Title: Electron spin resonance and optical spectroscopy of hydrocarbon radicals at 4°K in raregas matricas / by Keith Ingram Dismuke
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Title: Electron spin resonance and optical spectroscopy of hydrocarbon radicals at 4°K in raregas matricas / by Keith Ingram Dismuke
Physical Description: xiii, 193 leaves. : : ill. ; 28 cm.
Language: English
Creator: Dismuke, Keith Ingram, 1948-
Publication Date: 1975
Copyright Date: 1975
 Subjects
Subject: Radicals (chemistry)   ( lcsh )
Hydrocarbons -- Spectra   ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 191-192.
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00098927
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000580747
oclc - 14081020
notis - ADA8852

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ELECTRON SPIN RESONANCE AND OPTICAL SPECTROSCOPY OF
HYDROCARBON RADICALS AT 4 K IN RARE-GAS MATRICES



















by

KEITH INGRAM DISMUKE















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



UNIVERSITY OF FLORIDA

1975




































to

My Family














ACKNOWLEDGEMENTS


The author extends his deep appreciation to Professor

William Weltner, Jr., whose professional guidance and

support made this research possible. The author acknowl-

edges a special debt of gratitude to Dr. W. R. M. Graham,

for his collaboration and informative discussions during

the entire period of this work.

The author would also like to thank the members of

Professor Weltner's research group as well as the staff

of the machine and glass shops for the fabrication of

experimental apparatus.

The completion of this dissertation would not have

been possible without the love, support, and professional

typing ability of the author's wife, Lin, to whom the

author extends a very special appreciation.

The author would also like to acknowledge the support

of the Air Force Office of Scientific Research and the

National Science Foundation during this work.
















TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS ..... ........... .. ... iii

LIST OF TABLES . . . . . . ... ... . .vii

LIST OF FIGURES . . . . . . . . . ix

ABSTRACT . . . . . . . . ... . . . xi

Chapters

I INTRODUCTION . . . . . . . . 1

The Matrix Isolation Technique . . . 1
References Chapter I . . . . . 5

II EXPERIMENTAL . . . . . . . 6

Introduction . . . . . . . 6
Experimental . . . . . . . . 6
Reagents . . . . . . . 6
Apparatus and General Technique . .. 6
References Chapter II . . . . .. 22

III ESR THEORY . . . . . . . ... 23

Introduction .. ... . ... ... 23
Spin Hamiltonian for 2E Molecules .... 24
g Tensor . . . . . . . ... 28
A Tensors . . . . . . . .. 34
Spin Hamiltonian for 3Z Molecules ... . 37
Hyperfine Interaction for 3Z Molecules 41
Solution to the Spin Hamiltonian for
2Z Molecules and the Observed Spectrum 41
Solution to the Spin Hamiltonian for
3Z Molecules and the Observed Spectrum 52
Derived Molecular Parameters . . . .. 63
Coefficients of the Wave Functions . 63
Spin Densities . . . . ... 64
Ac and the Spin-Doubling Constant . 65
References Chapter III . . . . .. 68












IV C2H RADICAL . . . . . . . .


Introduction . . . . .
Experimental . . . .
ESR Spectra . . . . .
ESR Analysis . . .
g Tensor . . . . .
A Tensors . .
Forbidden Transitions .
Spin-Doubling Constant .
Optical Spec ra . . . .
10,0000 Bands, A2H. X2Z
3000 Bands, B2 I X2Z or
Discussion . . . . .
Hyperfine Tensors and Spin
g Tensor . . . . .
Optical Transitions . .
Summary . . . . .
References Chapter IV . .

V M C2 AND C2 RADICALS ...


B A' X2 .

Density
. .
, . . .
. . . .


Introduction . . . . . .
Experimental . . . . . .
Optical Spectra . . . . .
Optical Analysis . . . . .
ESR Sptctra and Analysis . . .
X 2- ... .
M C2 . . . . .
MC
Discussion . . . . . .
g Tensor . . . .
A Tensors . . .
Absence of the ESR Spectrum of
References Chapter V . . .

VI C4H RADICAL . . . . . .

Introduction . . . . . .
Experimental . . . . .
Optical Spectra and Analysis . .
Electronic Spectra . . .
Infrared Spectra . . . .
ESR Spectra and Analysis . . .
Discussion . . . . . .
Electronic Transitions . ..
Infrared Transitions . . .
ESR Observations . . . .
References --Chapter VI . . .


Page

71









Page

VII C4 MOLECULE . . . . . . .. 168

Introduction . . . . . . 168
Experimental .. . . . . . 169
ESR Spectra . . . . . . .. 170
ESR Analysis . . . . . . 176
Optical Spectrum and Analysis . . .. 179
Discussion . . . . . . . 183
Optical Transitions . . . . 183
g Tensor . . . . . . 184
A Tensors . . . . . . . 186
Zero-Field Splitting Parameter (D) 186
References Chapter VII .. . ... 191

BIOGRAPHICAL SKETCH . . . . . . . ... 193














LIST OF TABLES


Table Page

I Hyperfine splitting parameters for 13C H in the 83
2Z ground state in an Ar matrix

II Observed ESR lines in gauss for 22113C2H isolated 84
in solid argon at 4 K

III Isotropic and anisotropic hfs of 13C2H and 87
derived matrix elements

IV Bands of 2H. X2Z transition of C H in Ar at 93
-40K 1 2
~4oK

V Bands observed in the 3000 R region for C H:Ar 94
at 4K

VI Comparison between observed hfs parameters for 99
C2H and values obtained from INDO calculations

VII Approximate coefficients of Y(X2E) derived from 101
A tensors for C2H, and comparison with CN

VIII Hyperfine structure and spin doubling constants 104
from matrices and interstellar gas measurements

IX Tpansitions observed for X C and the ion pairs 116
M C2 (M = Li, Na, K, Cs) trapped in Ar at- 4 K

X T4ansitions observed for X 3^C and ion pairs 117
M 13C (M = Li, Na, K, Cs) tripped in Ar at
-4K 2

XI Dipole moment calculations for M C2 122

XII Cclculated ionicities and AG1/2 for C2 and 123
M C2

XIII Components of the g and A tensors for the M C2 127
species

XIV The isotropic constants and dipolar tensor 138
components derived from the alkali cation hfs
for M C2 (M = Li, Na, K)











XV Vibrational assignments for the 3000 R transi- 150
tions of C4H:Ar at 4K

XVI Vibrational assignments for the 3000 8 transi- 151
tions of C D:Ar at 4 K

XVII Vibrational assignments for the 3000 8 transi- 153
tions of C H:Ne at 4K

XVIII The frequency of vibrational modes in X2E ground 164
state and the 2H excited states of C4H and C4D
compared with the corresponding modes of C4H in
the 'I ground state
g
XIX Observed ESR lines in gauss for 12C /Ar, 177
13C4/Ar, and 12C4/Ne isolated at 4 0

XX Calculated D values for 2C isolated in argon 180
matrices at various temperatures

XXI Transitions observed for 12C in argon matrices 182
at 4K


viii


Table


Page














LIST OF FIGURES


Figure Page

1. Basic design features of variable temperature 9
liquid-helium dewar used for optical studies

2. Basic design features of liquid-helium dewar 11
used for ESR studies

3. Basic design features of variable-temperature 13
liquid-helium dewar used for ESR studies

4. Schematic drawing of flowing hydrogen-helium 17
quartz electrodeless discharge lamp

5. Emission spectrum from hydrogen-helium discharge 18
lamp measured through a LiF optical window

6. Idealized absorption line shape for a randomly 46
oriented system having an axis of symmetry and
no hyperfine interaction (gi < g i)

7. Theoretical absorption and first derivative 47
spectra for randomly oriented system having an
axis of symmetry and no hyperfine interaction
(9g< gjl)

8. Absorption line shape and first derivative for a 48
system with orthorhombic symmetry (gxx > gyy > g

9. First derivation absorption pattern for randomly- 51
oriented molecules with hyperfine splitting from
one nucleus with I = 1/2 (gll > gl, All > A)

10. Energies of the triplet state in a magnetic field 54
for a molecule with axial symmetry (HI[z)

11. Energies of the triplet state in a magnetic field 56
for a molecule with axial symmetry (Hlz)

12. Axial resonant fields with E = 0 for varying D 59
from 0 to 1.0

13. Theoretical ESR absorption pattern and first 61
derivative spectra for a randomly oriented triplet
system for a given value of D' and v (E = 0).









14. ESR spectrum of 12C2H isolated in argon at 4 K 74

15. Predicted hyperfine splitting for a mixture of 77
C H molecules containing all possible combinations
or 2C and '3C isotopes

16. ESR spectrum observed for C H:Ar at 40K produced 79
by the photolysis of 90% 13 substituted C2H2

17. ESR spectrum of '2''3C2H species at 4 K arising 81
from the natural abundance of 13C in the photoly-
sis products of 12C2HI

18. A comparison of the calculated ESR spectrum with 85
the observed for the outer doublet in which the
C nucleus of C H is 13C substituted
a 2
19. Optical spectra of M C2 (M = Li, Na, K, and Cs) 114
isolated in argon matrices at 4 K

20. ESR spectra of M+C (M = Li, Na, K) isolated in 125
argon matrices at oK

21. A comparison between the observed ESR spectrum 128
and the powder pattern spectrum calculated from
an exact solution of the spin Hamiltonian for
Na C2

22. The geometry and molecular orbital scheme for 132
M C2

23. Optical spectra of C4H and C4D isolated in argon 147
matrices at 4K

24. Optical spectrum of C4H due to CrC fundamental 149
vibrations, v2 and 3, isolated in argon matrices
at 4 K

25. Infrared spectra of C4H and C4D isolated in argon 155
matrices at 40K

26. E4R spectrum of C4H isolated in argon matrices at 157
4K

27. Theoretical absorption and first derivative 171
spectra for randomly orientated triplet (E = 0)

28. ESR spectra of 2C4 and '3C, isolated in argon 172
matrices at 40K -

29. ESR spectra of C isolated in argon matrices 175
at various temperatures


Page


Figure









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


ELECTRON SPIN RESONANCE AND OPTICAL SPECTROSCOPY OF
HYDROCARBON RADICALS AT 4K IN RARE-GAS MATRICES


by

KEITH INGRAM DISMUKE

March, 1975


Chairman: Professor William Weltner, Jr.
Major Department: Chemistry


Radical and molecular species including C2H, C2 ,

C4H, C4, and M C2 where M represents various alkali

metal cations, have been studied by the methods of

electron spin resonance (ESR) and optical spectroscopy.

