Spectroscopic characterization of novel cluster ions


Material Information

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


Subjects / Keywords:
Dissociation   ( lcsh )
Transition metals   ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
bibliography   ( marcgt )
non-fiction   ( marcgt )


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

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Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001813006
oclc - 29233126
notis - AJN6897
sobekcm - AA00004743_00001
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Full Text









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.







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


Threshold to Photodissociation .
Resonant Photodissociation of VAr*

. . ii

. . V

. . vii

. . x

. . 1

. . 7

. . 10
. . 19
. . 27
. . 36

. .

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

Analytic Potentials . .
Vibrational Eigenvalues from
Approximation . .

. .
* .
. .
. .

. .
. .
. .

. .
. .
. .

. .


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). .








. .

Threshold Photodissociation of Cr2 186
Photodissociation of Ca2 . .. 194



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

Lennard-Jones Potentials . ... 284
Born-Meyer Potential .. . 291


REFERENCES . ... 303



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. .







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


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.

Figure 32.

Figure 33.

Figure 34.

Figure 35.

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


. . 90











. .

. .

* .

. .

* .

. . . 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










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



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+.


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


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


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


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


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


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




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


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.





Ion Optics

MCP Detector


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.


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


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


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

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.


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


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


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


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

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


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


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


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


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"


(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


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


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


50 60 70 80 90 100
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.


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


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'.


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-

50 100 150 200 300 400 500 600 700

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.


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


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

E 40


: 10


Figure 6.
The figure
(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


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




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
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].


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





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


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.


> 0.16
-D -
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


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.


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


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


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


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.


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


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


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



200 Sweet

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.


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


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


I -


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.


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.




0 2 4 6 8
Laser Fluence (mJ/pulse)
Figure 12. Laser Fluence Dependence for Photodissociation of
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.


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:


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





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.


Table 2. Ground State Spectroscopic Parameters for NiAr+ and

"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


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.


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



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


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


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


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.
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


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,.


- 17000 V +
E VKr +

S16500- A

S 16000 VAr

. 15500

I /
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'


30- A
3 25-
r A
o 20



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


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.


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


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.


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.


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.


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)

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)

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


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

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


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)


180 A

160 A
m A
140 -

2 120

0 100 -

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)


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' -
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.


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.


7 -

6 VAr +



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


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


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





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.


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.


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

v' observe. o-c' v' observ. o-c" v' observ. o-c*





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






Table 5.

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







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





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 .

o 17000 "

S15000 ALA

.o 14000-

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.


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


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


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


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,




< 80 -


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.


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,.


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.