ELECTRON SPIN RESONANCE AND OPTICAL SPECTROSCOPY OF
HYDROCARBON RADICALS AT 4 K IN RAREGAS 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 SpinDoubling Constant . 65
References Chapter III . . . . .. 68
IV C2H RADICAL . . . . . . . .
Introduction . . . . .
Experimental . . . .
ESR Spectra . . . . .
ESR Analysis . . .
g Tensor . . . . .
A Tensors . .
Forbidden Transitions .
SpinDoubling 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
ZeroField 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
liquidhelium dewar used for optical studies
2. Basic design features of liquidhelium dewar 11
used for ESR studies
3. Basic design features of variabletemperature 13
liquidhelium dewar used for ESR studies
4. Schematic drawing of flowing hydrogenhelium 17
quartz electrodeless discharge lamp
5. Emission spectrum from hydrogenhelium 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 RAREGAS 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 raregas matrices at liquid helium temperatures.
From ESR spectra, magnetic parameters of the radicals
such as g tensors, hyperfine interaction tensors (hf),
and zerofieldsplitting tensors (D) are determined.
The value of these quantities allows the derivation of
fundamental quantities such as the spindoubling 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 ionpairs (M C2 ). Analysis
has demonstrated that the CC 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 carbonrich stars, has been produced by
the highenergy 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 CH, CC,
and two CEC symmetric vibrations. A CCH 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 highenergy
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 cm1
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 lowlying 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 lowlying
electronic states. Other shortlived 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 gasphase 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 motioni.e.,
diffusionand are usually prevented from rotating, but
may vibrate with frequencies within a few percent of the
gasphase 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 gashandling 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 cocondense the materials from
separate gas inlets. Photolytic dissociation may be
carried out by subjecting the material to radiation by
highenergy 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 isotopicallysubstituted parent species is
available, the investigation of the isotopicallysub
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 gaslike 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 (16).
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
~IA
Figure 1: Basic design features of variabletemperature
liquidhelium 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 (11/4" 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
vacuumtight 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
WATERCOOLED
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 XBAND CAVITY
QUARTZ
WINDOW
Figure 2: Basic design features of liquidhelium 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 variabletemperature
liquidhelium 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 0ring 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
BayertAlpert 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 hightempera
ture Knudsen cell while in the other technique, various
parent materials were photolyzed with radiation from high
energy sources including either a flowing hydrogenhelium
electrodeless discharge lamp or a high pressure mercury
lamp.
The mercury lamp consists of water cooled mercury
capillary lamp operated at 1000 watts (type AH6
obtained from G. W. Gates & Co., Inc., N.Y., water
jacket is PEKSEB 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 nontransmitting in the
visible and infrared regions. Normally a Corning 754
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 hydrogenhelium 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 hydrogenhelium 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
ORINGS
VACUUM
SCALE
Figure 4: Schematic drawing of flowing hydrogenhelium
quartz electrodeless discharge lamp.
1700 1500 1300 1100
WAVELENGTH (A)
Figure 5: Emission spectrum from hydrogenhelium 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 JarrellAsh 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 2D2 XY
recorder with the Varian V4500 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 Xband 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 1atm/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 103 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 (19). 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 gfactor
(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 ergsec),
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 Xband 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 spinorbit coupling usually expressed in the form
HLS = LS
where L and S are the orbital and electronspin
angular momentum operators. A is the molecular
spinorbit coupling constant.
HSI represents the hyperfine interaction arising
from the electronspin 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) (rI)
HSI = iNgeo r +
r r
SI 8r6(r)SI
+ = IAS (5)
r3 3
where I is the nuclearspin 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 LI 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 r3 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 6function indicates that this term has a
nonzero 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
(113).
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 ogS
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 oS + HI
spin o SI
= BHo"gS + 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
BSgH = 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 gtensor may
be interpreted as follows. gxy may be considered as
the contribution to g along the xaxis when the magnetic
field is applied along the yaxis. In general these
axes (x, y, z) are not the principal directions of the
g tensor, but by a suitable rotation of axes theoff
diagonal elements of the gtensor can be made equal to
zero. When the gtensor is so diagonalized the components
along the diagonal, gxx g yy and gzz, then are the
principal directions of the gtensor with respect to
the molecule.
As alluded to previously, the anisotropy of the
gtensor arises from the orbital angular momentum of the
electron through spinorbit 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 gfactor would have precisely the freeelectron 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 gfactor.
The orbital and spin angular moment will be coupled
through the spinorbit 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) + ,LS (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 "spinonly" electron
Zeeman energy. The second term may be expanded as
.
For an orbitally nondegenerate state, equals
zero. The secondorder 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 secondrank 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 SHS, the result is called the spin
Hamiltonian H spin which may be written
H = BH(g 1 + 2XA)S + X2S.AS = SH.j.S + SDS (18)
spin e  
where
g = ge1 + 2AA (19)
and
D = 2A .
(20)
The S.DS 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 gtensor
arises from the spinorbit 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 gtensor 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 nfold 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 gtensor can be
determined. The general formula, widely used in the
interpretation of ESR spectra, for the ijth term is
then (see 1522).
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 secondorder shift in energy of the
groundstate levels due to a combination of spinorbit
coupling and Zeeman energies. In a similar fashion
Tippins (22) has extended these calculations to the
thirdorder for the energy shift of the ground state and
has determined to the secondorder 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 LI 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 scharacter of the wavefunction (the
Fermi contact term) and to the nonscharacter of the wave
function.
The interaction due to the scharacter 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 scharacter). Here He and HN
are the electron and nuclear magnetic moments, respectively.
