
cls() ;
locate(2,0); printf("%22s",”Lecroy 4222");
locate(2,30); printf("%22s","Kinetic 3655 'B'");
locate(2,55); printf("%22s","Kinetic 3655 'A'");
for (i=0;i<8;i++) {
locate(4+i,50);
printf("%20s",iparm.pulseid[i]);
printf("%5u",iparm.p3655a[i]);
locate(4+i,25);
printf("%20s",iparm.pulseid[i+8]);
printf("%5u",iparm.p3655b[i]);
}
for (i=0;i<4;i++) {
locate(4+i,0);
printf("%15s",iparm.pulseid[i+16]);
printf("%101u",iparm.p4222[i]);
}
locate(14,0);
printf(
" DAC\n");
printf(
" 1 2 3 4 5
6 7\n");
printf(
" Sect (+) Sect (-)
etalonSout A VT0P\n");
printf(
SAout
SA2out
TDout

248
•I
8 9
10
11
12
13
14\n");
printf(
it
A VBOT A HFAR
A HNEAR
B VTOP B
VBOT B
HFAR
B HNEAR\n\n");
printf(
it
printf(
ADC\n");
it
0 1
2
3
4
5
6\n");
printf(
it
DIDDLER0 DIDDLER1
DIDDLER2
Power
etalons
\n");
getch();
>
/**********************************************************/
diddle_menu() {
int i;
char c;
cls() ;
locate(5,0);
for (i=0;i<12;i++) printf("%35s\n",iparm.scanid[i]);
do {
locate(20,10);
printf("enter scan number to be associated with
adc channel 1:");
didl = (unsigned)inf();
} while (didl >= 12);
do {
locate(21,10) ;
printf("enter scan number to be associated with
adc channel 2:");
did2 = (unsigned)inf();
} while (did2 >= 12);
locate(23,0);
printf(" proceedure cannot be activated during
time or voltage scan.");
locate(24,20); printf("Proceed with
(y/*)?:");
c = getche();
if ((c=='y') && !(action & ISCAN)) action ¡= (DIDDLE ¡
RECYCLE);
cls() ;
}
/**********************************************************/
scan_menu() {
int i, j, signal;
unsigned temp;

249
char c;
cls() ;
for (signal=0;sígnalo;signal++) {
printf("%s",signal_name[signal]);
printf("\n\tion channel start <%5u>
:",sachan[0][signal]/3) ;
temp=(unsigned)inf();
if (temp) sachan[0][signal]=temp*3;
printf("\n\tbaseline channel start <%5u> : ",
sachan[1][signal]/3) ;
temp=(unsigned)inf();
if (temp) sachan[l][signal]=temp*3;
printf("\n\tchannels to be integrated <%5u>
sachan[2][signal]/3);
temp=(unsigned)inf();
if (temp) sachan[2][signal]=temp*3;
printf("\n");
}
printf("%s",signal_name[3]);
printf("\n\tion channel start <%5u> sachan[0][3]);
temp=(unsigned)inf();
if (temp) sachan[0][3]=temp;
printf("\n\tbaseline channel start <%5u>
: ",sachan[1][3]);
temp=(unsigned)inf() ;
if (temp) sachan[l][3]=temp;
printf("\n\tchannels to be integrated <%5u>
:",sachan[2][3]) ;
temp=(unsigned)inf();
if (temp) sachan[2][3]=temp;
printf("\n");
locate(17,0);
printf("\tScan type:");
printf("Xt'e' = (stripchart) external scan\n");
printf("\t\t\t'i' = internal paramenter scan\n");
printf("XtXtXt'a' = alternating Dfire internal
scan\n");
printf("\t\t\t'*' = none\n\t\t\t?:");
c = getche();
if (c==/e/) escan_menu();
if (c=='i') {
els^ J •
for (j=0;j<12;j++) {
locate((1+j),0);
printf("%35s",iparm.scanid[j]) ;
locate((1+j),35);
printf("%101d",iparm.scan[j]);
}
iscan_menu();
}

250
if (c=='a') {
ds () i
for (j=0;j<12;j++){
locate((1+j) , 0) ;
printf("%35s",iparm.scanid[j]);
locate((1+j),35);
printf("%101d",iparm.scan[j]);
}
ascan_menu();
}
cls() ;
sdat = zero;
scanner = 0;
}
escan_menu()
{
char c;
start=0L;
bininc=lL;
locate(23,34);printf(");
locate(24,28)/printf("Clear SCAN buffer (y/*)?:");
c = getche();
if (c=='y') {
bin =0;
action ¡= (ESCAN ¡ RECYCLE } CLEARSA);
}
}
iscan_menu() {
long li;
unsigned i;
char c;
do{locate(14,10)/printf("Parameter to be scanned
(0->ll)?:");i=(int)inf();}
while ((i<0) && (i>=12));
iscanid = i;
locate(14,10)/printf("Scanning:
<<%s»" , iparm. scanid[ iscanid]) ;
locate(15,10)/printf("Scan start (%51d): ", start);
li = (long)inf();
if(li) start = li;
do {
locate(16,10)/printf("Scan end (%5ld): ",send)
li = (long)inf();
} while ((li <= start) && (li));
if (li) send = li;
locate(17,10)/printf("Scan increment per bin (%31d)
",bininc);
li = (long)inf();
if (li) bininc = li;

251
iscanlen = (send-start)/bininc;
send = iscanlen*bininc + start;
locate(16,10);printf("End of scan is: %51d
",send);
locate(24,28);printf("Clear SCAN buffer(y/*)?:") ;
c = getche();
if (c=='y') {
bin = scannumber = alte =0;
for (i=0;i<0xl000;i++)
wmove(0,(unsigned)&zero,SCANBUF,i*24,12,0);
action ¡= (ISCAN ¡ RECYCLE ¡ CLEARSA);
}
}
ascan_menu() {
long
unsigned
i;
char
c;
do {
locate(14,10);printf("Parameter to be scanned
(0->ll)?:");
i=(int)inf();
} while ((i<0) && (i>=12));
iscanid = i;
locate(14,10); printf("Scanning:
<<%s>>",iparm.scanid[iscanid]);
locate(15,10); printf("Scan start (%51d): ", start);
li = (long)inf();
if(li) start = li;
do {
locate(16,10); printf("Scan end (%51d): ",send);
li = (long)inf();
} while ((li <= start) && (li));
if (li) send = li;
locate(17,10); printf("Scan increment per bin (%31d):
",bininc);
li = (long)inf();
if (li) bininc = li;
iscanlen = (send-start)/bininc;
send = iscanlen*bininc + start;
locate(16,10);printf("End of scan is: %51d
",send);
locate(24,28);printf("Clear SCAN buffer(y/*)?:");
c = getche();
if (c=='y') {
bin = scannumber = alte =0;
for (i=0;i<0xl000;i++)
wmove(0,(unsigned)&zero,SCANBUF,i*24,12,0);