This work employed the techniques of matrix isolation

whereby the radicals to be studied were trapped in inert,

solid rare-gas matrices at liquid helium temperatures.

From ESR spectra, magnetic parameters of the radicals

such as g tensors, hyperfine interaction tensors (hf),

and zero-field-splitting tensors (D) are determined.

The value of these quantities allows the derivation of

fundamental quantities such as the spin-doubling constant,

Y, the electronic spin density at the site of a nucleus,

Y(0) 2, coefficients of the wavefunctions, and others.

This is supplemented by optical measurements taken









in the infrared, visible, and ultraviolet regions from

which vibrational and electronic energy level separations

can be determined.

The ethynyl radical, C2H, was prepared by the high-

energy photolysis of two different parent molecules,

acetylene and monoiodoacetylene. This research led to

the detailed characterization of the electronic and magnetic

properties of C2H, including complete spin density data

of the ground state and the identification of several

excited electronic states. It was determined that C2H,

in the ground state, is a linear 2E molecule with the

unpaired electron localized largely on the end carbon

nucleus. The possibility is also proposed that C2H

undergoes bent linear electronic transitions. The

results obtained in this work make possible the identifica-

tion of the previously unobserved C2H radical in inter-

stellar clouds.

Previous matrix isolation studies have shown that

the optical spectrum of C2 is enhanced upon the addition

of the alkali metal atoms (M). When the alkali metal

concentration is increased, it was found that C2 and

the alkali metal cations form ion-pairs (M C2 ). Analysis

has demonstrated that the C-C vibrational frequency in the

excited state is dependent on both size and polarizability

of the alkali metal used. Approximate ground state hf









coupling constants were determined. The shape of M C2 -

based on ESR analysis, is a triangular conformation with

C2v symmetry.

The previously unidentified C4H radical, predicted

to be a relatively abundant polyatomic species in the

atmospheres of carbon-rich stars, has been produced by

the high-energy photolysis of diacetylene (C4H2). The

ESR spectrum consisted of a doublet at g = 2.0004 due

to the magnetic interactions of the unpaired electron

and the hydrogen nucleus indicating an expected 2E ground

state. C4H absorbs strongly in the 3000 R region, with

progressions attributed to excitation of the C-H, C-C,

and two CEC symmetric vibrations. A C-C-H bending node

was also excited in the 3000 R system. The identification

was confirmed by the effects of isotopic substitution.

From the value of gi of C4H, a predicted value of y has

been determined, a value which may aid in the future

observation of C4H in interstellar atmospheres.

C4 has been prepared by two completely different

methods including the photolysis of C4H2 with high-energy

radiation and the vaporization of graphite. The ESR

spectra of both '2C4 and '3C4 have been observed and

analyzed, confirming that the ground state of C4 is 3Z.

From this analysis, the D value has been determined for

various conditions illustrating that the derived D value

is dependent upon the matrix environment, isotopic

composition, and temperature. From gj = 2.0042, Y for

C4 is predicted to be -0.0006 cm-1


xiii














CHAPTER I
INTRODUCTION


The Matrix Isolation Technique

Optical and electron spin resonance spectroscopy are

routinely used in the investigation of molecules in the

gas phase. Some molecules are very difficult or even

impossible to observe in the gas phase because of their

short lifetimes, reactivity, and/or method of preparation.

Some molecules are observed only under high temperature

conditions, for example in the atmospheres of stars or

in arcs, so that as a result of thermal excitation into

many rotational, vibrational, and low-lying electronic

states, the optical spectra are often quite complicated

and difficult to interpret. Even if the analysis problems

are solved, ambiguities may arise in the assignment of

the ground state because of the population of low-lying

electronic states. Other short-lived species, such as

free radicals, may be highly reactive or have very short

lifetimes thus making it impossible to produce a large

enough concentration for gas-phase observations.

In the matrix isolation technique, high temperature

species, reactive molecules, or free radicals are prepared

and trapped as isolated entities in inert, transparent

solids, or matrices, at cryogenic temperatures. These










trapped species can then be studied by optical or electron

spin resonance techniques more or less at leisure. The

isolated species do not undergo translational motion--i.e.,

diffusion--and are usually prevented from rotating, but

may vibrate with frequencies within a few percent of the

gas-phase values when excited with electromagnetic radiation.

Thus, the spectra of the material in these matrices are

frequently much simpler than those for any other state

of matter as they will show no rotational structure and

all absorptions will occur from the lowest vibrational

state of the ground state.

Several methods are employed for the production of

these species. A typical method used is the evaporation

of an active species from a Knudsen cell. The evaporated

species can then be deposited simultaneously with the inert

matrix material. The formation of many radicals does not

involve evaporation but the photolytic dissociation of a

parent molecule during deposition. If the parent is a

gas, then standard gas-handling techniques are employed

and one may either mix the gas with the matrix gas in

the desired proportion prior to spraying onto the

cryogenic surface or co-condense the materials from

separate gas inlets. Photolytic dissociation may be

carried out by subjecting the material to radiation by

high-energy sources such as microwave or electric dis-

charges, ultraviolet lamps, or gamma rays, or by electron









or ion bombardment. It is evident from this discussion

that if the isotopically-substituted parent species is

available, the investigation of the isotopically-sub-

stituted radical or molecule presents no problem.

The matrix material can be any gas which will not

react with the trapped species and which can be con-

veniently and rigidly solidified; however, it should be

chosen to have little effect on the trapped species so that

they will be in as nearly a gas-like condition as possible.

The solid rare gases are usually used as matrices since

they are relatively inert chemically, transparent to

light over a wide wavelength region, and offer a wide

range of melting points and atomic sizes. Since a neon

matrix has the least polarizable atoms, it is expected to

perturb the molecule least and is usually found to be

the best matrix. However, since it melts at 240K and

diffusion in the solid state probably begins at about

120K, it can only be used with liquid helium as a

refrigerant. It is found that, in general, the heavier

rare gases perturb the trapped molecules more then argon

and neon and therefore are less desirable as matrix

media.

SThere are some disadvantages to the matrix isolation

technique. The principal disadvantage is the effect of

the matrix on trapped species. Such effects caused by

the matrix environment, usually manifested as small










frequency shifts, multiple structures, and variation in

absorption intensities, are often complicating factors

in the initial spectral interpretation. A quantitative

explanation of the precise nature of the interactions

causing these perturbations is still lacking although

much work has been directed toward this problem. For

examples of theoretical treatments of matrix effects,

see (1-6).

This introduction is not designed to discuss in

depth the subject of matrix isolation techniques. How-

ever, several very good review articles and books have

been written on this technique and many aspects of

the methods used. Extensive details and reviews on

matrix isolation as applied to atomic and molecular

studies have been given by Bass and Broida (7), Jacox

and Milligan (8), Weltner (9), and Hastie, Hauge, and

Margrave (10).












References Chaoter I



1. G. C. Pimentel and S. W. Charles, Pure Appl. Chem.
7, 111 (1963).

2. E. D. Becker and G. E. Pimentel, J. Chem. Phys. 25,
224 (1956).

3. M. J. Linevsky, J. Chem. Phys. 34, 587 (1961).

4. M. McCarty, Jr. and G. W. Robinson, Mol. Phys. 2,
415 (1959).

5. E. S. Pysh, S. A. Rice, and J. Jortner, J. Chem.
Phys. 43, 2997 (1965).

6. D. McLeod, Jr. and W. Weltner, Jr., J. Phys. Chem.
70, 3293 (1966).

7. A. M. Bass and H. P. Broida, Formation and Trapping of
Free Radicals, New York: Academic Press, Inc.,
1960.

8. M. E. Jacox and D. E. Milligan, Appl. Opt., 3, 873
(1964).

9. W. Weltner, Jr., Advances in High Temperature Chemistry,
New York: Academic Press, Inc., 1970, Vol. 2,
p. 85.

10. J. W. Hastie, R. H. Hauge, and J. L. Margrave,
Spectroscopy in Inorganic Chemistry, New York:
Academic Press, Inc., 1970, Vol. 1, p. 57.















CHAPTER II
EXPERIMENTAL


Introduction

The general experimental procedure including apparatus,

reagents and techniques employed in this research will be

treated in this section and specific details relevant to

the study of a species will be presented under that given

species.


Experimental

Reagents

In a typical experiment, a sample of some small organic

gas molecule was premixed by standard manometric procedures

with a gas which was to be used as the inert solid when

trapped for observations at 4 K. The inert gases employed

were research grade rare gases (99.999% pure), usually

argon and occasionally neon or krypton, which were ob-

tained from commercial sources and used without further

purification.


Apparatus and General Technique

In this research all experiments were carried out

on two separate dewars both of which were adapted from

the design of Jen, Foner, Cochran, and Bowers (1). One

dewar is designed primarily for ESR experiments and the









other for optical experiments. Both systems are comprised

of an outer liquid nitrogen dewar which acts as a heat

shield and an inner liquid helium dewar which is in good

thermal contact with the trapping surface. The inner

dewar is positioned such that the trapping surface is

directly in the path of the sample inlets. Both systems

are designed so that the inner dewar is interchangeable

in order to hold either a variable temperature or constant

temperature liquid helium dewar.

For constant temperature optical studies, the inner

dewar consists of a deposition window which is in contact

on all four sides with a copper holder filled with liquid

helium. The holder is designed so that the deposition

windows are interchangeable and rotatable through 3600

By rotating the inner dewar by approximately 900, the

deposition window is directly in line with two windows

in the wall of the outer container so that optical

studies are made possible. By rotating the window

approximately 900 more, the trapping surface is now in line

with another window in the outer container which can be

used for photolysis of the sample.

The material of the outer window and deposition

window will depend upon which optical region is to be

studied. For an infrared study, all windows should

be made of cesium iodide (CsI) which transmit radiation

through the visible out to about 60u. Calcium fluoride









(CaF2) windows are used for study in the ultraviolet and

visible regions with either a CaF2 or sapphire deposition

window.

Figure 1 shows the basic features of the variable

temperature dewar used for optical studies. The liquid

helium reservoir is connected to a copper block by

1/8 inch stainless steel tubing. Again a deposition

window is fitted into the copper block so as to be in

contact on all four sides with the cooled block. The

reservoir is pressurized to about 2.5 psi causing the

liquid helium to flow through channels in the copper block

cooling it to liquid helium temperature. The rate of flow

of the helium is regulated by a Hoke micrometer needle

valve at the outlet. A thermocouple (Constantan vs.

Au 0.02 at.% Fe) is connected as closely as possible

to the deposition window for temperature measurements.

