F.‘".\CHW‘=?‘1 STATE lA‘!‘5in-:R3\TY
u; ABRVLKELHERE mo Ammo ESLENH’LE
DEPNWMEKT OF CHEE‘HS'TRY
EAST LANSlNG. MICHIGAN

, I'V‘

ABSTRACT

STUDIES OF THE MOLECULARSTRUCTURE OF
ETHYL CHLORIDE, CHLOROMETHYLSILANE,
AND CYCLOPROPYL CHLORIDE BY
MICROWAVE SPECTROSCOPY

by Gerald Daniel Jacobs

A brief outline of the history of microwave Spectroscopy is pre-
sented. The theory of rotational spectra as it pertains to the determin-
ation of molecular structure, barriers to internal rotation, and
quadrupole effects is discussed. A description of the microwave
spectrometer is also included.

The microwave spectra of C13H3CHZC135, CH3c13Hzc135, 0130320135,
and CHZDCHzCI35 have been examined and rotational constants assigned.
Both a-type and b-type Spectra have been observed. From these spectra
and those previously reported for CH3CHZC135, CH3CHZC137, and
r CHZDCHzCl35 a. complete structure has been obtained by means of the
substitution method. The bond distances and bond angles obtained are
as follows: CC = 1.520A,.CC1 = 1. 788 A, CH (methyl) = 1.091 A,

CH (methylene) o

1.089 A, cool: 111.0 , HCH (methyl) = 108.50,

HCH (methylene) = 109. 20,. CCH (methylene) = 111.60. The quadrupole
coupling parameters and barriers to internal rotation have been re-
evaluated in terms of the above structure. The quadrupole coupling
parameters are x bond = -68.80 Mc and ”bond = 0.035, if the angle
between the a axis and the CC1 bond is determined from the structure; or
Xbond = -71.24 Mc, if a cylindrical charge distribution is assumed
near the chlorine nucleus. The barrier to internal rotation is found to

be 3685 cal/mole.

Abstract Gerald Daniel Jacobs

Observations of the microwave spectra of seven grounds state
species and three first excited torsional state species of CH,,ClSil-I3
are reported. From an analysis of the moments of inertia of the various
species structural parameters are deduced as follows: bond distances;
CC1= 1.788 A, CSi = 1.889 A, CH = 1.096 A, SiH = 1.477 A, and bond
angles; $00 = 109. 3°, SiCH = 109. 3°, HSiH = 110.60, and HCH =
107. 50. An analysis of the hyperfine splitting leads to quadrupole
coupling parameters 9% bond = -68. 7 Mc, nbond = 0.048, if it is assumed
that the CC1 bond direction forms one principal axis of the quadrupole
tensor; and Xbond = -72. 0 Me if it is assumed that the quadrupole
tensor is cylindrically symmetric. Analysis of Splittings in the first
excited torsional state indicate that the height of the potential barrier
hindering internal rotation of the silyl group is Z. 55 kcal/mole.

The microwave spectra of the C1-35 and C1-37 Species of cyclo-
propyl chloride have been examined and R-branch a-type, R-branch

c-type, and Q-branch c-type transitions assigned.

STUDIES OF THE MOLECULAR STRUCTURE OF
ETHYL CHLORIDE, CHLOROMETHYLSILANE,
AND CYCLOPROPYL CHLORIDE BY
MICROWAVE SPECTROSCOPY

BY

Gerald Daniel Jacobs

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCT OR OF PHILOSOPHY

D epartm ent of Chemistry

1961

G‘

.1.)

To My Wife Linda

Ho
Ho

ACKNOWLEDGMENTS

The author wishes to express his sincere appreciation to
Dr. Richard H. Schwendeman for his assistance, encouragement,
and guidance which he so generously gave during the course of this
investigation and preparation of this thesis.

1 Financial aid in the form of Fellowships from the National
Science Foundation and Petroleum Research Foundation are grate-
fully acknowledged.