252
action ¡= (ASCAN ¡
}
firstc(d)
char
{
double
int i;
d;
dum, per;
switch(d) {
case
case
case
case
case
case
'1'
'2'
•2'
' 4'
'5'
'6'
if(action & SCANPLOT) {
for(i=0;i<6;i++) {
xi[i]=xi[page];
xs[i]=xs[page];
}
page = d -
new pvec =
'i';
new axis
= i;
");
case
's'
case
'9'
case
'd'
case
'c'
case
'r'
case
'1'
case
'n'
case
'k'
case
'h'
case
'p'
case
•o'
case
'O'
case
'i'
case
't'
}
break;
svscrn();
gtscrn();
(ns);
case
break;
break;
dump();new_axis=new_pvec=l; break;
time_axis *»1; new_axis=l; break;
new_pvec=new_axis=l; break;
lock_zero A=l; break;
locate(10,20);printf("Input shots to average:
iparm.n = (unsigned)inf();action ¡= NEWI;
new_axis=new_pvec=l; break;
action ¡= CLEARSA; break;
tddone =1; break;
new_pvec = 1; break;
filp(O); break;
filp(l); break;
fili();new_axis=new_pvec=l; break;
locate(10,20);printf("input SA channel period
iparm.period = (unsigned)inf(); action ¡= NEWI;
new_axis=new_pvec=l; break;
'y/* manual y scale factors */
locate(10,20);printf("Input vertical scale : ");
Vs[page] = inf();
locate(11,20);printf("Input vertical offset: ");
yi[page] = inf();
new axis =1;

253
break;
case 'b':
if(!(action & SCANPLOT)) {
if(xs[page] != (action &
TDPLOT)7TDARRLEN:ARRLEN) {
if (action & TDPLOT) {
xs[TD] = xs[page];
xi[TD] = xi[page];
xs[page] = TDARRLEN;
xifpage] =0;
} else {
xs[SA] = xs[page];
xi[SA] = xifpage];
xs[page] = ARRLEN;
xi[page] =0;
}
} else {
if (action & TDPLOT) {
xs[page] = xs[TD];
xi[page] = xi[TD];
} else {
xs[page] = xs[SA];
xi[page] = xi[SA];
}
}
new_axis =1;
}
break;
case 'x': /* manual x scale factors */
locate(10,20); printf("Input horizontal scale
in") ;
printf((time_axis)?" us: ":" chan: ");
per = (action & TDPLOT)7TDPERIOD:iparm.period;
dum = inf();
if(time_axis && !(action & SCANPLOT))
dum=dum*1000/per;
dum = (dum>len)?len:dum;
dum = (dum<32)732:dum;
scalemod = (dum>XRES)7XRES:32;
xs[page] = dum;
xs(page] -= (xs[page]%scalemod);
xs[page] = (xs[page] locate(10,51);
printf("%8.31f[us] (%4d chan)",
(double)xs[page]*per/1000,xs[page]);
locate(ll,20); printf("Input horizontal offset
in") ;
printf((time_axis)7" us: ":" chan: ");
dum = inf();
if(time_axis && [(action & SCANPLOT)) {
dum = (dum*1000 - iparm.scan[2])/per;
if(action & TDPLOT) dum -= iparm.scan[4]/per;

254
}
dum = ((xs[page]+dum)>len)?(len-xs[page]):dum;
dum = (dum<0)?0:dum;
xi[page] = dum;
locate(11,51);
dum = (xi[page]*per+iparm.scan[2])/1000;
if(action & TDPLOT) dum += iparm.scan[4]/1000;
printf("%8.31f[us] (%4d chan)",dum,xi[page]);
new_pvec = new_axis =1;
break;
case 'z
lab_date set ();
strcpy(filnam,labdatestring);
break;
case 'q
case 27 :
case 32 ¡break;
default:
help_menu();
new_pvec = new_axis =1;
break;
}
>
/**********************************************************/
shand(key)
char key;
{
char c;
len = (action & TDPLOT)7TDARRLEN:ARRLEN;
if (action & SCANPLOT) len = SCANLEN;
if(key!=0) firstc(key);
else
switch(c=getch()) { /* c switch */
case 77:
if (s_o) { /* change scale */
xs[page] /=2;
xs[page] = (xs[page]>len)?len:xs[page];
scalemod = (xs[page]>XRES)?XRES:32;
xs[page] -= (xs[page]%scalemod);
xs[page] =
(xs[page] } else { /* change origin */
xifpage] -= xs[page]/2;
xi[page] = (xi[page]<0)?0:xi[page];
}
new_pvec=new_axis=l;
break;
case 75:
if (s_o) {
/* right arrow */
/* change scale */

255
xs[page] *=2;
xs[page] = (xs[page]>len)?len:xs[page];
scalemod = (xs[page]>XRES)?XRES:32;
xs[page] -= (xs[page]%scalemod);
xs[page] =
(xs[page] if ((xs[page]+xi[page])>len)
xifpage] = (len-xs[page]);
} else { /* change origin */
xifpage] += xs[page]/2;
xi[page] =
((xs[page]+xi[page])>len)?(len-xs[page]):xi[page];
}
new_pvec=new_axis=l;
break; /* left arrow */
case 72:
if (s_o) { /* change scale */
ys[page] /= 2;
if (lockzero) yi[page]/=2;
}
else /* change origin */
yi[page] -= ys[page]/8;
new_axis=l;
break; /* up arrow */
case 80:
if (s_o) { /* change scale */
ys[page] *= 2;
if (lockzero) yi[page]*=2;
}
else /* change origin */
yi[page] += ys[page]/8;
new_axis=l;
break; /* dn arrow */
case 115:
xi[page] += xs[page]/8;
xi[page] =
((xs[page]+xi[page])>len)?(len-xs[page]):xi[page];
new_pvec=new_axis=l;
break; /* control left arrow */
case 116:
xifpage] -= xs[page]/8;
xi[page] = (xi[page]<0)?0:xi[page];
new_pvec=new_axis=l;
break; /* control right arrow
*/
case
case
73:
break;
81:
/*
PgUp
*/
break;
82:
/*
PgDn
*/
s_o 1;
locate(0,0);
case

256
printf((s_o)?" ":"<0R> ");
break; /* Ins */
case 83:
break; /* Del */
case 59:
iparm_menu();
new_axis =1;
break; /* FI */
case 60:
action *= RECYCLE;
break; /* F2 */
case 61:
if(!(action & DIDDLE)) {
diddle_menu();
new_axTs =1;
>
break; /* F3 */
case 62:
if (action & DIDDLE) {
action &= ~DIDDLE;
didon =0;
new_axis =1;
temppar=iparm;
}
break;
case 63:
if(!(action & (ESCAN
temppar=iparm;
scan_menu();
}
break;
case 64:
if (action & (ESCAN ¡
action &= -(ESCAN ¡ ISCAN ¡ ASCAN)
action ¡= INVALID;
iparm=temppar;
action &= -INVALID;
action ¡= NEWI;
if(action & SCANPLOT) {
/* F4 */
¡ ISCAN ¡ ASCAN)))
/* F5 */
ISCAN ¡ ASCAN)) {
{
case
opage=page;
page=6;
action &= -SCANPLOT;
new_axis=l;
}
}
break; /* F6 */
67:
if (!(action & TDPLOT)) {
action ~= SCANPLOT;
if (action & SCANPLOT) page = opage;
else {
opage = page;

257
page =6;
}
}
new_axis = 1;
break; /* F9 */
case 68:
if(!(action & SCANPLOT)) {
action ~= TDPLOT;
if (action & TDPLOT) page = 6;
else {
page = 7;
}
}
new_axis =1;
break;
/*
F10
*/
case 104: break;
/*
Alt
FI */
case 113: break;
/*
Alt
F10 */
default:
help_menu();
newaxis =1;
break;
}
if (newaxis ¡¡ new_pvec) plot();
}
/************************* MAIN ***************************/
main()
{
char c=0;
int i ;
cls() ;
printf(HEADLN);
lab_date_set();
strcpy(filnam,lab_date_string);
printf("\n\n\t!! Insure the CAMAC crate is on and
connected to the AT !!\n");
printf( M\ti! then hit {enter} !!");
getch();
init() ;
if(!(action & CRATEOK)) dum_data();
do {
set_mode(6);
s_hand('r');
do {
do {
if (action & (ESCAN ¡ ISCAN ¡ ASCAN))
do{} while (scanner);
else action |= READSA;
if (kbhit()) s_hand(c=getch());