Temperature measurements are made using the thermocouple

in conjunction with a Leeds and Northrup potentiometer.

To vary the temperature of the window, the micrometer

needle valve can be closed to limit the flow of liquid

helium into the lower chamber. As the helium evaporates,

it forces the liquid out of the channels in the copper

block thereby causing a rise in the temperature. The

temperature change is carefully followed by monitoring

both the temperature and pressure in the dewar. The







































COPPER


WINDOW


1 j






~I-A


Figure 1: Basic design features of variable-temperature
liquid-helium dewar used for optical studies.










window and matrix can be quickly quenched back to liquid

helium temperature by opening the needle valve and

allowing the liquid to flow again.

Figure 2 shows the dewar arrangement as well as the

furnace system used for constant temperature ESR

experiments. The trapping surface is single crystal

sapphire (1-1/4" long, 1/8" wide, 3/64" thick) with one

end securely embedded by Wood's metal solder into the

inner dewar which is cooled to 4 K. By means of a

vacuum-tight bellows assembly located at the top of

the dewar (not shown in the Figure) the sapphire rod

can be lowered or raised and rotated 360 inside or

outside of the microwave cavity. When the rod is in

the raised position, it is directly in line with the gas

inlet and any beam of high temperature molecules being

produced in the furnace. When the rod is in this

position, it is in the optical path of two inter-

changeable windows in the outer container which makes

it possible to photolyze a sample during or after deposition

or to study a sample optically. If the furnace section

has been used, after deposition of a sample, the entire

furnace assembly may be uncoupled from the dewar by a

double gate valve system without breaking the vacuum in

either section. Then the rod can be lowered into the

microwave cavity and.the entire dewar can be rolled on

fixed tracks between the pole faces of the ESR magnet.
















LIQUID He


LIQUID N2


WATER-COOLED


ROTATABLE VACUUM TEMPERATURE
SFLAP T [ r /_U ,' r T MEASUREMENT
SAPPHIRE
ROD



TO-
ROWAVE_ H NEON\
BRIDGE ;.. INLET SA.,pi WINDOW


UARTZ CELL
WINDOWW
'SLOTTED X-BAND CAVITY


QUARTZ
WINDOW


Figure 2: Basic design features of liquid-helium dewar
used for ESR studies.









The inner dewar design for variable temperature ESR

experiments is shown in Figure 3. As in the optical vari-

able temperature dewar, the desired temperature is obtained

by controlling the rate of helium flow through a copper

section at the bottom of the pressurized liquid helium

reservoir. A thermocouple (Chromel vs. Au 0,02 at.% Fe)

is connected to the copper section for temperature measure-

ments.

In preparing a matrix for study several different

techniques were employed depending upon the required

species. In some cases the substance to be isolated could

be prepared by photolysis of a gaseous parent molecule.

In other cases, the substance to be isolated could only be

prepared from a nonvolatile parent species. And in

some instances it was required to isolate both volatile

and nonvolatile species together.

If the species to be isolated could be prepared

from a volatile parent compound, standard manometric

techniques were employed to premix the inert gas with the

volatile parent compound in the desired proportion. The

gases could then be sprayed onto the cryogenic surface

and photolyzed either during or'after the deposition.

The rate at which the gases are introduced is controlled

by a needle valve adjustment and monitored by a Heise

Manometer.












T.C. Connection
- Pres. Release Valve


INNER CONTAINER
VARIABLE TEMPERATUI
ESR DEWAR


Figure 3: Basic design features of variable-temperature
liquid-helium dewar usec for ESR studies.


LIQ. He
Inlet \









When the species to be isolated could be prepared

only from a nonvolatile substance, a Knudsen cell was

used to produce a molecular beam from a parent substance

which was codeposited with the inert gas. Figure 2 shows

how the furnace section containing the Knudsen cell was

designed so that the trapping surface was directly in

line with the molecular beam. The cell to be resistance

heated was constructed of tantalum tubing which was

filled with the nonvolatile species. The cell was

supported on water cooled copper electrodes and heated

to the desired temperature. The temperature was measured

with either a vanishing filament optical pyrometer through

an 0-ring sealed glass viewing port equipped with a

magnetic shutter to prevent film formation on the glass

or a (Chromel vs. Alumel) thermocouple in conjunction

with a Leeds and Northrup potentiometer connected

directly to the tantalum cell. The distance between

the Knudsen cells in the furnace and the trapping

surface was approximately twelve centimeters.

The furnace and dewar are independently pumped

by mechanical and two inch silicone oil diffusion pumps.

When the dewar contains liquid nitrogen in the outer

shield and liquid helium in the inner dewar, pressures
-8
as low as 3 x 10 mm Hg are obtained while pressures
-6
down to 1 x 106 mm Hg were obtained with liquid nitrogen

in the furnace systems. Pressures were monitored by

Bayert-Alpert ionization gauges.









Some experiments require premixed gas to be co-

deposited with a nonvolatile substance in which case a

combination of the two techniques described above was

employed.

Two basic techniques were used for the production of

the desired molecular species or radical species. One

technique employed the previously discussed high-tempera-

ture Knudsen cell while in the other technique, various

parent materials were photolyzed with radiation from high-

energy sources including either a flowing hydrogen-helium

electrodeless discharge lamp or a high pressure mercury

lamp.

The mercury lamp consists of water cooled mercury

capillary lamp operated at 1000 watts (type A-H6

obtained from G. W. Gates & Co., Inc., N.Y., water

jacket is PEK-SEB type single ended water jacket obtained

from PEK labs). This lamp radiates energy in the ultra-

violet and visible region which is composed of two

principal components: (a) characteristic mercury line

spectra and (b) a strong base continuum.

To limit heating effect of the mercury lamp, it was

usually operated in conjunction with an ultraviolet

transmitting filter which was non-transmitting in the

visible and infrared regions. Normally a Corning 7-54

filter was employed. For photolysis of a sample with the

mercury lamp, the dewar was equipped with a quartz optical

window to transmit the ultraviolet radiation.









The flowing hydrogen-helium electrodeless discharge

lamp radiates high energy radiation in the vacuum ultra-

violet region. The lamp, shown schematically in Figure 4,

is constructed after the design of David and Braun (2).

A cylinder of the hydrogen-helium gas mixture (approxi-

mately 10 percent hydrogen by volume) was attached to the

lamp gas inlet. A mechanical forepump was employed to

evacuate the entire system to a pressure of about 30J

which effectively seals the lamp to a LiF window by means

of a brass fitting with two "0" rings. The gas flow was

then adjusted with a Hoke needle valve to a pressure

of approximately 1 torr. The gas mixture is led into

and out of the lamp with flexible Tygon tubing. The LiF

window was positioned in the dewar so that the incoming

parent material would be photolyzed by the radiation

produced by this lamp.

A Raytheon PGM 10, 85 W, 2450 MHz microwave generator

in conjunction with a tunable cavity was used to excite

the discharge in the flowing gas. Figure 5 shows the

emission spectrum from the lamp in the vacuum ultraviolet

region measured through a LiF optical window.

Due to the very high energy radiation being trans-

mitted by the LiF windows yellow color centers were

noticeable after five to ten hours of normal use of the

lamp. This cut the efficiency of the lamp measurably.

In order to rid the LiF windows of these color centers













GAS INLET
S MICROWAVE
CAVITY


LiF
OPTICAL
WINDOW


O-RINGS


VACUUM


SCALE


Figure 4: Schematic drawing of flowing hydrogen-helium
quartz electrodeless discharge lamp.

































1700 1500 1300 1100

WAVELENGTH (A)




Figure 5: Emission spectrum from hydrogen-helium flowing
discharge lamp measured through a LiF optical
window.









these windows were removed from the dewars and annealed

at approximately 800F for one to two hours. LiF

windows were changed and annealed normally after every

two or three experiments to maximize the efficiency of

photolysis and the yield of products.

As stated previously, the optical dewar could be

equipped with various windows and trapping surfaces in

order to analyze the prepared matrix in the regions ranging

from the infrared to the far ultraviolet.

For investigations of the infrared region (4000-
-l
200 cm -), a Perkin Elmer 621 spectrophotometer with

interchangeable grating and calcium fluoride prism

optics was used. Optical spectra in the range 3500

to 10,500 A were recorded using a Jarrell-Ash 0.5 m Ebert

scanning spectrometer with gratings blazed at 5000 A

and 10,000 A and fitted with RCA 1P21 or 7102 photo-

multipliers. A GE tungsten lamp provided the continuum

and spectra were calibrated with mercury lines from a

low pressure Pen Ray Quartz mercury lamp source. From

2000 to 3500 A an evacuated McPherson monochromator with

a RCA 941 photomultiplier monitoring the radiation from

the exit slits through a sodium salicylate window was

employed. The continuum was provided by a microwave

discharge through a lamp filled with xenon to a pressure

of approximately 400 torr.









ESR spectra were recorded on a Mosely 2D-2 XY

recorder with the Varian V-4500 instrument employing

superheterodyne detection. The magnetic field was

measured by using an Alpha Scientific Model 675 NMR

fluxmeter whose frequency was determined with a Beckman

6121 counter. The X-band microwave cavity frequency

(v = 9.4 GHz) was measured with a Hewlett Packard high

Q wavemeter.

For a typical experiment the area around the

trapping surface was evacuated to a pressure as low as

possible (= 2 x 10- mm of Hg) with a mechanical and

a silicone oil diffusion pump. The outer dewar was filled

with liquid nitrogen and then the inner dewar was pre-

cooled with liquid nitrogen prior to filling with liquid

helium. After the inner dewar was filled with liquid

helium, the temperature of the trapping surface was

near 4K.

The matrix gas was deposited at a rate of 0.1 to

0.3 1-atm/hr with a total consumption of approximately

300 cc (STP). The rate of deposition was maintained at

a steady rate throughout by needle valve adjustment with

the rate depending upon the effectiveness of production

of the desired species. If a metal was codeposited, the

temperature of the cell was adjusted such that the vapor

pressure of the metal produced in the furnace was

approximately 10-3 mm of Hg. Matrix components could





21




be photolyzed during or after deposition, or both, with

either the electrodeless discharge flow lamp or the mercury

lamp.

The products were then analyzed by means of optical

or electron spin resonance spectroscopy. If it was

necessary, experiments were performed on the variable

temperature dewars so that the matrices could be

annealed to any desired temperature and then observed

again.