************

iii

TABLE OF CONTENTS

Page

I. HISTORICAL BACKGROUND .................. 1
II. THEORY OF ROTATIONAL SPECTRA ............. 4
2.1 Introduction ....................... 4

2.2 Moments of Inertia ................... 5

2.3 Energy of Rotation ................... 9

2.4 Nuclear Quadrupole Hyperfine Structure ........ 14

2. 5 Internal Rotation .................... 21

2. 6 Stark Effect ....................... 27

111. DESCRIPTION OF THE MICROWAVE SPECTROMETER . . . 32

3. 1 Introduction ....................... 32
3. 2 Reflex Klystron Oscillators ............... 32
3. 3 Waveguide Absorption Cell ............... 35
3. 4 Sample Introduction System ............... 37
3. 5 Detection ........................ 37
3.6 Square Wave Generator ................. 40
3. 7 Frequency Measurements .............. . 43
IV. MOLECULAR STRUCTURE OF ETHYL CHLORIDE ...... 49
4. 1 Introduction ....................... 49
4. 2 Preparation of Samples ................. 50
4. 3 Microwave Spectra ................... 52
4.4 Molecular Structure . ................. 66
4. 5 Discussion of Structure ................. 73
4.6 Quadrupole Analysis . . ................ 75
4. 7 Barrier to Internal Rotation .............. 78

V. MOLECULAR STRUCTURE OF CHLOROMETHYLSILANE . . 81

5. 1 Introduction ....................... 81
5. 2 Preparation of Samples ................. 81
5. 3 Microwave Spectra ................... 85
5.4 Molecular Structure .................. 91
5. 5 Quadrupole Hyperfine Structure ............ 98
5. 6 Barrier to Internal Rotation .............. 102
5. 7 Discussion ........................ 104

iv

TABLE OF CONTENTS -= Continued

Page
VI. MICROWAVE SPECTRA OF CYCLOPROPYL

CHLORIDE ...................... 107

6. 1 Introduction ................... 107

6. 2 Preparation of Samples ............. 108

6. 3 Microwave Spectra ................ 109

6.4 Molecular Structure . . . . . .......... 112

6. 5 Quadrupole Analysis and Discussion ...... 112
REFERENCES ........................... 120

TABLE

II.

III.

IV.

VI.

VII.

VIII.

XI.

XII.

XIII.

XIV.

XV.

LIST OF TA BLES

Parameters used in the Analysis of Internal Rotation
in Chloromethylsilane . . . . . . . ..........

Calculation of Corrections to A and E Levels of
Chloromethylsilane . . . . . . . . . . . . . . . .

Klystrons Presently Available at Michigan State
University. .......

Wavemeters in use at Michigan State University . . .

Computation of Hyperfine Structure for the 404 9 413
Transition in CH3CHZC135. . . . . . . . . . . . . . ..

Frequencies of Hyperfine Components in Ethyl
Chloride ....... . . . .............

Other Measured Frequencies in Ethyl Chloride . . .

Comparison of Calculated and Observed Frequencies
of Hyperfine Components in CH3CHZC135 . . . . . .

Hypothetical Unsplit Frequencies in Ethyl Chloride .

Rotational Constants, Moments of Inertia, and
Second Moments for Ethyl Chloride . . . . . . . . . .

Variation of Parameters in Ethyl Chloride with
Choice of Moments of Inertia . . . . . . . . . . . .

Coordinates of the Atoms in the CH3CH2C135 Principal
AxisSystem. . . . . . . . . . ............

Molecular Parameters for Ethyl Chloride . . . . . .
Comparison of Ethyl Chloride with Similar Molecules

Quadrupole Coupling Constants for Ethyl Chloride . .

vi

Page

28

29

36

44

57

59

62

64

65

67

70

71

72

76

77

LIST OF TABLES - Continued

TABLE

XVI.

XVII.

XVIII.

XIX.

XX.

XXI.

XXII.

XXIII.

XXIV.

XXV.

XXVI.

XXVII.

XXVIII.

XXIX.