258
else s_hand(c='p');
} while (ltddone && (c!='q') && (c!=27));
shand('p');
do {
if (kbhit()) shand(c=getch());
} while (tddone && (c! = 'q') && (cl=27));
} while ((c!='q') && (c!=27));
set_mode(3) ;
locate(5,10);
printf(HEADLN);
printf("\n\t\tAre You Ready to Exit This Routine
(*/*)?••) ;
getch();
printf("\n\t\tAll Experimental Control Will
Cease(*/*)?”);
getch();
printf("\n\t\t hit to exit (/*):M);
c=getch();
} while (c!='q');
leave();
}
Supporting Assembly Language Routines
FILENAME; BMOVE.ASM
PAGE 60,132
TITLE BMOVE - BLOCK MOVE FUNCTION (SMALL memory
model)
•ft*********************************************************
; void
bmove(unsigned,unsigned,unsigned,unsigned,unsigned,unsigned)
r
/
; A simple byte string block move function to be called from
C progs.
•
/
; use in form
t
bmove(from_seg,from_off,to_seg,tooff,count,direction)
/
;where from_seg = source segment ( 0 uses current DS
from C prog.)
; from_off = source offset
; to_seg = destination segment ( 0 uses current ES
from C prog.)
; to_off = destination offset
; count = number of bytes to move

259
; direction= direction of move ( O=foreward, else
backward)
•A**********************************************************
. 286c
_TEXT SEGMENT BYTE PUBLIC 'CODE'
ASSUME CS: TEXT
PUBLIC _bmove
_bmove proc NEAR
push
bp
mov
bp, sp
pusha
push
ds
push
es
cld
mov
ax,[bp+14]
or
ax, ax
jz
set regs ;
std
I
set regs:
mov
si,[bp+6] ;
mov
ax,[bp+8] ;
or
ax, ax
register?
jz
this seg ;
mov
es, ax
this seg:
mov
di,[bp+10]
index
mov
cx,[bp+12]
mov
ax,[bp+4] ;
or
ax, ax
DS register?
jz
doit ;
mov
ds, ax
doit:
rep
movsb
; set for foreward direction
; get direction
; is direction foreward?
yes - don't change direction flag
no - set for backward move
get from_off & put in source index
get to_seg
; is to_seg the current C prog ES
if so, stay in this seg.
; set destination segment
; get to_off & put in destination
; put count in count register
get from_seg
; is from_seg the current C prog.
if so, let's go
; set source segment
; do the move [DS:SI] —> [ES:DI]
cld
(reguired for C)
pop es
pop ds
popa
mov sp,bp
pop bp
ret
_bmove endp
; insure direction flag cleared
/
t
; restore registers

260
_TEXT ends
end
•it********************************************************
FILENAME; DOS.ASM
PAGE 60,132
NAME dos
TITLE dos GENERAL int 21h FUNCTION CALL (SMALL memory
model)
COMMENT $
void dos(unsigned *,unsigned *,unsigned *,unsigned *);
To be called from a C program the in form:
dos(&ax,&bx,&cx,&dx);
where &ax = pointer to variable (int) which is the
ax register
contents at time of the DOS function call.
ah selects the particular DOS function
called
al is used for value returns from the
DOS function
&bx,
the
call.
$
&cx, &dx = pointers to 16bit variables for
bx,cx,and dx registers at time of DOS
.286c
_TEXT SEGMENT BYTE PUBLIC 'CODE'
ASSUME CS:_TEXT
PUBLIC _dos
dos PROC NEAR
push bp
mov bp,sp
pusha
push ds
push es
9
mov
si,
[bp+4]
; get
pointer
to
ax
value
mov
ax,
[si]
; put
in ax register
mov
si,
[bp+6]
; get
pointer
to
bx
value
mov
bx,
[si]
mov
si,
[bp+8]
; get
pointer
to
cx
value
mov
cx,
[si]
mov
si,
[bp+10]
; get
pointer
to
dx
value
mov
dx,
[si]

261
int 21h
mov si,[bp+10]
for return
mov [si],dx
mov si,[bp+8]
FILENAME: DOS6.ASM
; make the DOS call
; get pointer to dx storage area
; now update
page 60,132
COMMENT $
•A*********************************************************
; dot6.asm Version 09-10-86
/pjb
; Places a dot on the screen in the position (x,y)
(MODE 6 ONLY!)
; use in form
/
; in mode 6:
200
•
of the screen
dot6(x,y) x,y unsigned or int
0 <= x < 640 0 <= y <
(0,0) is the upper left hand corner
; For the 80286!
; No choice of color or erase provided
; No range checking on input x,y performed
; For Microsoft C Version 3 code calls
•A**********************************************************
$
. 286c
_TEXT SEGMENT BYTE PUBLIC 'CODE'
JTEXT ENDS
_CONST SEGMENT WORD PUBLIC 'CONST'
_CONST ENDS
_BSS SEGMENT WORD PUBLIC 'BSS'
_BSS ENDS
_DATA SEGMENT WORD PUBLIC 'DATA'
_DATA ENDS
DGROUP GROUP _CONST, _BSS, _DATA
ASSUME CS: _TEXT, DS: DGROUP, SS: DGROUP, ES: DGROUP
_TEXT SEGMENT
public _dot6
dot6 proc near
Save registers on the stack
push bp
mov bp,sp
pusha
push ds
push es

262
Set Video Segment
mov axf0B800h
mov ds,ax
Calculate bit mask and store x
for later
mov ax,[bp+4]
mov di,ax
and ax,00007h
fetch x
; store x in di
; mask off first three bits of
times
mov cx,ax
mov ax,00080h
shr ax,cl
mov cx,ax
Calculate Video address offset
; set count register to x%8
load 128 into ax
; shift ax to the right ax&7
cx is the pixel mask
mov ax,[bp+6]
mov ah,al
and ax,01FEh
shl ax,3
mov bx,ax
and bh,7
shl ax,2
add bx,ax
mov ax,di
sar ax,3
add bx,ax
or ds:[bx],cl
; Restore the registers
pop es
pop ds
popa
mov sp,bp
pop bp
ret
dot6 endp
"TEXT ENDS
END
; fetch y
move y into al
; mask off unwanted parts
(y/2) *16 + (y%2)*2048
into bx
bx = (y/2)*16
; ax = (y/2)*64 + (y%2)*8k
address = y*80 + adjust for even\odd
get x-coord
(x/8)
this is the video address offset
; add new pixel
FILENAME: PIC.ASM
page 60,132
COMMENT $
************************************************************
TIC FUNCTIONS
Version date = 10/07/86
/Pjb
use with Microsoft C version 4.00
MODEL)
(SMALL MEMORY
unsigned ticon(void);

263
Installs a timer tic interupt handler at interupt
vector 1C.
present interrupt frequency is 18.2 Hz
Each timer interrupt will invoke a C function named
cvoid tic(void)>
Return Value:
0 if Tic turned on OK
1 if Tic was already on
? offset of int vector 1C if different from
expected and
Tic was not on.
void ticoff(void);
Turns off the function call. MUST BE CALLED
BEFORE EXITING
THE MAIN PROGRAM THAT CALLED !!!
unsigned isticon(void);
returns a 1 if tic is being repetatively invoked and 0
if not.
The _CINT_HAND cannot interrupt itself. Therefore a
tic routine
that takes too long will slow the repetition frequency
of interrupts
never allow the host program to regain control. Be
careful!
RESTRICTIONS
The Stack Size of the host C program must not exceed
the value of
CSTACK (now 0x2000=8k) minus the stack allocation at
the time of the
call to ticon(). The host program must be linked with
a stack
segment exceeding this value by the expected size of
the interrupt
stack. I suggest a link stack size of 0x4000 giving
approximately
8k for the interrupt stacks use.
************************************************************
$