22








References Chapter II

1. C. K. Jen, S. N. Foner, E. L. Cochran, and V. A.
Bowers, Phys. Rev. 112, 1169 (1958).

2. D. David and W. Braun, Appl. Opt. 7, 2071 (1968).















CHAPTER III
ESR THEORY


Introduction

The principles of ESR spectroscopy have been

thoroughly studied and are discussed in detail in a

number of excellent references (1-9). The basic

principles of ESR theory will be presented for molecules

of 21 type and in a later section, for molecules of 3E

type.

A 2E molecule is a linear molecule with zero orbital

angular momentum and one unpaired electron (S = 1/2,

L = 0). In the presence of an externally applied magnetic

field, the degenerate spin state will be split and the

difference in energy of the states will.be approximately

equal to ge H, where ge is the free electron g-factor

(2.0023), 9o is the Bohr magneton (eh/4imc = 9.2732

x 102 erg/G) and H is the strength of the magnetic

field. If electromagnetic radiation of frequency vo

is present which satisfies the resonance condition,


LE = hv = g B H, (1)
0 eo


where h is Planck's constant (6.6256 x 102 erg-sec),

transitions between these Zeeman levels can occur.










Resonances for a given microwave frequency do not always

occur at the same magnetic field strength so that g may

be taken as a parameter which governs the position of the

resonance absorption. In this study, an X-band instru-

ment with v = 9400 MHz was employed.


Spin Hamiltonian for 2Z Molecules

The terms in the general Hamiltonian for those

molecules in an external magnetic field can be written as


H = HE + HLS + HSI + HSH + HIH (2)


where:


HE is a composite term expressing the total kinetic

energy of the electrons, the coulombic attraction

between the electron and nuclei, and the repulsions

between the electrons

2
Pi Ze2 e2
HE = ( ) + (3)
E 2m ri ij r..


where pi is the momentum of the ith electron, and

r. is its distance from the nucleus. Z is the nuclear

charge. r. is the distance between electron i and

electron j. HLS represents the potential energy due

to spin-orbit coupling usually expressed in the form


HLS = L-S










where L and S are the orbital and electron-spin

angular momentum operators. A is the molecular

spin-orbit coupling constant.

HSI represents the hyperfine interaction arising

from the electron-spin orbital angular momentum

and magnetic moment interacting with any nuclear

magnetic moment present in the molecule and may be

expressed



[ L .I 3(S'r) (r-I)
HSI = iNgeo -r +
r r

S-I 8r6(r)S-I
+ = I-A-S (5)
r3 3


where I is the nuclear-spin angular momentum

operator, N is the nuclear magneton, g and gN

are the electronic and nuclear g factors and A is

a second order tensor (see discussion of A tensor

below).

This interaction consists of three parts. The

first involves a L-I interaction between the magnetic

field produced by the orbital momentum of the electron

with the nuclear moment. For a 21 molecule in

which L = 0, this term will be zero except for any

small orbital angular momentum entering through the

L~S interaction. The next two terms are the Hamiltonian









for the interaction of the two magnetic dipoles of

the nuclear magnetic moment and the magnetic moment

produced by the electron spin. This produces an
-3
angularly dependent term varying as r-3 and depends

upon the p or d character of the odd electron.

The last term represents the isotropic Fermi (contact)

term and depends on the spin density at the nucleus

i.e., on the s character of the odd electron. The

Dirac 6-function indicates that this term has a

non-zero value only at the nucleus.

HSH (Electron Zeeman term) represents the interaction

of the spin and orbital angular moment of the

electrons with the externally applied magnetic field

written


H =8 (L + g S) H (6)
SH o- e- -


where H is the magnetic field.

HIH (Nuclear Zeeman term) represents the interaction

of the angular moment of the nuclei with the exter-

nally applied magnetic field written


H h- Y'I. *H (7)
IH 2n i i 7)


where yi is the magnetogyric ratio of the ith nucleus.


The energy contributions from the various terms

vary over a wide range and it is obvious that HE and HLS









involve too much energy for excitation by ESR. HSI'

HSH and HIH involve energies ideally suited for ESR

and frequently HIH energies are too small to be observed

in the presence of HSI. Due to the magnitude of these

various interactions, other types of interactions are

neglected here since in general they are much smaller.

For detailed discussions of these terms, see references

(1-13).

Calculations with the general Hamiltonian are very

difficult; therefore, a simplified accounting of the

more likely interactions is performed with a spin

Hamiltonian (Hspin). In the spin Hamiltonian the terms

HE, HLS, and HSH are replaced by a single term -BH o-gS

where S is the effective electronic spin and 9 is a

second order tensor (see discussion on g tensor below)

(1). By convention S is assigned a value that makes

the observed number of energy levels equal to (2S + 1).

Thus we can relate all the magnetic properties of a system

to this effective spin by the spin Hamiltonian since it

combines all the terms of the general Hamiltonian which

are sensitive to spin.

If the nuclear Zeeman term (HIH) is neglected the

spin Hamiltonian can be written


H spin = BH o-S + HI
spin o SI


= BHo"g-S + IA*S .










g Tensor

In the absence of hyperfine interaction, the spin

Hamiltonian for S = 1/2 is


Hspin = BS-'H. (9)


The complete interaction of S and H must take into account

the effect of each component of S on each component of H.

For an arbitrary set (x,y,z) of orthogonal axes then


BS-g-H = xS YS z gxxgxygxz x

yx yy yz Hy
ag g H (10)
-zxgzygzz z


Sx, S and Sz are components of the effective spin

along the x, y, and z axes. g is strictly a 3 x 3 matrix

and is referred to as a symmetrical tensor of the second

order (6). The double subscripts on the g-tensor may

be interpreted as follows. gxy may be considered as

the contribution to g along the x-axis when the magnetic

field is applied along the y-axis. In general these

axes (x, y, z) are not the principal directions of the

g tensor, but by a suitable rotation of axes the-off-

diagonal elements of the g-tensor can be made equal to

zero. When the g-tensor is so diagonalized the components

along the diagonal, gxx g yy and gzz, then are the

principal directions of the g-tensor with respect to

the molecule.









As alluded to previously, the anisotropy of the

g-tensor arises from the orbital angular momentum of the

electron through spin-orbit coupling. The intrinsic

spin angular momentum of a free electron is associated

with a g factor of 2.0023 (14). However the electron

in a molecule may also possess orbital angular momentum.

The corresponding orbital angular momentum adds vectori-

ally to the spin angular momentum. Since the ground

states of many linear molecules have zero orbital angular

momentum (E states), it is likely that in these cases

the g-factor would have precisely the free-electron value.

However, the interaction of a presumably "pure spin"

ground state with certain excited states can admix a

small amount of orbital angular momentum into the ground

state. This interaction is usually inversely proportional

to the energy separation of the states and results in a

change in the components of the g-factor.

The orbital and spin angular moment will be coupled

through the spin-orbit interaction term, which may be

given as


HL= XL*S = [L S + LySy + LzS] (11)


This term must be added to the Zeeman terms in the

Hamiltonian i.e.


H = HSH + HLS = SH(L + g S) + ,L-S (12)
on ia -- e- -









For a E molecule, the ground state represented by

IG,Ms> is orbitally nondegenerate. The energy (to

the first order) is given by the diagonal matrix element

(6)


G(1) = +
ASz)L G,Ms> (13)


The first term represents the "spin-only" electron

Zeeman energy. The second term may be expanded as


.


For an orbitally non-degenerate state, equals

zero. The second-order correction to each element in the

Hamiltonian matrix is given by (6)



-E' I2
H = (14)
HMSM's W () WG )
n G


The prime designates summation over all states except

the ground state. Neglecting all zero terms and

expanding this, it is seen that the quantity A may be

factored out where


-Z'
A = (n ( (15)
W (0) W(0)
n G










and is a second-rank tensor. The ijth element of this tensor

is given by


-T'
A = n
SW (0) (0) (16)
n G


where L. and L. are orbital angular momentum operators

appropriate to the x, y, or z directions. Substitution

of this tensor into the term H SM S yields



HM = (17)
MS' S S - _ S

The first operator represents a constant contribution to

the paramagnetism and need not be considered further.

The second and third terms constitute a Hamiltonian

which operates only on spin variables. When combined with

the operator g SH-S, the result is called the spin

Hamiltonian H spin which may be written


H = BH-(g 1 + 2XA)-S + X2S.A-S = SH.j.S + S-D-S (18)
spin e- - -

where


g = ge1 + 2AA (19)


and


D = 2A .


(20)










The S.D-S term is effective only in systems with S > 1

and will be considered later, but for 2Z molecules it may

be deleted. The first term then is the spin Hamiltonian

given in the beginning of this discussion. It is evident

from this derivation that the anisotropy of the g-tensor

arises from the spin-orbit interaction due to the

orbital angular momentum of the electron.

If the angular momentum of a system is solely

due to spin angular momentum, the g-tensor should be

isotropic with a value of 2.0023. That is, the principal

components of the g tensor are g = g = gzz ge
xx -'yy zz e
2.0023. Any anisotropy or deviation from this value

results from the A tensor which involves only contribution

of the orbital angular momentum from excited states. For

a completely isotropic system, Hspin may be written


H spin = [x S yS 'ge 0 0 Hxl









system in which none of the x, y, and z axes are equivalent,
the spin Hamiltonian must be written
e y
0 0 g Hx (21)

= g Be S H + SYH + SH .