The interaction due to the nonscharacter of the
wavefunction is called Adip since it arises from the
dipoledipole 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 3cos201
^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 dipoledipole interaction. The
electron spinelectron spin interaction is given by
a spinspin 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 spinspin Hamiltonian (4, 6, 8, 11)
HSS = S'DS (38)
where D is a secondrank 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 zerofield 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 + SDS (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 randomlyoriented triplet molecules are usually caused
by the large linewidths; however, '3C, H, and F
hyperfine splitting have been observed (2427).
Generally, the hyperfine interaction is small compared to
the fine structure (D term) and the electronic Zeeman
energy, so that firstorder 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 gvalue in the direction of H, 0 is
the angle between the zaxis of the molecule and the
field direction and $ is the angle from the xaxis 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
2940.) 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 randomlyoriented
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 firstorder 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 randomlyoriented 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
randomlyoriented 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 spin1/2 nucleus, where g and A are
varied from isotropic to completely anisotropic forms,
and one spin1 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 spinorbit 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> = IY12 + 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 I1>,
respectively. At zero field the +1 and 1 states are
degenerate and the appropriate wavefunctions are
S ( +1 I1>) = 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
II>
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 = sina1[ I+1> + I1>] + 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 randomlyoriented 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 cm1. 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 oddelectron 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 oddelectron 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 SCFMOINDO
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 SpinDoubling Constant
It was shown that perturbation theory gives
corrections to the various components of the gtensor
and the equations for these shifts were given (see
section on gtensor). For linear molecules with axial
symmetry it can be seen that gl and gl involved summa
tions of terms which depend upon spinorbit coupling
with excited H states to the ground state. Also the
gshifts 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 lowerlying 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
lowestlying 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 spindoubling 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<0XL 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 gasphase 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
Interscience, 1968.
3. C. P. Poole, Jr., Electron Spin Resonance, New York:
WileyInterscience, 1967.
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,
New York: Harper and Row, 1963.
6. J. C. Wertz and J. R. Bolton, Electron Spin Resonance,
New York: McGrawHill, 1972.
7. H. M. Assenheim, Introduction to Electron Spin
Resonance, New York: Plenum, 1966.
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:
Academic, 1960.
10. I. N. Levine, Quantum Chemistry, Volume II, Boston:
Allyn and Bacon, 1970.
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:
Benjamin, 1962.
14. B. Taylor, W. Parker, and D. Langenberg, Rev. Mod.
Phys. 41, 375 (1969).
15. P. H. Kasai, J. Chem. Phys. 49, 4979 (1968).
16. L. B. Knight, Jr. and W. Weltner, Jr., J. Chem.
Phys. 54, 3875 (1971).
17. L. B. Knight, Jr. and W. Weltner, Jr., J. Chem. Phys.
55, 2061 (1971).
18. J. M. Brom, Jr. and W. Weltner, Jr., J. Chem. Phys.
57, 3379 (1972).
19. J. M. Brom, Jr., W. R. M. Graham, and W. Weltner, Jr.,
J. Chem. Phys. 57, 4116 (1972).
20. W. C. Easley and W. Weltner, Jr., J. Chem. Phys. 52,
197 (1970).
21. A. J. Stone, Proc. Roy. Soc. 271, 424 (1963).
22. H. H. Tippins, Phys. Rev. 160, 343 (1967).
23. E. Fermi, Z. Physik 60, 320 (1930).
24. The Triplet State, Proceedings of the International
Symposium held at The American University of
Beirut, Lebanon, February 1419, 1967.
Cambridge University Press, London, 1967.
25. J. Mispelter, J. P. Grivet, and J. M. Lhoste, Mol.
Phys. 21, 999 (1971).
26. R. A. Bernheim, H. W. Bernard, P. S. Wang, L. S. Wood,
and P. S. Skell, J. Chem. Phys. 54, 3223 (1971).
27. E. Wasserman, V. J. Kuck, R. S. Hutton, E. D. Anderson,
and W. A. Yager, J. Chem. Phys. 54, 4120 (1971).
28. J. A. McMillan, Electron Paramagnetism, New York:
Reinhold, 1968.
29. B. Bleaney, Proc. Roy. Soc. 63, 407 (1950).
30. B. Bleaney, Phil. Mag. 42, 441 (1951).
31. R. H. Sands, Phys. Rev. 99, 1222 (1955).
32. D. E. O'Reilly, J. Chem. Phys. 29, 1188 (1958).
33. J. W. Searl, R. C. Smith, and S. J. Wyard, Proc.
Phys. Soc. 74, 491 (1959).
34. B. Bleaney, Proc. Phys. Soc. 75, 621 (1960).
70
35. E. M. Roberts and W, S, Koski, J. Amer, Chem. Soc,
82, 3006 (1960).
36. F. K. Kneubuhl, J. Chem. Phys. 33, 1074 (1960).
37. J. A. Ibers and J. P. Swalen, Phys. Rev. 127, 1914
(1962).
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98 (1965).
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3416 (1969).
41. P. W. Atkins and M. C. R. Symons, The Structure of
Inorganic Radicals, New York: Elsevier Pub
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Phys. 41, 1763 (1964).
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45, 3715 (1972).
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53, 4111 (1970).
CHAPTER IV
C2H RADICAL
Introduction
A study of ethynyl (C2H) is of importance for three
reasons; (1) because of its interest as a aelectron 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 carbonrich
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 AbouafMarguin (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% '1Cenriched 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 1atm/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 randomlyoriented
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 '3Csubsti
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, 13Csubstituted 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 secondorder 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 IAII 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.
360 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 secondorder perturbation
theory that transitions of the type AMS = +1, AM, = +1,
are weakly allowed, whereas to the firstorder, 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.) <(3coas2l)/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).