264
. 286c
.287
EXTRN
tic:NEAR,
_fpreset:NEAR
TEXT
SEGMENT
BYTE PUBLIC
'CODE'
TEXT
ENDS
CONST
SEGMENT
WORD PUBLIC
'CONST'
CONST
ENDS
BSS SEGMENT WORD PUBLIC 'BSS'
BSS ENDS
DATA
SEGMENT
WORD PUBLIC 'DATA'
DATA
ENDS
DGROUP
GROUP
_CONST
, _BSS, _DATA
TEXT
SEGMENT
PUBLIC
ticon
, _ticoff,
isticon ;
INTNUM
EQU
OlCh
; Interrupt to be intercepted
VECSEG
EQU
OFOOOh
; Expected Segment of int
1C vec
VECOFF
EQU
0FF53h
; Expected offset of int
1C vec
CSTACK
EQU
02000h
; Host Stack Size
DOSINT
EQU
021h
; DOS function interrupt
GETVEC
EQU
035H
; DOS function to get int vec
ES:BX
SETVEC
EQU
025h
; DOS function to set int vec
DS:DX
0 VEC
dd
0
; storage for int 1C vector
C DS
dw
0
•
9
C's data (DGROUP) segment
TIC SP
dw
0
; sp for tic()
SP ON INT
dw
0
•
9
sp upon entry of _CINT_HAND
SS ON INT
dw
0
•
9
ss on entry
TIC ON FLAG
dw
0
; a flag to see if ticon() is
set
RET VAL
dw
0
; return value for.ticon()
DAT
dw
lOOd
dup(O)
; Storage for 80287 parameters
STATE
dw
lOOd dup(O) ; Storage for 80287
parameters
ASSUME
cs:
TEXT
, ds: DGROUP, ss: DGROUP
ticon PROC NEAR
push bp
mov bp, sp
pusha
push ds
push all registers
save segment regs

265
push es ;
cmp [TIC_ON_FLAG],0
je putiton ;
mov [RET_VAL],1
but
jmp return
tic already on)
putiton:
mov [TIC_ON_FLAG],1
calls
mov [C_DS],ss ;
mov ax,sp ;
sub ax,CSTACK ;
below call
mov [TIC_SP],ax
CSTACK !!
mov al,INTNUM ;
mov ah,GETVEC ;
int DOSINT ;
mov WORD PTR [0_VEC],bx
mov WORD PTR [0_VEC+2],es
mov ax, WORD PTR [0_VEC] ;
cmp ax,VECOFF ;
jne bad ;
mov ax, WORD PTR [0_VEC+2]
cmp ax,VECSEG ;
jne bad ;
vector
mov [RET_VAL],0
address ok
too!
; see if tic is off
if not, put it on
; otherwise do nothing
; return value 1 (for
; set flag for additional
save DGROUP
set interrupt stack CSTACK
; Limits C's stack to
Use DOS int 21 func 35h
to get original
int 1C vector into ES:BX
; and store in OLD_VEC
; ..done
/
test for proper initial
; set return value 0 for
mov dx,OFFSET
mov ax,_TEXT
mov ds,ax
mov a1,INTNUM
mov ah,SETVEC
int DOSINT
jmp return
CINT_HAND ; set address of _CINT_HAND
!
; set code segment as well
; and use DOC func 25h
; to load it into vector table
; ..done
bad: ; if previous interrupt vector
unknown
mov ax,WORD PTR [0_VEC] ; set return value to
egual
mov [RET_VAL],ax ; offset of installed vector
; and return without installation
return:
pop es
pop ds
popa
mov sp,bp
mov ax,[RET_VAL]
; restore seg regs
restore all registers
; send return value in ax

266
pop bp
; (return is unsigned)
ret
•
9
return to caller
_ticon
ENDP
page
ticof f PROC
NEAR
push bp
•
9
mov bp,sp
7
pusha
9
mov ax,[TIC_ON_FLAG]
; Test flag to see
is enabled
or ax,ax
•
9
jz noton
•
9
;must be on
push ds
•
9
push es
; save seg regs
mov [TIC_ON_FLAG],0
mov dx,WORD PTR [0_VEC]
_ticon
mov ds,WORD PTR [0_VEC+2]
mov al,INTNUM
mov ah,SETVEC
int DOSINT
pop es
pop ds
noton:
popa
mov sp,bp
pop bp
ret
ticoff ENDP
_isticon PROC NEAR
mov ax,[TIC_ON_FLAG]
ret
isticon ENDP
Clear flag
; get vector stored by
and reinstall with DOS
..done
restore seg regs
; restore all registers
; return to caller
page
CINT HAND
sp
PROC FAR
mov [SP_ON_INT],sp
mov [SS_ON_INT],ss
mov sp,[TIC_SP]
mov ss,[C_DS]
pusha
pushf
push ds
; Far call from ROM BIOS?
; store whatever was in
; and ss
; setup 'interrupt' stack
; pointer and segment!
now push all parameters

267
push es
on stack
everything on 286 saved
waitl: ; wait until 80287 free
fnstsw ax
and ax,08000h
jnz waitl
cli
fsave cs:STATE ; save 80287 state
fwait ; wait til done
sti
cld
C)
mov es,[C_DS]
registers for
mov ds,[C_DS]
call tic
wait2:
fnstsw ax
and ax,08000h
jnz wait2
cli
frstor cs:STATE
fwait
sti
clear direction flag (needed in
; setup other segment
; 'small' memory model
call C tic function (no args)
; wait until 80287 free
; restore 80287 state
; wait til done
pop es
pop ds
popf
popa
mov sp,[SP_ON_INT]
mov ss,[SS_ON_INT]
iret
CINT HAND ENDP
t
I
; restore 286 registers and flags
; restore old sp
; and ss
; return? (we hope!)
JTEXT ENDS
END
• i***********************************************************
FILENAME: PRSCRN()
PAGE 60,132
COMMENT $
prscrn() SUBROUTINE:
void prscrn(void);

2 68
Calls interupt 5h to implement screen dump
$
. 286c
_TEXT SEGMENT BYTE PUBLIC 'CODE'
PUBLIC _prscrn
ASSUME CS:_TEXT
_prscrn proc near
push bp
mov bp,sp
pusha
push ds
push es
INT 5H ; call the prscrn interupt routine
pop es
pop ds
popa
mov sp,bp
pop bp
ret
_prscrn ENDP
_TEXT ENDS
END
FILENAME: PTIC.ASM
page 60,132
COMMENT $
************************************************************
TIC FUNCTIONS
Version date = 10/07/86
/Pjb
use with Microsoft C version 4.00
MODEL)
(SMALL MEMORY
unsigned ticon(void);
Installs a timer tic interupt handler at interupt
vector 1C.
present interrupt freguency is 18.2 Hz
Each timer interrupt will invoke a C function named