For a system with orthorhombic symmetry, i.e., for a

system in which none of the x, y, and z axes are equivalent,

the spin Hamiltonian must be written


H = =(g SH + g S II + g SH ) (22)
spin xx x x yy y y zz z z


Here gxx yy zz









Some systems may have an n-fold axis of symmetry

(n > 3). These systems are described as having axial

symmetry for which two axes are equivalent. The unique

axis is usually designated as z and the value of g

for Hi z will be called g I. If HIz, then the g value

will be termed g The spin Hamiltonian is then


Hspin = i(gSxH + gSyHy + g SZH) (23)


From the equation given for the g tensor (i.e. g =

g 1 + 2XA) the various components of the g-tensor can be

determined. The general formula, widely used in the

interpretation of ESR spectra, for the ijth term is

then (see 15-22).


gij = g 6j 2Xj'<0Li n>/E (24)


In this notation 6.. is the Kronecker symbol and E is
13 n
the energy separation of the state n, SM > from the

ground state. As shown, this result is obtained by

calculation of the second-order shift in energy of the

ground-state levels due to a combination of spin-orbit

coupling and Zeeman energies. In a similar fashion

Tippins (22) has extended these calculations to the

third-order for the energy shift of the ground state and

has determined to the second-order similar correction

terms for the g tensor components. Only the result of

these calculations will be given. It was found, letting








Xjk represent , that


Ag (2) 2 k(i/E.E (Z Y + X Y
zz2 = 2(i/jEk) oj jkko + ojYjkko

+ XjZ jkYko) Z(/E2)(IXoj 2 + IY j2)],(25a)


Ag (2) =2Z(i/EjE) (YjXjkZk + X YjkZ
xx 3k j k oj jk ko oj jk ko

+ YjZjkXko '(l/E2) (Y ojl2

+ IZoj 2)], (25b)


and

Ag (2) = A2 Z(i/EjEk) (ZojX kYk + Z Yjk


+ Y jkko) '(l/E2)( IX 12
ojZjkxko j oj

+ Iz oj 2)]. (25c)


For the special case of axial symmetry, it is evident
that Ag (2) = A (2 and Ag(2) (2) g (2)
Sthatzz ad A gxx =Agyy


A Tensors
As shown in the equation for HS the hyperfine
tensor A will be comprised of three types of interactions.
The first term which is dependent on L-I involves the
interaction between the magnetic field produced by the
orbital momentum and the nuclear moment. This term









will necessarily be zero for 27 molecules since L = 0,

except for any small orbital angular momentum entering

through the L'S interaction. The other interactions are

due to the amount of s-character of the wavefunction (the

Fermi contact term) and to the non-s-character of the wave-

function.

The interaction due to the s-character is called

Aiso since the interaction is isotropic. Fermi (23)

has shown that for systems with one electron the iso-

tropic interaction energy is given approximately by


Wi. =- -[WP (o)H 12H
iso 3 1 eUN (26)


where (0O) represents the wave function evaluated at

the nucleus (i.e. the s-character). Here He and HN

are the electron and nuclear magnetic moments, respectively.

The interaction due to the non-s-character of the

wavefunction is called Adip since it arises from the

dipole-dipole interaction of the electron and nucleus.

In a rigid system such as we have in matrix isolation,

this dipolar interaction gives rise to the anisotropic

component of hyperfine coupling. The expression for the

dipolar interaction energy between a fixed electron and

nucleus separated by a distance r is

He Hn 3(e -r) ('n r)
dipolar 3 (27)
r r5









HSI can be written then



HSI = Hiso + Hdip

= [A. + A ]T.S
iso dip

where


81N
Aiso = 9N gBNeo I(0) 2


Adip NBNge 3cos20-1
^ip V~o< 2r' >


The brackets indicate the average of the expressed

operator over the wave function Y. In tensor notation

(it can be seen that the dipolar component involves a

tensor interaction by expanding the vector notation

term for Hdip) then


HSI = I*A*S
SI


where A = A. 1 + T.
iso- -
Here 1 is the unit tensor

the dipolar interactions.

tensor may be given


and T

Thus


is the tensor representing

the components of the A


A.. = A. 1 + T.
1j iso- ij


(28)


(29)


(31)










By a method similar to that used for the g tensor,

the components of the A tensor for a completely isotropic

system may be written


A = A = A = A. (33)
xx yy zz iso


For a system with axial symmetry, we find


A = A = A Ais + Tx (34)
xx yy ] iso xx


and


Az = Al = A.is + T (35)


If the system exhibits a completely anisotropic

A tensor then


Axx / A Azz. (36)



Spin Hamiltonian for 3Z Molecules

Until now, we have considered only systems with

S = 1/2. In the absence of a magnetic field, the spin

states for these systems are degenerate.

For a system with two noninteracting electrons,

four electronic configurations may be constructed.


a(l)a(2) a(1) (2) B(1)a(2) 3(1)6(2)










Where interactions occur, these configurations are combined

into states which are either symmetric or antisymmetric

with respect to exchange of the electrons. These states

are (11)


a(l)a(2)
1 1
[a(l)B(2) + B(1)a(2)] --[a(1)B(2) B(l)a(2)].
/2 /2
(1) B(2)

Symmetric Antisymmetric


The multiplicity of the state with S = 1 is

(2S + 1) = 3. This is called a triplet state. Similarly

the state with S = 0 is called a singlet state. If the

two electrons occupy the same spatial orbital, only the

singlet state is possible. However, if the two electrons

occupy different spatial orbitals then both the singlet

and triplet states exist.

For systems with two or more unpaired electrons, the

degeneracy of these spin states may be removed even in

the absence of a magnetic field. This is called zero-

field splitting. If this separation is larger than the

energy of the microwave quantum, it may not be possible

to observe an ESR spectrum. If the splitting is less

than the energy of the microwave quantum, the resulting

ESR spectra will show considerable anisotropy.










At small distances, two unpaired electrons will

experience a strong dipole-dipole interaction. The

electron spin-electron spin interaction is given by

a spin-spin Hamiltonian (HSS). Written in terms of the

spin operators


,22 S S2 3(Sl*r) (S2r)
SS r22 (37)
r3 r5


Substitution of the scalar products and the total spin

operator S = S + S2 in the above equation leads to the

following form of the spin-spin Hamiltonian (4, 6, 8, 11)


HSS = S'D-S (38)


where D is a second-rank tensor with a trace of zero.

The individual components of the D tensor may be written

as


D j = (g2'2/2) < (r. 2 3 )/r 5 > (39)
Di3 ij


where i and j represent x, y, and z in the equation

r2 = x2 + y2 + z2, with r representing the distance

between the electrons. This tensor can be diagonalized

with the principal components equal to Dxx, Dyy, and D Z

For this axis system then


H = D S 2 + D S 2 + D S 2
SS xx x yy y zz z









where D + D + D = 0, This is customarily written
xx yy zz


S = -XS YS -2 ZS 2 (41)


where X = -Dx, etc. X, Y, and Z are the respective

energies of this system in zero magnetic field. Since

the tensor is traceless, the zero-field splitting can

be written in terms of just two independent constants

called D and E where D = -3Z/2 and E = 1/2(X Y).

Therefore, the correct spin Hamiltonian for S > 1 must

now be written


Hspin = S-*g.H + S-D-S (18)


or


Hspin = BS'g'H + D[S 2 1/3 S(S + 1)]

+ E[S 2 S 2] (42)
x y


where hyperfine interactions and nuclear Zeeman interac-

tions have been ignored.

For a linear molecule where z is the axis of symmetry

of the molecule, the x and y directions are equivalent

and the term involving E is zero. Then for S = 1 in a

linear case, H reduces to


Hspin = gsH S + g s(HS + H S ) + D(S2 2/3). (43)
spin zz xx yy z









Hyperfine Interaction for 3Z Molecules

The difficulties in observing hyperfine splitting

in randomly-oriented triplet molecules are usually caused

by the large line-widths; however, '3C, H, and F

hyperfine splitting have been observed (24-27).

Generally, the hyperfine interaction is small compared to

the fine structure (D term) and the electronic Zeeman

energy, so that first-order perturbation is sufficient

to account for the hfs. In linear molecules the tensors

g, D, and A must all be coaxial which simplifies inter-

pretation of the hfs. Then for one magnetic nucleus in

a linear molecule, the complete spin Hamiltonian can be

written


Hs = g HS + g(HxS + H S ) + D(S 2 2/3)
spin I IzZ jxx yzy

+ Al SI + A1(SI + SyI) (44)


neglecting any nuclear Zeeman interactions.


Solution to the Spin Hamiltonian for
2F Molecules and the Observed Spectrum

As shown previously, if nuclear effects are ignored,

the spin Hamiltonian reduces to


H spi = BS.H (9)


When g is diagonalized then


Hspin = (g1SH + g2SH + g3S H )


(45)









The energy of the levels (obtained from the eigenvalve

equation HIS,M > = EM IS,MS>) will then be given by (28)



E = SH H(g12sin20cos2t + g22 sinn2Sin2

+ g3 os2o)1/2 = BgHSHH (46)


where SH represents the component of spin vector S

along H, gH is the g-value in the direction of H, 0 is

the angle between the z-axis of the molecule and the

field direction and $ is the angle from the x-axis to

the line of the projection of the field vector in the

xy plane.

In the case of axial symmetry, gl = g2 = gi and

g3 = gll 9H reduces to


gH = (g2sin2 + g, cos 0)1/2 (47)

and the energy of the levels is given by


E = BSHH(g 2sin 2 + g2cos20)1/2 (48)


For the allowed transitions, what type of a

spectrum will be observed if the molecules are randomly-

oriented but rigidly held, as in a solid matrix? (See

29-40.) The spectrum will be independent of the angle

that the magnetic field makes with the solid sample.









Consider first the case of axial symmetry. If N
o
molecules are randomly oriented with respect to the

applied magnetic field, then the number within an increment

of angle dO, where 0 is the angle measured from the field

direction, is


N
dN = sin0d0 .(49)
2


That is, dN is proportional to the area of the surface

of a sphere included within an angle variation of dO;

the factor two enters because it is only necessary to

cover a hemisphere. The absorption intensity as a

function of angle is proportional to the number dN of

molecules lying between 0 and 0 + d3, assuming the

transition probability is independent of orientation.

Since g is a function of 0 for a fixed frequency v, the

resonant magnetic field is


H = --- (g, 12cs20 + g2sin2o)- 1/2 (50)


and from this


(g H /H)2 g ]2
sin20 = (51)
g12 g112


where go = (gl + 2g )./3









and


Ho = hv/goB. (52)


Therefore


-g Ho 2
sinOde -= H { (g1 2 g 2) (g H /H) 2
H3 I0I 0

g12}- 1/2dH. (53)


The intensity of absorption in a range of magnetic

field dH is proportional to


[dN/dHI = idN/de *Ijd/dHj (54)

N
where dN/dO = -- sino and de/dH is obtained from the

equation for sin0de. From the above equations


H = hv/g, j = goHo/gl at 0 = 00 (55a)


and


I = hv/gi = o H /g, at 0 = 900. (55b)


At these two extremes, the intensity of absorption varies

from


IdN/dHJ = Nog 10/2goHo(g, 2 g2) at 0 = 0 (56a)








to


IdN/dHlI= m at 0 = 90 (56b)

If the resonant field is plotted versus the magnetic field

the absorption will have the following shape (for

gl > g ), Figure 6. If the natural width of the lines

of the individual molecules contributing to this

absorption is considered then the sharp angles in the

above curve become rounded (33), and it takes the

appearance shown in Figure 7 (a). Since in ESR the

first derivative of the absorption curve is usually

observed the spectrum would then appear as in Figure 7 (b).