Page
Internal Rotation in Ethyl Chloride .......... 80

Frequencies of Hyperfine Components in C13H2C13SSiH3
and CH2C13SSi29H3 ........ . . ......... 87

Hypothetical UnSplit Frequencies of Observed Transi—
tions in Ground State Species of Chloromethylsilane . 89

Hypothetical Unsplit Frequencies of Observed Transi-
tions in First Excited Torsional State Species of

Chloromethylsilane .................. 90

Rotational Constants and Moments of Inertia for
Ground State Species of Chloromethylsilane ..... 92

Rotational Constants and Moments of Inertia for
First Excited Torsional State Species of Chloromethyls-

Silane ..................... . . . . . 93

Second Moments for Ground State Species of Chloro-
methylsilane.............. ....... .94

Coordinates of the Atoms in the Principal Axis
System of CH2C13SSiH3 . . ............... 96

Bond Distances and Bond Angles in.Chloromethy1-
silane.. ....... 97

Frequencies of Hyperfine Components in CHZCIBSSng . 100
Quadrupole Coupling Constants in CH2C135SiH3. . . . . 101
Internal Rotation in Chloromethylsilane. . . . . . . . 103

Comparison of Chloromethylsilane with Similar
Molecules ............... . . . . . . . . . 106

Frequencies of Hyperfine Components and Hypotheti-
cal UnSplit Frequencies of the R-branch and Qubranch
c-type Transitions in. C3H5C135 and C3H5C137 ..... . 111

vii

LIST OF TABLES - Continued

TABLE

XXX .

XXXI.

XXXII .

XXXIII .

XXXIV .

Page
Frequencies of Hyperfine Components of R-branch
a-type Transitions in C3H5C135 and C3H5C137 ...... 113
Hypothetical Unsplit Frequencies of the R-branch
a-type Transitions in C3H5C135 and C3H5C137 ...... 114

Rotational Constants, Moments of Inertia, and Second
Moments for C3H5C135 and C3H5C137 .......... 115

Quadrupole Parameters and Coupling Constants for
C3H5C135 and 03H5C137 ................ . 117

Values of the Coupling Constant in the Bond Direction
for Cyclopropyl Chloride and Some Related
Compounds ....................... 119

viii

LIST OF FIGURES

FIGURE Page
1. Schematic Representation of Splittings in 10 ——> 9
Transitions of Chloromethylsilane ........... 30
2. Block Diagram of the Microwave Spectrometer . . . . 33
3. Schematic Diagram of a Reflex Klystron Oscillator . . 34
4. Stark-Waveguide Cross Section ............. 34
5. Sample Introduction System ............... 38
6. Recorded Spectrum of the 404 —-> 413 Transition in
CHZDCHZCI35 (trans) Showing Quadrupole Hyperfine
Structure........................ 41
7. Recorded Spectrum of the 1“ —> 212 Transition in
CHZDCHzCl35 (gauche) Showing Quadrupole Hyperfine
Structure . ........... . . . . . ....... 42
8. Reference Frequency Generator . ......... . . 45
9. Difference Frequency Generator ............ 47
10. A Projection of Ethyl Chloride in its Plane of Sym-
metry Showing the Location of the a and b Principal
Axes. The c Axis is Perpendicular to the Page . . . . 55
11. A Projection of Chloromethylsilane in its Plane of
Symmetry Showing the Location of the a and b Princi-
pal Axes. The c Axis is Perpendicular to the Page . . 86
12. A Projection of Cyclopropyl Chloride in its Plane of

Symmetry Showing the Location of the a and c Princi-
pal Axes. The b Axis is Perpendicular to the Page. . 110

ix

I. HIST ORICA L BACKGROUND

Apart from the pioneering work of Cleeton and Williams (1) in
1933 on the absorption of centimeter radiation by ammonia, microwave
spectrosc0py must be regarded as a post-World War II development.
The unique combination of graduate students with previous electronic
training and the availability of discarded 1. 25 centimeter radar equip-
ment contributed strongly to the early development.

Additional stimulation for the early development of microwave
Spectrosc0py was the high resolution obtainable as demonstrated in the
early experiments of Bleaney and Penrose (2, 3) and Coles and Good (4).
Furthermore it soon became obvious that the pure rotation spectra of
a large number of molecules would appear in this spectral region.