Return Value:
0 if Tic turned on OK
1 if Tic was already on

269
? offset of int vector 1C if different from
expected and
Tic was not on.
void ticoff(void);
Turns off the function call. MUST BE CALLED
BEFORE EXITING
THE MAIN PROGRAM THAT CALLED !!!
unsigned isticon(void);
returns a 1 if tic is being repetatively invoked and 0
if not.
The _CINT_HAND cannot interrupt itself. Therefore a
tic routine
that takes too long will slow the repetition frequency
of interrupts
never allow the host program to regain control. Be
careful!
RESTRICTIONS
The Stack Size of the host C program must not exceed
the value of
CSTACK (now 0x2000=8k) minus the stack allocation at
the time of the
call to ticon(). The host program must be linked with
a stack
segment exceeding this value by the expected size of
the interrupt
stack. I suggest a link stack size of 0x4000 giving
approximately
8k for the interrupt stacks use.
************************************************************
$
. 286c
.287
EXTRN _TIC:NEAR, fpreset:NEAR
_TEXT SEGMENT BYTE PUBLIC 'CODE'
TEXT ENDS

270
CONST
SEGMENT
WORD PUBLIC
'CONST'
CONST
ENDS
BSS SEGMENT WORD
PUBLIC 'BSS
9
BSS ENDS
DATA
SEGMENT
WORD PUBLIC
'DATA'
DATA
ENDS
DGROUP
GROUP
_CONST,
BSS, _DATA
TEXT
SEGMENT
PUBLIC
TICON
, _TICOFF, _ISTICON ;
INTNUM
EQU
OlCh
9
Interrupt to be intercepted
VECSEG
EQU
OFOOOh
; Expected Segment of
int
1C vec
VECOFF
EQU
0FF53h
; Expected offset of
int
1C vec
CSTACK
EQU
02000h
; Host Stack Size
DOSINT
EQU
021h
9
DOS function interrupt
GETVEC
EQU
035H
•
9
DOS function to get int
vec
ES: BX
SETVEC
EQU
025h
9
DOS function to set int
vec
DS: DX
0 VEC
dd
0
•
9
storage for int 1C vector
C DS
dw
0
; C's
data (DGROUP) segment
TIC SP
dw
0
9
sp for tic()
SP ON INT
dw
0
; sp
upon entry of CINT HAND
SS ON INT
dw
0
; ss
on entry
TIC ON FLAG
dw
0
9
a flag to see if ticon()
is
set
RET VAL
dw
0
•
9
return value for ticon()
DAT
dw
200d
dup(0)
•
9
Storage for 80287 parameters
ASSUME
cs:
TEXT
, ds: DGROUP
, ss: DGROUP
_TICON
PROC
NEAR
push
bp
•
9
mov ]
bp, sp
•
9
pusha
push ds
push es
cmp [TIC_ON_FLAG],0
je putiton
mov [RET_VAL],1
but
jmp return
tic already on)
push all registers
save segment regs
too!
; see if tic is off
if not, put it on
; otherwise do nothing
; return value 1 (for
putiton:

271
mov [TIC_ON_FLAG],1
calls
mov [C_DS],ss ;
mov ax,sp ;
sub ax,CSTACK ;
below call
mov [TIC_SP],ax
CSTACK !!
mov al,INTNUM ;
mov ah,GETVEC ;
int DOSINT ;
mov WORD PTR [0_VEC],bx
mov WORD PTR [0_VEC+2],es
mov ax, WORD PTR [0_VEC] ;
cmp ax,VECOFF ;
jne bad ;
mov ax, WORD PTR [0_VEC+2]
cmp ax,VECSEG ;
jne bad ;
vector
mov [RET_VAL],0
address ok
; set flag for additional
save DGROUP
set interrupt stack CSTACK
; Limits C's stack to
Use DOS int 21 func 35h
to get original
int 1C vector into ES:BX
; and store in OLD_VEC
; ..done
9
test for proper initial
; set return value 0 for
mov dx,OFFSET _CINT_HAND
; mov dx, WORD PTR [0_VEC]
(for Debug)
mov ax,_TEXT ;
mov ds,ax ; set code
; mov ds, WORD PTR [0_VEC+2]
backi (for Debug)
mov al,INTNUM ; and use
mov ah,SETVEC ; to load
int DOSINT ; ..done
jmp return ;
set address of _CINT_HAND
set old vector offset back
segment as well
â–  set old vector segment
DOC func 25h
it into vector table
bad: ; if previous interrupt vector
unknown
mov ax,WORD PTR [0_VEC] ; set return value to
egual
mov [RET_VAL],ax ; offset of installed vector
; and return without installation
return:
pop es
pop ds
popa
mov sp,bp
mov ax,[RET_VAL]
pop bp
ret
TICON ENDP
9
; restore seg regs
; restore all registers
9
; send return value in ax
; (return is unsigned)
; return to caller
page

272
TICOFF PROC NEAR
push bp
mov bp,sp
pusha
mov ax,[TIC_ON_FLAG] ; Test flag to see if
is enabled
or ax,ax ;
jz noton ;
/must be on
push ds
push es
mov [TIC_ON_FLAG],0
mov dx,WORD PTR [0_VEC]
_ticon
mov ds,WORD PTR [0_VEC+2
mov al,INTNUM
mov ah,SETVEC
int DOSINT
save seg regs
Clear flag
; get vector stored by
7
and reinstall with DOS
..done
pop es
pop ds
noton:
popa
mov sp,bp
pop bp
ret
; restore seg regs
; restore all registers
7
/
; return to caller
TICOFF ENDP
_ISTICON PROC NEAR /
mov ax,[TIC_ON_FLAG]
ret ;
_ISTICON ENDP
page
_CINT_HAND PROC FAR
mov [SP_ON_INT],sp
sp
mov [SS_ON_INT],ss
mov sp,[TIC_SP]
mov ss,[C_DS]
pusha
pushf
push ds
push es
on stack
mov es,[C_DS]
registers for
mov ds,[C_DS]
/
; Far call from ROM BIOS?
; store whatever was in
; and ss
; setup 'interrupt' stack
; pointer and segment!
; now push all parameters
; everything on 286 saved
; setup other segment
; 'small' memory model
cli

273
fsave _TEXT:DAT
bytes above stack
fwait
sti
cld
C)
; save 80287 state in 94
; wait til done
clear direction flag (needed in
call tic
call C tic function (no args)
cli
frstor _TEXT:DAT
fwait
sti
restore 80287 state
wait til done
pop es
pop ds
popf
popa
mov sp,[SP_0N_INT]
mov ss,[SS_ON_INT]
iret
CINT HAND ENDP
9
9
9
; restore 286 registers and flags
; restore old sp
; and ss
; return? (we hope!)
_TEXT ENDS
END
j***********************************************************
FILENAME: SAVE.ASM
•A**********************************************************
; SAVE 8-11-85 (SMALL memory
version)
•
9
; The function to save part of screen.
; Called from C progs in form
; save(yl,xl,y2,x2,to_seg)
; where xl & yl = coordinates of upper left corner of the
block to be saved
; x2 & y2 = coordinates of lower right corner
; to_seg = segment address for saving the block
•
9
•A**********************************************************
*
TEXT SEGMENT BYTE PUBLIC 'CODE'
ASSUME CS: TEXT
PUBLIC
save

274
xl
dw
?
yi
dw
7
x2
dw
7
y2
dw
7
count
dw
7
stop
dw
7
displayl
equ
0B800H
odd
equ
01FFFH
proc
NEAR
push
bp
mov
bp,sp
push
ax
push
bx
push
cx
push
dx
push
ds
push
es
push
si
push
di
mov
bx,[bp+6] ;
get xl
mov
xl,bx
mov
bx,[bp+4] ;
get yl
mov
yi, bx
mov
bx,[bp+10]
; get x2
mov
x2, bx
mov
bx,[bp+8] ;
get y2
mov
y2, bx
mov
ax,displayl
; from seg
mov
ds, ax
mov
bx,[bp+12]
; to_seg
mov
es,bx
mov
ax, yl
mov
dx,320
mul
dx
add
ax, xl
mov
si, ax
; from_off
mov
di, ax
; to_off
mov
ax, x2
sub
ax, xl
add
ax, 2
mov
count,ax ;
counts
mov
ax,y2
add
ax, 1
mov
dx,320
mul
dx
add
ax, xl
mov
stop,ax
; set end
cmp
si,stop
jg
outl
doit