In the case of an orthorhombi& system in randomly-

oriented and rigidly held sample, instead of the two

turning points in the spectrum corresponding to g and

911' there will be three turning points corresponding

to gl' g2, and g3. The shapes of the absorption line
and to its derivative are given in Figure 8 (a) and

(b).

If now there is also hyperfine interaction in the

randomly oriented molecules the previously discussed

pattern will be split into 21 + 1 patterns, if one

nucleus of spin I is involved. The spin Hamiltonian for

an axially symmetric molecule is given


Hspin = 8[g SzHz + gi(SHx+ SyHy)] + AjSzIz

+ AI(SxIx + SyIy) (57)



























911, 9 H


Figure 6: Idealized absorption line shape for a randomly
oriented system having an axis of symmetry and
no hyperfine interaction (g1 < g )).








(a)












(b)


dl
dH





91



Figure 7: (a) Theoretical absorption and (b) first
derivative spectra for randomly-oriented
system having an axis of symmetry and no
hyperfine interaction (gi < g i).




























(a) gYY


'zz


Figure 8: (a) Absorption line shape for a system with
orthorhombic symmetry, (b) first derivative of
the curve in (a). (gxx 9yy > )








When g is given by equation (47), the nuclear hyperfine

splitting can be included in the equation for the resonant

magnetic field to a first-order approximation by (9)


hv K
H = gB mI (58)
gS gS I

where K2g2 = A 1g 12cos20 + A2g 2sin 0. The intensity

of absorption |dN/dHI, can again be derived and is found

to be


dN o 2cos0 (g 2 g12)goH
dH 2 g2 2g
m (g A 2 gi2A
B 2K
K(g| 2 g,2)2 (59)

g2


Here sinedO cannot be solved explicitly so that dN/dH

cannot be written as a function of only the magnetic

parameters. Equations 58 and 59 must be solved for a

series of values 0 to obtain the resonant fields and

intensities as a function of orientation. However

H = (goHo/gl) (miA11/8g1 ) at 0 = 00, (60a)

H = (goHo/gi) (mIA /Bg) at 0 = 90, (60b)


and again IdN/dHI -m at 0 = 900. The absorption pattern

for a randomly-oriented molecule in which there is also









hf interaction is then a superposition of 21 + 1 pattern

of the type shown in Figure 6. The first derivative of

that pattern is the observed spectrum. Figure 9 shows

a typical case in which g1l > gl and All > A Here

the patterns do not overlap so that the spectrum is

relatively simple. If overlap does occur, the total

absorption curve and its first derivative will be more

complicated. The best approach is to solve the given

euqations (58 and 59) by computer for a trial set of

magnetic parameters g and A for 0 = 0 to 900, and have

the absorption and its first derivative plotted as a

function of H. (For example, see ESR discussion

concerning C2H.)

It should be noted here that second order perturbation

theory applied to the spin Hamiltonian for axial symmetry

including hyperfine interaction yields results similar to

equation (58) for the allowed ESR transitions. This is

derived in Low (9) and given as



LE = hv = gBH + Km + 4A ( K2 ) I(I + 1) m2


1 An2 A g/ g
+ ( -- A )( --2 sin20cos2m2 (61)
2gHo K2 g2 /


where K and H are the same terms as given previously.
o




























AL


I, A I_- - -
911








Figure 9: First derivation absorption pattern for
randomly-oriented molecules with hyperfine
splitting from one nucleus with I = 1/2
(gl[ > g|, A ll > A,).









The same general techniques can be used to solve

for the spin Hamiltonian of various cases and then the

expected powder spectrum plotted. Several typical

situations have been illustrated by Atkins and Symons

(41). These cases cover examples of powder spectra of

radicals with one spin-1/2 nucleus, where g and A are

varied from isotropic to completely anisotropic forms,

and one spin-1 nucleus.


Solution to the Spin Hamiltonian for
3 Molecules and the Observed Spectrum

The solution to the general Hamiltonian is given.

by Wasserman, Snyder, and Yager (42) for the triplet

states of randomly oriented molecules. Here, the special

case for linear molecules will be briefly discussed.

Neglecting hyperfine and other spin-orbit interac-

tions, a linear triplet molecule in a magnetic field

will have the spin Hamiltonian:


Hspin = g9 THS + g9 (HxSx + HySy)


+ D(S 2 2/3) (43)


where z is the molecular axis.

The basis functions are the orthonormal spin wave-

functions


|+1> = 1a12>


(62a)









10> = I|Y12 + P1a2> (62b)



-1> = 182> (62c)


If y is chosen arbitrarily to be perpendicular to the

fixed magnetic field H, then H = 0 and the spin Hamiltonian

reduces to


spin = g9I HzS = gIHxSx + D(S2 2/3) (63)


Consider the cases now where (1) H is parallel to the

z axis and (2) when H is perpendicular to the z axis.

For case (1) with HI |z, H = H and H = 0 the matrix
2 x
of the Hamiltonian with respect to the basis functions can

be determined, the eigenvalues of which are


W+ = + gjBH (64a)

W = D (64b)
o 3

W D = H (64c)


with the corresponding eigenvectors 1+1>, 10>, and I-1>,

respectively. At zero field the +1 and -1 states are

degenerate and the appropriate wavefunctions are


S- ( +1 I-1>) = T (65a)
1 x

S 1 (+1> + -1>) = T (65b)
2 y

3 = 10> = T (65c)


The eigenvalues for Hi z are plotted versus H in Figure 10.














hi>


Hlz ,D POSITIVE


E=O


I-I>


0 1 2 34
911g H/D


Figure 10: Energies of the triplet state in a magnetic
field for a molecule with axial symmetry.


IT> ITy

ITz>








For case (2) Hiz, H = Hx, H = 0 and the roots of

the secular determinant are


W1 = D/3 (66a)

W = [-D/3 + (D2 + 4g 2 2H2)1/2]/2 (66b)

W3= [-D/3 (D2 + 4g 22H21/21/2 (66c)


Substitution of each of these eigenvalues into the

secular equation and solving for the eigenvectors, with

normalization, yields


S 1 [j+l> -1> ] = (67a)
1 x
1
D2 = cosa -- [1+1> + -1>] + sinalo> = T (67b)

D = sina-1[ I+1> + I-1>] + cosajo> = T (67c)
3 z


where tan2a = 2g1 H/D. As H approaches zero where a = 0,

the D. reduce to


i = T (65a)

= T (65b)
2 y

S= T (65c)
3 z

where T. are the same as for case (1). The eigenvalues

for Hjz are plotted versus H in Figure 11. Only at high

fields, where a -* H/4 do the lines become straight. In the

intermediate region, w and Y are mixed and lead to a
curvature of the energy with H.
curvature of the energy with H.






















H.z, D POSITIVE


E=O


0 1 2 3 4
gp H/D


Energies of the triplet state in a magnetic
field for a molecule with axial symmetry.


ITy>
ITx >
ITz>


Figure 11:









It is evident that the energy levels and the fields

at which transitions occur are dependent upon the orienta-

tion of the axis of the molecule relative to magnetic

field, i.e. the spectra of randomly-oriented molecules

will be broad and more difficult to observe.

If transition probabilities are considered, it can

be shown that with the oscillating magnetic field Hosc H,

transitions are allowed between energy levels characterized

by the following wavefunctions: (1) T -- T designated
x z
z1, (2) Ty *< T z22 (3) Ty Tx', xY2' and (4) Z 4- T x,

xy1. These transitions are indicated in Figures 10 and

11 and all correspond to AM = +1 transitions. When

H |oH, another type of transition is allowed (Y --- T ),
os c y z
referred to as a "forbidden" transition because it connects

the two outermost energy levels and corresponds to a

AM = +2 transition. The AM = 2 transition usually has

a finite transition probability when H is not parallel

to any of the x, y, or z axes, even if HoscIH (11).

Therefore for our experimental apparatus with HoscH,

the AM = 2 will be observable if D is not too large.

Employing the exact solution of the matrix of the

spin Hamiltonian, the resonant field positions for the

transitions can be determined (42). Then


(68a)


xy 2 = (g/g)2H 0( D')









H x22 = (g/gji 2H(H + D') (68b)


Hzl = (g /g D'I (68c)


Hz2 = (ge/g[ )(H + D') (68d)



where D' = D/g e. For the AM = +2 transition (6)

1 h V2 D2 1/2
AM = +2 gB 4 3


For a fixed cavity frequency of 9.39 GHz,

hv = 0.3 cm-1. Using this hv and g = ge, Figure 12

shows a plot of Hr for the above energy levels as D is

varied from 0 to 1.0. As D increases from zero and

approaches hv, it is seen that the transition zl

approaches H = 0 and for D>hv the zl and z2 transitions

appear but at increasingly higher values of H. Both

the xyl and AM = 2 transitions will not be able to be

observed for D>hv and only the xy2 transition can possibly

be seen.

For linear molecules, it was shown (see previous

section) that the transition probability was proportional

to sin0/dH/d0 or for the unnormalized absorption


Intensity = sin/(3Hr/p0) (70)


where H = H + [(D'/2)sin20 D'cos2]0 in polar
r o
coordinates. Thus




























(A 2 x ' xy2
E .
0.4

Z2
0.3


0.2 -
S xy
(o, A 2) xy i
0. I



0 I 2 3 4 5 6 7 8
Hr (Kilogouss)




Figure 12: Axial resonant fields with E = 0 for varying
D from equations 68 and 69.









Intensity [(D'/2) + (H H ) 1/2 (71)


The upper sign refers to the region about H of -D' to

+D'/2 and the lower sign to the region -D'/2 to +D'.

The total absorption is the sum of these terms. As

indicated in Figure 13 (a), there is a step in the curve

at +D'. At these fields absorption is due to molecules

when H[ z. The absorption rises without limit at

+D'/2 due to those triplets where H lies in the x,y

plane or Hiz. In Figure 13 (b), the first derivative

curve of the theoretical absorption spectrum is shown.

This contains only the region corresponding to

AM = +1 transitions. Due to the small anisotropy of
s
the AM = 2 transitions, i.e. a small value of dH/dO,

these transitions exhibit relatively large amplitude.

As previously stated, generally the hyperfine

interaction is small compared to the fine structure and

the electronic Zeeman energy so that first order

perturbation is sufficient to account for the hfs. For

one magnetic nucleus in the molecule the hf contributions

to the energy levels is found to be (for Hi[z)


W+1 = A im (72a)

W = 0 (72b)
o


W_1 = -Ai im .


(72c)































I
B


H


(a) Theoretical ESR absorption spectrum for
a randomly oriented triplet system for a
given value of D' and v (E = 0).