- Most of the early work in microwave Spectroscopy was concerned
with the development of more sensitive instruments for detecting the
absorption of the microwave radiation, with the investigation of the
pure rotation spectra of linear and symmetric top molecules, with the
extension of the frequency range available for spectroscopy, with the
characterization of the inversion of ammonia, and with a number of
measurements of physical quantities (e. g. the magnetic moment of H20).
1 An extremelyimportant development was the suggestion by Hughes and
Wilson (5) that a periodic Stark effect field be applied to the sample
gas to modulate the absorption. The relatively high sensitivity obtained
with such Stark effect microwave Spectrometers has made them the most
important instruments in this region.

. The preoccupation of the early workers with the spectra of linear
and symmetric t0p-molecules was due to the simplicity of the spectra
and to the availability of simple, precise quantum mechanical expressions

for their energy levels and absorption frequencies. The study of

asymmetric rotor molecules did not become widespread until after
several years when good approximate methods for the calculation of the
energy levels of asymmetric top molecules and the development of
computers to use the methods became available.

Theory predicted that the Stark effect Shift and Splitting for a linear
molecule Should be proportional to the square of the electric field
strength and to the square of the dipole moment. Measurements on the
molecule OCS (6) confirmed the theory and now dipole moments are
measured quite routinely by microwave Spectroscopy.

The examination of a rotational transition under high resolution
very often reveals a complex structure of many lines. Such Splitting of
the rotational (transitions can occur if internal rotation is possible in
the molecule or if a nucleus with a quadrupole moment is present.

The first work on the calculation of barriers to internal rotation by
microwave spectroscopy was performed by Burkhard and Dennison (7)
on the molecule methyl alcohol. 1 Later, extensive work on this problem
was carried out by E. B. Wilson, Jr. , and co-workers (see section
2.5, this thesis).

A development of great interest to chemists is the interpretation
of nuclear quadrupole coupling constants in relation to chemical bond
type. These constants are obtained directly from microwave spectra
and measure the variation of electrostatic energy with orientation of
the nucleus. From the coupling constants and an approximate treatment
developed by Townes and Bailey (8) it is possible to obtain information
about the hybridization and the covalent or ionic character of chemical
bonds.

The determination of bond distances and bond angles is the most
common application of microwave Spectroscopy. The rotational con-
stants obtained from the microwave spectra are essentially reciprocal

moments of inertia and are determined by the location of the atoms in a

molecule and their masses. Bond distances and bond angles were first
determined by fitting the moments of inertia of several isotopic species.
This procedure was later refined to include a fit by the method of

least squares of differences between observed and calculated moments.
A method was presented by Kraitchrnan (9) which provided for fitting
differences in moments of inertia of two isotopically different molecules
to determine the position coordinates of the substituted atom. . The large
number of isotOpic species required discouraged the use of Kraitchman's
equations until it became apparent that essentially the same number of
species was required for the least squares method owing to the insensi-
tivity of the moments of inertia of some of the species to the locations

of some of the atoms. Furthermore it was pointed out by Costain (10)
that for theoretical and practical reasons the structures obtained by
means of Kraitchman's equations were more reliable than those obtained

by fitting the moments of inertia directly.

II. THEORY OF ROTATIONAL SPECTRA

‘ 2. 1 Introduction

 

In the microwave region of the electromagnetic Spectrum (0.06m
30 cm wavelength) we are concerned mainly with transitions between
rotational energy levels of molecules in their ground vibrational and
electronic states. Occasionally, however, ground state to first excited
state vibrational transitions are found in this region (e. g. the ammonia
inversion spectrum) and, in addition, rotational transitions in excited
vibrational States often contribute to the spectrum.

Due to quantization of the rotational energy levels a discrete
rather than a continuous Spectrum is observed. , The frequency of a given
transition is obtained from the Bohr frequency relation h‘z) = Wz-Wl,
where W2 represents the final and W1 the initial energy state.

The problem resolves itself into one of finding suitable relation-
ships for the evaluation of these energy levels from molecular parameters.

From the theory of Born and Oppenheimer, we may break the
complete wave equation for a molecule into two main parts, one being the
electronic wave equation and the other the wave equation for nuclear
motion. The wave equation for nuclear motion may be further separated
into two parts, one expressing the vibrational motion and one dealing with
the rotational motion of the nuclei. ~ In the separation of the nuclear wave
equation it is customary as a first approximation to consider the vibrational
motion of a non-rotating molecule followed by the rotational motion of a
rigid body, and neglect interaction between these two parts. The theory
of interaction, however, has been well characterized.