275
cld
mov
cx,count
rep
movsb
add
si,odd
add
di,odd
std
mov
cx,count
rep
movsb
sub
si,odd
sub
di,odd
add
si, 80
add
di,80
cmp
si,stop
jl
doit
outl:
cld
pop di
pop si
pop
es
pop
ds
pop
dx
pop
cx
pop
bx
pop
ax
mov
sp, bp
pop
bp
ret
save
endp
TEXT
ends
end
FILENAME:
STL.ASM
; do the mov [DS:SI] —> [ES:DI]
; do odd row
; mov odd row
; back to even row
stl(xl,yl,x2,y2,color)
model)
; version date = 8-11-85
(SMALL memory
ROUTINE TO DRAW A LINE ON A MEDIUM RESOLUTION SCREEN
From "BLUEBOOK OF ASSEMBLY ROUTINES FOR THE IBM PC & XT"
By C.L. MORGAN
adapted for linking with Microsoft C programs
by pjb
TEXT
SEGMENT
BYTE PUBLIC 'CODE'
PUBLIC
stl
ASSUME
cs: TEXT
xl
dw ?

276
x2 dw
7
yl dw
7
y2 dw
7
color
dw
7
deldx
dw
7
deldy
dw
7
delde
dw
7
delsx
dw
7
delsy
dw
7
delse
dw
7
delp
dw
7
dels dw
7
stl
storey:
storex:
proc
NEAR
push
bp
mov
bp/sp
push
bx
push
cx
push
dx
push
si
push
di
push
ax
mov
bx,[bp+4]
mov
xl, bx
mov
bx,[bp+6]
mov
yi, bx
mov
bx,[bp+8]
mov
x2, bx
mov
bx,[bp+10]
mov
y2, bx
mov
bx,[bp+12]
mov
color,bx
mov
si, 1
mov
di, 1
mov
dx,y2
sub
dx, yl
jge
storey
neg
di
neg
dx
mov
deldy,di
mov
cx, x2
sub
cx, xl
jge
storex
neg
si
neg
cx
mov
deldx,si
cmp
cx, dx
jge
setdiag
mov
si, 0

277
setdiag:
storedelsxy:
lineloop:
xchg
cx, dx
jmp
storedelsxy
mov
di, 0
mov
dels,cx
mov
delp,dx
IliOV
delsx,si
mov
delsy,di
mov
si,xl
mov
di,yl
mov
ax,delp
sal
ax, 1
mov
delse,ax
sub
ax, cx
mov
bx, ax
sub
ax, cx
mov
delde,ax
inc
cx
mov
dx,color
push
ax
push
bx
push
cx
push
dx
straight:
diagonal:
lineexit:
mov bh,
0
mov
al,dl
mov
cx, si
mov
dx, di
mov
ah, 12
int
lOh
pop
dx
pop
cx
pop
bx
pop
ax
cmp
bx, 0
jge
diagonal
add
si,delsx
add
di,delsy
add
bx,delse
loop
lineloop
jmp
lineexit
add
si,deldx
add
di,deldy
add
bx,delde
loop
lineloop
cld
pop
ax
pop
di
pop
si
page
0!
write dot

278
stl
TEXT
pop
dx
pop
cx
pop
bx
mov
sp, bp
pop
bp
ret
endp
ends
end
FILENAME: STL6.ASM
page 60,132
COMMENT $
stl6(xl,yl,x2,y2) xl,x2,yl,y2 unsigned
Version date = 09-03-86 \pjb
ROUTINE TO DRAW A STRAIGHT LINE ON A MODE 6
SCREEN
ADAPTED FROM "BLUEBOOK OF ASSEMBLY ROUTINES FOR THE
IBM PC & XT"
By C.L. MORGAN
for linking with Microsoft C Version 3.0 programs
$
. 286c
_TEXT SEGMENT BYTE PUBLIC 'CODE'
_TEXT ENDS
_CONST SEGMENT WORD PUBLIC 'CONST'
_CONST ENDS
_BSS SEGMENT WORD PUBLIC 'BSS'
_BSS ENDS
_DATA SEGMENT WORD PUBLIC 'DATA'
_DATA ENDS
DGROUP GROUP _CONST, _BSS, _DATA
ASSUME CS: TEXT, DS: DGROUP, SS: DGROUP, ES: DGROUP
_TEXT
SEGMENT
public
stl6
xl
dw
7
x2
dw
7
yi
dw
7
y2
dw
7
deldx
dw
deldy
dw
delde
dw

279
delsx
dw
7
delsy
dw
7
delse
dw
7
delp
dw
7
dels dw ?
_stl6
PROC
NEAR
push
bp
mov
bp, sp
pusha
mov
bx,[bp+4]
mov
xl, bx
mov
bx,[bp+6]
mov
yi, bx
mov
bx,[bp+8]
mov
x2, bx
mov
bx,[bp+10]
mov
y2, bx
mov
si, 1
mov
di, 1
mov
dx,y2
sub
dx,yl
jge
storey
neg
di
neg
dx
storey:
mov
deldy,di
mov
cx, x2
sub
cx, xl
jge
storex
neg
si
neg
cx
storex:
mov
deldx,si
cmp
cx,dx
jge
setdiag
mov
si, 0
xchg
cx, dx
jmp
storedelsxy
setdiag:
mov
di, 0
storedelsxy
:
mov
dels,cx
mov
delp,dx
mov
delsx,si
mov
delsy,di
mov
si,xl
mov
di,yl
mov
ax,delp
sal
ax, 1
mov
delse,ax
sub
ax, cx

28.0
mov
sub
mov
inc
bx, ax
ax, cx
delde,ax
cx
lineloop:
pusha
push ds
***
write a dot to x=si y=di
* * *
; fetch y
into al
Set video segment
mov ax,0B800h
mov ds,ax
Calculate Video address offset
mov ax,di
mov ah,al ; move y
and ax,01FEh ; mask off unwanted parts
(y/2) *16 + (y%2)*2048
into bx
bx = (y/2)*16
; ax = (y/2)*64 + (y%2)*8k
address = y*80 + adjust for even\odd
get x-coord
(x/8)
this is the video address offset
shl ax,3
mov bx,ax
and bh,7
shl ax,2
add bx,ax
mov ax,si
sar ax,3
add bx,ax
Calculate bit mask
mov ax,si
and ax,00007h
fetch x
mask off first three bits of
times
mov cx,ax
mov ax,00080h
shr ax,cl
mov cx,ax
or ds:[bx],cl
straight:
diagonal:
Restore
the registers
pop ds
popa
cmp
bx, 0
jge
diagonal
add
si,delsx
add
di,delsy
add
bx,delse
loop
lineloop
jmp
lineexit
add
si,deldx
add
di,deldy
add
bx,delde
; set count register to x%8
load 128 into ax
; shift ax to the right ax&7
; cx is the pixel mask
; add new pixel
(done)