(b) Derivative curve computed from (a) (Only
the field region corresponding to AM = +1
is shown).


(o)





A


Figure 13:








For a AM = +1 transition of hv then

hv = -D + gl1 H + Ai m (73)


so that the resonant field is

H = [hv + D A im]/gj j. (74)


For hf interaction with a nucleus of spin I = 1/2,
the hfs is then

AH = A 1/g 1 (75)


In the same way, it can be shown that the AM = +2
transition will have the same hfs,

For Hiz, it is found that

W = W1 (76a)

A sin2a
W2 = 2 2 (76b)

A sin2a
W' = W + (76c)
3 3- 2

where W1, W2 and W3 are the same as given before and

sin2a = [1 (D/hv)2]1/2. Then in the limit of small D
relative to hv, H approaches A /g W. When D and hv are

comparable


A (hv + D/2)[hv(hv + D) 1/2 (77)
g j8 I









Derived Molecular Parameters

Coefficients of the Wave Functions

It is easily shown, using the relations developed

for the A tensor of a linear molecule, that the observed

ESR parameters Al and Ai can be related to the fundamental

molecular parameters in terms of Aiso and Adip by the

relations


CAli + 2A )

Aiso = gN Nsge BO'(0 (78)


(A A) /
A -(II g g 3 cos 2 1
dip = eoN N 82r- (79)
3 2r3


In order to describe the odd-electron distribution, an

approximate wavefunction can be constructed using a

simple linear combination of the essential atomic

orbitals for a given species (41). A procedure which

is sometimes used to determine the coefficients in the

ground state wavefunction depends upon a comparison of

molecular hfs constants with those in the free atoms.

The s or p character of the odd-electron at a particular

nucleus is then obtained by taking the ratio of

A. (molecule)/Ais (atom) or Adip (molecule)/Adip (atom).

As an example of this, consider C2H. The ground state

wavefunction could then be written:









C H = alX(2sc ) + a2x(2p ) + a3X(2c ) + a4x(2p
2 a a 4

+ a5X(lsH). (80)


In this approximation,


A so(C in CH) A (C in C H)
2 iso a 2 2 dip a 2
a1 Aso(C atom) 2 A dip( atom) etc.,



where Aso (molecule) and Adip (molecules) values are

obtained from the hfs of 13'3C 2H. If this were correct,

then a a2 = 1. A. (atom) and Ad (atom) values
i 1 Iso dip
are obtained from experiment and/or theory and a list

has been compiled in Ayscough (1). [Note: in reference

(1), Adip is designated as Bo.] This procedure depends

upon the doubtful supposition that the atomic properties

are unchanged in the molecule.

A more general statement of this method is, that

if we know what splitting an entire electron will give

with a nucleus when it is in either an ns or an np-

orbital on that nucleus we can estimate the actual

occupancy of those orbitals and compare these with the

calculated values of the coefficients of the molecular

orbitals.


Spin densities

From the experimentally determined values of A.
ISO
and Adip for a particular nucleus, the basic quantities

j'(0) 2 and <(3cos20 l)/r3> may be determined. As









shown previously, the relation may be written


A.N = 8- eggNo N l(0)N12 (78)


and


Ad gegNoN N<3cos 0 1)/2rN> (79)


Where N stands for a particular nucleus. It would be

helpful to compare these values with calculated values.

Morikawa and Kikuchi (43) have presented an SCF-MO-INDO

method for predicting the values for Aiso and Adip

which have been used in a comparison with the observed

values, for example in C2H.


Ag and the Spin-Doubling Constant

It was shown that perturbation theory gives

corrections to the various components of the g-tensor

and the equations for these shifts were given (see

section on g-tensor). For linear molecules with axial

symmetry it can be seen that gl and gl involved summa-

tions of terms which depend upon spin-orbit coupling

with excited H states to the ground state. Also the

g-shifts were dependent upon the energy separation of

these states from the ground state. It is evident that


<01L xn>
Ag1 = g g = -2)-,' (81)
e n E E
n o









Therefore, the lower-lying the n state and the larger

the value of A, the more effective the coupling. gl

should always be close to ge, however, since the matrix

elements are zero, and it is normally found that

g9l ~ ge. However, Agl is more affected by the coupling,
and it can be positive or negative depending upon the

character of the i state involved. In general the

lowest-lying n state will dominate the summation so that

higher states can be neglected, and the sign of Agi

will depend upon whether that excited state has the

properties of an electron in a T orbital or of a "hole"

in a i orbital. In molecular orbital notation, the

excited state would be obtained by excitation of a

ground 2Z state with a configuration ... 1i o to

...wT 2 1 2 r(r for regular) or to ...i 302
2 .(i for inverted). Mixing of the 2' state with the
1 r
ground state will cause Agi to be negative whereas a

2fi state will cause AgL to be positive. In the simplest

case, it can be said that if the experimental value of

Ag, is negative, usually a 2.H excited state lies lowest

and if Ag is positive, a 2 i state is lowest. In this

way qualitative information about the excited state of

a 22 molecule is immediately obtained from the value of



2E molecules in the gas phase also exhibit a

splitting of their rotational levels given by y(K + 1/2),









where y is very small compared with the rotational

constant, B, and K is the rotational quantum number.

y is called the spin-doubling constant and has been

shown by Van Vleck (44) to be given by


y = 4E<011L xn>/E E (82)
n x x n o


when In> includes all excited 2H states, B is the

rotational operator h2/(8r2pr2) and all other terms have

been defined previously. If B is assumed to be constant

then y reduces to


y = 4BZ<0|XL xn>/E E (83)


Then


y = -2BAgl (84)


for a molecule in a 2Z state [derived.by Knight and

Weltner, (45)]. Thus from Agi values, the sign and

magnitude of y can be predicted. Since y can often be

determined with good accuracy by gas-phase spectroscopists

from analysis of the rotational structure of high-

dispersion optical spectra, a check of the experimental

data from two quite different sources is allowed. For

an example, see the discussion of C2H.














References Chapter III

1. P. B. Ayscough, Electron Spin Resonance in Chemistry,
London: Methuen, 1967.

2. R. S. Alger, Electron Paramagnetic Resonance:
Techniques and Applications, New York: Wiley-
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3. C. P. Poole, Jr., Electron Spin Resonance, New York:
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4. A. Carrington and A. D. McLachlan, Introduction to
Magnetic Resonance, New York: Harper and Row,
1967.

5. C. P. Slichter, Principles of Magnetic Resonance,
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6. J. C. Wertz and J. R. Bolton, Electron Spin Resonance,
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7. H. M. Assenheim, Introduction to Electron Spin
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8. A. Abragam and B. Bleaney, Electron Paramagnetic
Resonance of Transition Ions, London: Oxford
University, 1970.

9. W. Low, Paramagnetic Resonance in Solids, New York:
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10. I. N. Levine, Quantum Chemistry, Volume II, Boston:
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11. S. P. McGlynn, T. Azumi, and M. Kinoshita, Molecular
Spectroscopy of the Triplet State, Englewood
Cliffs, New Jersey: Prentice Hall, 1969.

12. Hyperfine Interactions, edited by A. J. Freeman and
R. B. Frankel, New York: Academic, 1967.

13. G. E. Pake, Paramagnetic Resonance, New York:
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14. B. Taylor, W. Parker, and D. Langenberg, Rev. Mod.
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CHAPTER IV
C2H RADICAL


Introduction

A study of ethynyl (C2H) is of importance for three

reasons; (1) because of its interest as a a-electron free

radical, (2) because of its possible relevance to astro-

physical phenomena, and (3) because this work was done in

conjunction with a study of the C2 radical (also included

in this dissertation) in which '3C substitution was re-

quired for the ESR identification of that radical. In

the production of '3C2 3C2H was simultaneously produced

as an impurity, therefore its ESR spectrum needed to be

characterized.

Tsuji (1) and Morris and Wyler (2) have predicted

from theoretical studies of molecular distribution in

stellar atmospheres that C H is one of the most abundant

polyatomic species in the atmospheres of carbon-rich

stars, especially below 28000K. The electronic properties

were expected to be similar to CN, its isoelectronic

diatomic counterpart, which is indeed a ubiquitous stellar

molecule. C2H, prior to this study however, had not been

observed spectroscopically in the gas phase.

C2H had been investigated previously by two groups of

researchers. Cochran, Adrian, and Bowers (3) had observed









the hydrogen and deuterium hyperfine splitting in an

electron spin resonance experiment. Milligan, Jacox,

and Abouaf-Marguin (4,5) observed the CEC stretching
-l
frequency of C2H in argon matrix at 1848 cm This

identification was confirmed by the effects of isotopic

substitution however, no electronic transitions were

observed in their work. In both of the above cases,

C2H was prepared by the ultraviolet photolysis of

acetylene and then trapped in argon matrices at liquid

helium temperatures.

The object of this research was to investigate

further the properties of the C2H radical by means of ESR

and optical spectroscopy. As a result of the ESR study,

complete spin density data have been obtained for C2H

such that a detailed comparison can be made with theoreti-

cally derived spin distributions.

As mentioned previously, C2H is isoelectronic with CN,

therefore it is expected that there should be optical

absorptions corresponding to the red and violet systems

of CN. As a result of these optical studies, two weak

absorption systems of C2H have been found in the. general

regions of the CN bands.


Experimental

Acetylene (99.5% pure) was obtained from Airco and

90% '1C-enriched acetylene was obtained from Merck, Sharpe

and Dohme of Canada, Ltd. Both were used without further









purification. Monoiodoacetylene (C2HI) which was also

used as a parent molecule for C2H was prepared after the

method described by Carpenter et al. (6) by the reaction

of acetylene with iodine in an alkaline solution. The

purity of the product was established by comparison with

the published infrared spectrum (6).

These gases were mixed with argon prior to deposition.

Samples of mole ratio (argon: acetylene or monoiodoacetylene)

between 100 and 1000 were prepared using standard manometric

procedures. For maximum production of C2H gas mixtures

were deposited at the rate of = 0.1 1-atm/h. During

deposition of acetylene mixtures the incoming gas was

subjected to direct irradiation produced by the electrode-

less flowing hydrogen discharge lamp through a lithium

fluoride window. Similarly, monoiodoacetylene mixtures

were irradiated with a high pressure mercury lamp through

a quartz window.


ESR Spectra

The linear C2H molecule in its 2Z ground state should

have an ESR spectrum which is a doublet due to the

interaction of the one odd electron with the single proton.