The classical quantum mechanical problem of the rotation of

diatomic and symmetric top molecules has been described by many

authors (11). The solution for the case of an asymmetric top molecule

is considerably more difficult but has been worked out in detail (12}.
Since microwave spectroscopy affords values of the soucalled

rotational constants, which are essentially reciprocal moments of inertia,

it seems appropriate to first consider the subject of moments of inertia.

2. 2 Moments of Inertia

 

For a rigid molecule, the moment of inertia about any axis passing

through. the center of mass is defined by

I ‘-= Zim-r-z (Zr-1)

- is the mass

where ri is the perpendicular distance from the axis and rn1

of the igl- nucleus. A theorem of mechanics states that the locus of
points formed by plotting Imlz-along axes through the center of mass is

the surface of a triaxial ellipsoid, known as the momental ellipsoid.
Moments of inertia about the three mutually perpendicular principal axes
of the ellipsoid are called principal moments of inertia. It is customary
to label the axes of the ellipsoid a > b > c so that for the principal
moments of inertia Ia < 1b < Ic- . Molecules are then described as linear
if one of their principal moments of inertia is zero, as symmetrical
rotors if two of the moments are equal, and as asymmetrical rotors if
all three moments are different.

The direction of one or more of the principal axes of a molecule
may often be determined from the symmetry of the molecule. ~ If a mole-
cule possesses a plane of symmetry, the plane will be a principal section
of the ellipsoid. The principal section will contain two of the principal
axes and in addition be perpendicular to the third axis. This is the case
in the molecules ethyl chloride, Chloromethylsilane, and cyclopropyl

chloride with which we will be particularly concerned in this thesis.

In the usual case where symmetry does not permit the location of
all the principal axes, they may be found by means of angular momentum
calculations .

Angular momentum may be defined as

R: I a (2’2)
whereg = vector of angular momentum
a: vector of angular velocity
I = moment of inertia (a tensor of second rank or a dyadic)

In generalfi andngill be column matrices of the same rank and there-
fore I will have square dimensions. The inertia dyadic may be written
(13):

.. 2
1- Zimi(ri 1 -gi-gi) (2-3)

.th
where m~ - mass of 1 — atom

. . h
distance of 1t— atom from the center of mass

1|

H
II

unit dyadic

In matrix form:

xx xy Ixz
I = I I I
yx yy yz (2'4)
zx zy Izz
. _ 2 z _ _
where. I X - Eimi(yi + Z1 ) Ixy " Iyx _ -zimixiyi
_. Z .3 : : .. .
IYY — Zimi(xi + Z1 ) Ixz sz 21mixizi
_ z z _ _
Izz — Eimibq + Vi ) Iyz - Izy - 'Eimiyizi

. .th
and xi, Yi’ 21 are the coordlnates of the 1 — atom measured from the

center of mass. The quantities I ,' I , and I are often called the
xx yy zz

axial moments of inertia or simply moments of inertia, and Ixy” Ixz

, etc. ,

the product moments of inertia or Simply products of inertia. Diagonal-

ization of the inertia tensor will give the principal moments of inertia.
The discussion of the moments of inertia of an asymmetric top

is Simplified by defining a matrix of the second moments, the P matrix.

We define P as

P = 10 1 - I (2-6)
where

. Z

a scalar quantity, and 1 is the unit or identity matrix. This new matrix

has the form

P P P

xx xy xz
P== P P .P
yx yy yz (2-8)
P P P
zx zy zz

l
where in general Puv = Zimiuivi , and u, v = x, y, or z. This matrix

is diagonalized by the same coordinate transformation which diagonalizes

the I matrix as may be seen by the following:

-1 -1
S IS=iol-S PS (2-9)

-1
Since i0 1 is diagonal S PS will be diagonal when S'IIS is and vice versa.