281
loop
lineloop
lineexit:
popa
mov
SP, bp
pop
bp
stl6
ret
endp
_TEXT
ENDS
END
FILENAME VIDIO.ASM
PAGE 60,132
TITLE _vidio SUBROUTINE
; VERSION DATE 10-13-86
7
version 3.00
; void vidio(unsigned
*,unsigned *);
(SMALL memory version)
/Pjb
For use with Microsoft C
*,unsigned *,unsigned
; Call as: vidio(&AX,&BX,&CX,&DX);
/
BX,
where the arguments are pointers to the C variables AX,
CX, DX.
.286c
TEXT SEGMENT BYTE PUBLIC 'CODE'
PUBLIC _vidio
ASSUME CS: TEXT
9
_vidio proc NEAR
PUSH BP
MOV BP,SP
pusha
mov si,[BP+4]
;get
mov ax,[si]
/•put
mov si,[BP+6]
/•get
mov bx,[si]
/•put
mov si,[BP+8]
/•get
mov cx,[si]
/•put
mov si,[BP+10]
/•get
mov dx,[si]
/•put
INT 10H
; ca
routine
pointer to AX
AX in ax register
pointer to BX
BX in bx register
pointer to CX
CX in cx register
pointer to DX
DX in dx register
1 the vidio_io interupt
mov si,[bp+10]
mov [si],dx
mov si,[bp+8]
mov [si),cx
;get pointer to DX
;update DX value
;get pointer to CX
/update DX value

282
mov si,[bp+6]
mov [si],dx
mov si,[bp+4]
mov [si],ax
old
popa
MOV SP,BP
POP BP
RET
vidio endp
TEXT ENDS
END
FILENAME: WMOVE.ASM
PAGE 60,132
TITLE wmove - BLOCK MOVE FUNCTION (SMALL memory
model)
•a**********************************************************
; void
wmove(unsigned,unsigned,unsigned,unsigned,unsigned,unsigned)
;get pointer
/update BX
;get pointer
/update AX
/ clear direction
to BX
to AX
flag for C return
/ A simple word string block move function to be called from
C progs.
•
/
/ use in form
9
wmove(from_seg,from_off,to_seg,to_of f,count,direction)
/where from_seg = source segment ( 0 uses current DS
from C prog.)
/ from_off = source offset
/ to_seg = destination segment ( 0 uses current ES
from C prog.)
/ to_off = destination offset
/ count = number of bytes to move
/ direction= direction of move ( 0=foreward, else
backward)
/ VERSION DATE = 10-13-1986
/Pjb
•A**********************************************************
*
. 286c
_TEXT SEGMENT BYTE PUBLIC 'CODE'
ASSUME CS: TEXT

283
PUBLIC wmove
wmove proc NEAR
push
bp
mov
bp, sp
pusha
push
ds
push
es
cld
mov
ax,[bp+14]
or
ax, ax
jz
set_regs ;
std
/
set_regs:
mov
si,[bp+6] ;
mov
ax,[bp+8] ;
or
ax, ax
register?
jz
thisseg ;
mov
es, ax
this seg:
mov
di,[bp+10]
index
mov
cx,[bp+12]
mov
ax,[bp+4] ;
or
ax, ax
DS register?
jz
doit ;
mov
ds, ax
doit:
rep
movsw
; set for foreward direction
; get direction
; is direction foreward?
yes - don't change direction flag
no - set for backward move
get from_off & put in source index
get to_seg
; is to_seg the current C prog ES
if so, stay in this seg.
; set destination segment
; get to_off & put in destination
; put count in count register
get from_seg
; is from_seg the current C prog.
if so, let's go
; set source segment
; do the move [DS:SI] —> [ES:DI]
cld
(required for C)
pop es
pop ds
popa
mov
sp
pop
bp
ret
wmove
endp
TEXT
ends
; insure direction flag cleared
/
/
; restore registers
end
*********************************************************

APPENDIX C
ANALYTIC PAIR POTENTIALS
Lennard-Jones Potentials
One of the goals of this research is to establish a
potential energy surface that will accurately describe the
interatomic forces of an inductively bound pair. Even with
little spectroscopic data, some fundamental analytic
potentials may be parameterized. In the case of Lennard-
Jones types potentials the determination of single adjustable
parameter reveals the vibrational frequency, ve, the
Dissociation energy, De, and the internuclear distance, re.
An approximation for the potential energy surface of a
transition-metal rare gas diatomic is given in analytic form
by Lennard-Jones [8,4]. The attractive part is described by
the polarizability over re4. The repulsive part is
proportional to l/re8. The form of the potential is then given
by the following equation117
U{z) = -2- - (39)
r8 2r4
where a is the polarizability for the rare gas species, e is
the proton charge, and /? is an adjustable parameter fit to
284

285
experiment data. For transition-metal rare gas diatomic
systems the polarizability may be closely approximated to that
of the rare-gas atom. Thus, the analytic equation becomes
adjustable with a single parameter, /3.
Often experimental data is sufficient enough to determine
the equilibrium vibrational frequency, vef or the dissociation
energy De, and in some instances both. With a single
adjustable parameter in the Lennard-Jones expression only one
experimentally determined parameter is necessary to determine
all the others, i.e., De, ve, or re. This appendix derives
expressions relating or De, to /3, re, and ke, the force
constant, using cgs units.
The first derivative of Eq. (39) is ?ero at r = re,
dU(re) = _q£ + 2oce2 = Q (40>
The second derivative of Eq. (39) is defined118 as the force
constant ke,
&U(re)
dr
720 _ lOae2
.10
(41)
Solving Eq. (40) for /3 results in the following expression:
P =
(42)

286
Substituting this back into the potential energy Eq. (39) , one
may express /3 in terms of the dissociation energy De/ recall
that U(re) = -De,
P =
g2e4
16 V
(43)
The internuclear distance may be easily expressed in terms of
the dissociation energy by combining Eq. (42) and Eq. (43) ,
then solving for re/
r
e
1/4
(44)
Conversely the dissociation energy may be expressed in terms
of re:
D
e
(45)
Substitution of from Eq. (42) into Eq. (41) results in
an expression relating the force constant to internuclear
distance as:
ke =
8 or re = y^e1/3^)
ke
1/6
(46)
The force constant may be expressed in terms of De by
substitution of Eq. (44) into Eq. (46), as:
(ekj 2/3 K =
64 V2
ey/a
or De =
16
(47)

287
For a harmonic oscillator the equilibrium vibrational
frequency, vc is a function of the force constant and the
reduced mass, /¿,
v
e
_i_ ti
2n \ n
(48)
Substitution of ke from Eq. (47) into Eq. (48) one may relate
v. and D„ as follows:
4 D.
3/4
=
na1/4 (ne)1/2
it v 4/3
or De = (—-^) a1/3 (jxe) 2/3
(49)
Another useful equation is the relation of the vibrational
frequency to the internuclear distance, which may be
determined by the substitution of Eq. (45) into Eq. (49):
1/3
v*=
/ 2a e
V V nr
or r - <2“)1/6(_íL
)
(50)
These manipulations may be done for other Lennard-Jones
potential energy expressions. The most relevant of these
relations, i.e., with respect to inductively bound systems,
the [12,4], [8,4] and [6,4] have been determined, and are
displayed in the following tables.

288
Table 18. Lennard-Jones [8,4] Relations.
v*
K=
H (27tvJ 2
Dl'2
64 *
a1/2e
4 z?j/4
a1/4 (ne) 1/2rc
De=
_L_o1/3 (jxe) 2/3 (itve) 4/3
&=
1 ( a5e10 x i/3
24^3 fi2(iive)4
a2e4
16Z?e
re=
2«(“)1/‘( e )1/3
_i_e1/2 ( —)1/4
De
For CoAr+ ; De = 2.8688 (ve)4/3 where v is in cm'1.
For CoKr+ ; De = 4.2314 (i>e)4/3 where v is in cm'1.