Since the C2H was trapped in argon matrices at liquid

helium temperatures, the molecules are randomly-oriented

and rigidly held. Therefore, each line of the C H doublet

should exhibit both perpendicular and parallel components.

Figure 14 shows the ESR spectrum which was obtained after



























I I I I I


350
3350


3370


H (Gauss)


ESR spectrum of '2C H isolated in argon at
4K. The weaker inner doublet arises from the
forbidden transitions (v = 9398 MHz).


33
3330


Figure 14:









photolysis of 0.1% C2H2;Ar samples. It is consistent with

an isotropic g tensor which was verified when 13C substi-

tution was made. The proton hyperfine splitting is 14.5 G

for the large perpendicular components observed. Analysis

of the H hfs observed in the spectrum with '3C-substi-

tuted C2H yields values of A (H) = 14.5 G and Al (H) =

18.2 G. Since there is an isotropic g tensor and AI(H)

is approximately equal to All H), the two components are

overlapped, which effectively leads to broadening of the

perpendicular lines on the outside by the smaller parallel

line, also making the lines appear slightly asymmetric.

This is similar to the spectrum reported by Cochran, Adrian,

and Bowers (3). They observed a line to line splitting of

16.1 G which is an average of our A values.

Also shown in Figure 14 is an additional, weaker double

with a splitting of 9.7 G. These lines had not been pre-

viously observed and they only appeared for high yields

of the C2H radical in this work. They have been attributed

to forbidden transitions in which AMs = 1 and AMI = 1.

The small hydrogen hfs is of the same order as the nuclear

Zeeman energy so that the forbidden transition becomes

observable.

When the concentration of C2H2 in argon was increased

to 1% or more, other species not seen in Figure 14 were

enhanced. These species were identified as vinyl radicals

(C2H3) (3, 7, 8) and methyl radicals (CH ) (8). It was









also found that C2H spectrum was observed only when the

matrix material was irradiated with the H2:He lamp

during deposition and that irradiation after deposition

was ineffective.

If instead of '2C2H, 13C-substituted C2H is formed,

additional hfs should be observed due to interaction of the

magnetic moment of the unpaired electron with the magnetic

moments of these nuclei. Since the two carbon nuclei are

inequivalent, the hfs will also be inequivalent. Here the

carbon nucleus interacting strongly with the unpaired

electron will be designated Ca and the more weakly

interacting nucleus C The complete hfs pattern that

is expected for a 50% 13C enrichment of C H is shown in

Figure 15. The original line in C2H should actually be a

doublet due to H hfs but this hyperfine interaction has

been initially neglected for the sake of simplicity. Due

to strong interaction with the '3C (I = 1/2) nucleus,

the original line is split in two. Each of these lines

will then be split to a less amount due to interaction with

the '3C (I = 1/2) nucleus and split again by the hydrogen

hfs. Therefore, in a sample of C2H containing 50% of

13C and 12C, there should be a total of eighteen perpendicular

and eighteen parallel lines with all perpendicular lines

of equal intensity and all parallel lines of equal

intensity.


















'3Ca hfs

'3Ca hfs

H hfs

A- (3C a)

Scale












Predicted hyperfine splitting for a mixture of
C H molecules containing all possible combina-
tions of 12C and 13C isotopes.


A -C)
A---)


Figure 15:









If 13C enrichment were increased to 90%, then the

most abundant species would be I3C 3CH (31%), least

abundant 12C12CH (1%) and "2C'CH equal to 3C12CH (9%).

Figure 16 shows experimental results when the 13C enrichment

was 90%. (The parent compound was 90% ]'C enriched C2H2.)

The perpendicular components of the hfs are clearly

observed for both '3C nuclei, however, due to overlap

by the perpendicular lines of the 12C'3CH and '3C12CH

species the parallel lines are obscured even at high gain.

These parallel lines are also overlapped by weak lines

attributable to C2H3 and CH3 radicals.

A new route was sought by which to prepare C2H in

an effort to find a new parent compound which (1) could

be enriched to a larger extent with '3C and (2) would not

produce the CH and C2H impurities present in the C 212

method of preparation. An alternate method was found in

which C2H was prepared from the photolytic decomposition

of C2HI. In this preparation C2HI was deposited with

argon in a 1:1000 ratio while being irradiated with light

from the previously described high pressure mercury lamp.

The resulting ESR spectrum was much simplified, consisting

at low gain of a very intense C2H doublet and very weak H

lines. The absence of intense H lines indicated that the

principal effect of the photolysis was detachment of the

halogen. Due to this, there were only very small amounts

of background impurities and it was possible at high gains





















-1--


Ai('3C,)


H

3100


Af(-C4)


Ai('Ca)


3300


H (Gauss)



Figure 16: ESR spectrum observed for C H:Ar at 4 0
produced by the photolysis of 90% 13C-
substituted C2112 (v = 9398 MHz).


-


3500









to see lines attributable to 12C'1CH and 13C"CH species

due to the 1% natural abundance of 13C in the parent molecule.

Figure 17 shows the lines that are observable due to the
12'13C2H species. The outer doublets around 3500 and

3200 G are attributable to species in which 13C is sub-

stituted for the C nucleus. Only one parallel and two

perpendicular lines are visible. The second parallel

line is overlapped by the perpendicular lines. The inner

doublets around 3380 and 3320 G arise from species in

which 13C is substituted for the C8 nucleus.

It should be noted that these inner doublets occur

on the background of the steeply rising limbs of the

'2C2H doublet. Both parallel and perpendicular com-

ponents are observed for these inner doublets although

one perpendicular line of each double is slightly over-

lapped by weak lines due to the CH3 impurity. The clearly

resolved perpendicular and parallel components of the

lines split by the hf interactions establish that C2H is

indeed linear and has a 2Z ground state.


ESR Analysis

g Tensor

By substituting the line positions that were obtained

from the ESR spectrum shown in Figure 17 into the second-

order solution of the axially symmetric spin Hamiltonian,

the values of AI |I, .|A 1, g ,and g1 can be obtained.














--------A,,(C,)-
Aj(C.) -
SfA,(CHsf

CH,


v

A,(H)


A,(H)


3160 3180 3200 3300 3320 3380 3400 3480 3500 3520
H (Gouss)













Figure 17: ESR spectrum of 12'13C2 H species at 4K
arising from the natural abundance of 13C
in the photolysis products of 12C HI. The
intense C12C lines have been omitted from
the central portion of the spectrum (v = 9398 MHz).


LA,(CO)








From the ESR theory recall that the second-order solution

of the axially symmetric spin Hamiltonian is given by


H = g BHzSz + g (HxSx + HySy)


+ E[A (N)ISZ + A (N)(I S + IySy). (57)


Table I shows the values of I|AII and |Ai| for each

nucleus found in this analysis. It was found that the g

tensor was isotropic with gi = gI = 2.0025 (5). Table II

lists the ESR lines observed in solid argon. The four

values in parentheses refer to parallel lines which underlie

perpendicular lines and were calculated from the observed

values of A I(H). By using gl and gl values calculated

from line positions and hfs for the 3C -substituted

molecule, with A ("3C ) and Ai (3Ca), line positions for

13C -substituted molecule were generated. The agreement

of the generated line positions with the observed positions

is within + 0.1 G. Figure 18 shows a comparison between

the observed and simulated spectra for '3C -substituted

C2H. The calculations used the parameters given in Table

I and assumed randomly oriented molecules.


A Tensors

As shown in the section on ESR theory, the hfs for a

particular nucleus can be expressed in terms of isotropic

(Aiso ) and dipolar (Adip) components.
iso dip











Table I

Hyperfine splitting parametersa for '~C2H

in the 2 ground state in an Ar matrix.


Nucleus A I (MHz) IAI (MHz)


H 41(1) 51(1)

63C 863(1) 980(1)

CC 139(1) 191(1)




g = g = 2.0025(5)
gjj= l












Table II


Observed ESR lines in gaussa for
12tC 2H isolated in solid argon at 4 K.


M (13C) M ( CC) MI(H) I lines i lines




+ 1/2 (3343.7) 3346.6

1/2 (3361.9) 3361.1

+ 1/2 + 1/2 3161.6 3183.5

+ 1/2 1/2 (3179.9) 3198.1

- 1/2 + 1/2 (3511.5) 3491.5

- 1/2 1/2 3529.7 3506.0

+ 1/2 + 1/2 3309.4 3320.6

+ 1/2 1/2 3327.7 3335.1

1/2 + 1/2 3377.5 3370.2

1/2 1/2 3395.8 3384.7




a = 9398 MHz.

bEntries in brackets are positions of parallel lines over-
lapped by perpendicular lines; the values shown are
calculated from the parameters in Table I.


































3--60 3180 32
3!60 3180 32C


Figure 18:


-- EXPERIMENTAL

--- CALCULATED

I # I I 1 I I I
)0 3480 3500 3520

H (Gauss)


A comparison of the calculated ESR spectrum with
the observed for the outer doublet in which
the C nucleus of C H is '1C substituted
(v = 9398 MHz) .


H-









Aiso(N) = 1/3(AW + 2Ai) (78)

= (81/3)ge n Sn (0))

Adip(N) = 1/3(Al A )


= geg nn<(3cos20 1)/2r3>N. (79)


These derived parameters are shown in Table III for each

of the three nuclei (N). From these values of A. (N)
iso
and Adip(N), the fundamental quantities i((0) 2 and

<3cos20 l/r3> for interaction with that nucleus can

be derived. These values are also given in Table III.

The signs of A and Ai are assumed to be positive for

interaction with all nuclei since variation of signs

indicate that this is the only condition for which

physically reasonable spin densities are obtained.


Forbidden Transitions

The appearance of the weak inner doublet in Figure 14

can be accounted for by the methods of McConnell et al.(9,7)

and are attributed to the appearance of forbidden transi-

tions. It has been shown using second-order perturbation

theory that transitions of the type AMS = +1, AM, = +1,

are weakly allowed, whereas to the first-order, the

transitions are strictly forbidden. The theory of these

transitions has been discussed and treated mathematically

by Miyagawa and Gordy (10), McConnell et al. (9), Poole

and Farach (11), and others. Analysis shows that for





87























Table III

Isotropic and anisotropic hfs of

'C2 H and derived matrix elements.a




Nucleus Ais(MHz) Adip(MH) p(O) (a.u.) <(3coas2-l)/r'> a.u.)



"Cs 902(1) 39(1) 0.803(1) 0.58(1)
"C5 156(1) 17(1) 0.139(1) 0.26(1)
H 44(1) 4(1) 0.0098(1) 0.013(2)




agl = g1 ~ 2.0025(5).




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