289
Table 20. Lennard-Jones [6,4] Relations.
"e
De
ke=
H (2nve) 2
r,3/2
4'6>3/2JV
a1/2e
"e=
6D¡/a
a1/4(ne) 1/2tc
De=
(-£)1/3 (^e) 2/3 (ve7i) 4/3
O
0=
1 / a4e8 »i/3
3 v2e*2n
e3a3/2
3y/ZD¡/2
re=
( a ) 1/6 ( e ) 1/3
1 e1/2 ( a ) V4
6>'* ‘V

290
Table 22. Lennard-Jones [12,4] Relations.
"e
Dc
*e=
\l (2rcve) 2
£)3/2
16 (3>3/2 7,2
a1/2e
"e=
d3/4
2 (3) 3/4 *
a1/4(*ie) 1/2m
De=
, * a1/3(ne)2/3Uve)4/3
3(2) 4/3
0=
25/3 { a7e14 v1/3
3 n4n8v|
a3e6
54 D\
re=
21/3 ( a ) i/6 ( e ji/3
1 pi/2 / a ) i/4
3^ lK.

291
Born-Mever Potential
The second type of analytic potential that has been found
to adequately describe the interactions of a transition-metal
cation with a rare gas atom is the Born-Meyer potential. The
attractive part of this potential is also described with a
1/r4 term. The repulsive part of the analytic function
involves an exponential term. Again, approximating the
polarizability of the interaction with that of the rare-gas
atom the Born-Meyer is of the following form:
U{r) = be~r/p - C/r4 (51)
The two adjustable parameters in the equation, b and p may be
calculated from the experimentally determined dissociation
energy and vibrational frequency. Unlike the Lennard-Jones
type potentials, two experimental quantities must be available
to uniquely determine the potential surface. For many of the
systems previously discussed, both the dissociation energy and
the vibrational frequency may be determined, thus leaving only
re to be predicted by the parameterization of the potential
function. In this case a polynomial expression in re may be
derived as a function of ve and De.
The first and second derivative of Eq. (51) are listed
The first derivative is zero at re:
below.

292
U'UJ = e’r

(52)
The second derivative is defined as the force constant, k
U"{re) = -Ae“r#/p - =
= k.
(53)
Equation (51) is equal to the dissociation energy, De, at
re. Solving Eq. (51) for the exponential: (By convention
U(rJ) = -De)
e"r*/p
(54)
Similarly, solving Eq. (52) for the exponential results in
q ~ZJ P = p4C
brl
And finally, for Eq. (53) one gets
e"r*/p = £ (k + i2£) .
D r6
(55)
(56)
Now we may eliminate both the exponential term and the
adjustable parameter b with the combination of Eq. (54) and
Eq. (55) and the combination of Eq. (55) and Eq. (56) .

293
Setting Eq. (54) and Eq. (55) equal to other and solving for
p we get the following equation:
P = -¿(Cr. - Der¡) . (57)
Setting Eq. (55) and Eq. (56) equal to each other we get the
following equation:
p (k rj + = 4C. (58)
re
By substituting Eq. (57) into Eq. (58) and rearranging we get
a polynomial in re;
kD
-—2 r¿°+ icr| - 20De r* + 4C =0.
Recall that the force constant may be expressed in terms of
the vibrational frequency and reduced mass as follows:
k = 4n2o¿l\i.
Substituting this expression into the above equation we get a
polynomial in re that may be solved numerically given the
experimentally determined terms of the vibrational frequency
and dissociation energy,
(47i2w|n) (rj - -^re10) - 20Der\ + 4C = 0.
Once rc is known one may determine p from Eq. (57) . The
constant C is determined from the polarizability, a, and is

294
defined as q2a/2, where q is the proton charge. The other
adjustable parameter b will follow from Eq.(54).

APPENDIX D
UNASSIGNED PHOTODISSOCIATION SPECTRA
During the course of the research, a number of spectra
for various systems have remained unassigned. Many of these
spectra are included as figures in this section. Note, none
of the spectra have been rigorously calibrated, but they are
not inaccurate by more than ± 15 cm'1. The relative accuracies
of band positions, within a given spectrum, are good to ca.
± 2 cm1.
295

18000 19000
20000
21000 22000
23000
Laser Frequency (wavenumber)
Figure 57. Photodissociation Spectrum of Fe2+.

Ni Photocurrent
297
60Ni16O +
“ní 16o*
*
y
n 1 r
iW^Jí
I I
«y
16900 17300 17700 18100
Laser Frequency (wavenumber)
Figure 58. Photodissociation of NiO+ -» Ni+ + O.

15100
Figure 59.
15300 15500 15700 15900 16100
Laser Frequency (wavenumber)
Photodissociation Spectrum of ZrOAr+ -*• ZrO+ +
Ar.

Relative Zr+ Photocurrent
299
Laser Frequency (wavenumber)
Figure 60. Photodissociation Spectrum for Zr(OCO)+ -+ Zr+ +
OCO.

Relative Co+ Photocurrent
300
15000 16000 17000 18000
Laser Frequency (wavenumber)
Figure 61. Photodissociation of Co(HOH)+ -*• Co+ + H20.

Relative Co+ Photocurrent
301
Laser Frequency (wavenumber)
Figure 62. Photodissociation of Co(OCO)+ -*• Co+ + C02.

Relative Co+ Photocurrent
302
15800 16200 16600 17000 17400 17800
Laser Frequency (wavenumbers)
Figure 63. Photodissociation of Co(NN)+ -» Co+ + N2.

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59. S. H. Linn, J. M. Brom, Jr., W.-B. Tzeng and C. Y. Ng, J.
Chem. Phys. 82 (1985) 648.
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61. C. W. Bauschlicher Jr., H. Partridge, S. R. Langhoff, J.
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62. H. Partridge, C. W. Bauschlicher Jr., and S. R. Langhoff,
J. Phys. Chem., 96 (1992) 5350.
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64. P. M. Holland and A. W. Castleman, Jr., J. Chem. Phys. 76
(1982) 4195.
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Soc. Ill (1989) 4100.
66. M. Karplus, R. N. Porter, Atoms & Molecules: An
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307
67. H. Partridge, C. W. Bauschlicher, Jr., and S. R.
Langhoff, J. Phys. Chem., 96 (1992) 5350.
68. G. von Helden, P. R. Kemper, M-T Hsu, M. T. Bowers, J.
Chem. Phys., 96 (1992) 6591.
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BIOGRAPHICAL SKETCH
The author was born September 27, 1962, to Donald W.
Lessen and Gayle A. Lessen in Lincoln, Illinois. He graduated
from Lincoln High School in 1980, enrolled the following fall
at Southern Illinois University, and received an Associates
degree in electronic technology in the spring of 1982. After
one summer of work in this field he returned to SIU in the
fall of 1982. Four years later he graduated with a Bachelor
of Science degree majoring in chemistry. From the fall of
1986 to the present the author has studied physical chemistry
as a graduate student at the University of Florida.
On September 21, 1991, he was married to Christine
Erickson.
310

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
5hilip Jj. 'Bruéatf Chairirtári
Associate Professor of Chemistry
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
!
William Weltner
Professor of Chemistry
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
'Jl/C
Martin Vala
Professor of Chemistry
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Mark Meisel/”
Assistant Professor of Physics
This dissertation was submitted to the Graduate Faculty
of the Department of Chemistry in the College of Liberal Arts
and Sciences and to the Graduate School and was accepted as
partial fulfillment of the requirements for the degree of
Doctor of Philosophy.
December 1992
Dean, Graduate School





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