Due to trace invariance under a similarity transformation we have

+ z: + + :. 2‘10
pxx+ 1Dyy pzz Paa Pbb Pcc 10' ( )

_1
where Paa’ P and FCC are the diagonal values of S PS. . Finally we

bb'
may relate P , - P
aa

and P to I ,, I and I , the principal moments
cc a c

bb’ b"
of the molecule as follows:
Paa+ Pbb = 1° - Pcc = Ic
Paa + Pcc = 10 - Pbb = 1b (2-11)
Pbb+ pcc = 1° "Paazla

1The components of the P matrix, Puv’ are written with two sub-
scripts and should not be confused with the components of angular
momentum which will be written with only one subscript.

If a coordinate system x', y’, z', parallel to the x, y, z system
is used, whose origin is not at the center of mass of the molecule, then
the second moments in the x, y, z system are related to those in the
x', y', 2' system by the equation

PuV : Pu'v' " MlloVo (2912)

where Muo = Z,m,u, ,» M = 21m, and u,, v, are x., y,, 2.. If the mass
1 1 1 l 1 1 1 1 1 1
of one of the atoms, ms, is increased by an amount Am (as would occur

in isotopic substitution) the second moment tensor becomes

P a 2
aa T Ha'S p"Elsbs pascs
P'; = P + b 7- 2-13
Hbsas bb H s Hbscs ( )
b P ’-
Hcsas ”Cs S cc + MCs
where P , P , P are the principal second moments of the original
aa bb cc

molecule, as, bs’ cS are the coordinates of the augmented mass and
p. = (M' - M)M/M'. Here MandM' are the masses of the original and
substituted molecules respectively.

1 Kraitchman (9) has shown that the diagonal values of P and P' may
be used to determine the values of a

s’ bs’ and cs. The expression for

ais
3

las I {u'l [(Paaup >(1+§l;b—P—hb—m+ Egg—in} T <2-14)
and similar expressions for bS and cS may be obtained by cyclic
permutation of the subscripts.

Using arguments similar to those used by Kraitchman (9) the follow-
ing equation and one similar to it for lbs) may be derived for the in-
plane coordinates of a pair of atoms which straddle a plane of symmetry

(the ab plane in this case):

-1 P '-P P -P . 1
[as I s {H [( 10109253”??? 8.1.4.11}T. (2-15)

 

The out-ofc-plane coordinates of these atoms which straddle the plane

of symmetry are found from an expression of the form:

A.
I Cs I : {Erin-3- (Pcc' ' Pcc)} 2 RIM)

where mo is the difference in mass between the substituted and unsub-
stituted atoms. Again, arguments similar to those used by Kraitchman
(9) were used in the derivation (14).

. Measurements with the spectrometer yield values of la, lb, IC,
principal moments for the unsubstituted or "parent" molecule and
Ia', Ib', IC', principal moments of the isotopically substituted molecule.

These may be related to the second moments by the equations

apaa = IC + 1b - Ia
zpbb = 1a + IC - 1b (2-17)
ZPCC == 1a+ lb — IC

The coordinates of the substituted atom (as, bs’ cs) are then computed
using Equations (2-14), (2-15), or (2-16) depending on the position of

substitution.

2. 3 Energy of Rotation

 

The total energy of a rigid rotator can be expressed in terms of
its principal moments of inertia Ia, Ib, and IC and angular momenta

Pa, «Eb’ P as:

M MC
_ .13; .2122 11292
WR— 213 + 21b + 21C . (2 18)

P’- sgaz +3137- + P ’- (2-19)

The total angular momentum fiis quantized taking only the values

10

1
P = [J(J + 1)]? h/zn , (2-20)

M

where J is a quantum number limited to positive integers or zero. The
component of}: along a direction fixed in space obeys the quantum
condition

Pz = M h/21r (2-21)

where M can assume the 2.1 + 1 values
M=O,:tl, i2, :tJ .

If there is a fixed component of J along an internal molecular axis then

it is quantized according to the relation

PK: K h/217, (2-22)
where K may assume the values
K:O,:tl,d:2,'°°iJ.

The quantized rotational energy levels of a rigid linear or sym-
metric top molecule may now be easily computed. For a linear molecule,

Ia = 0, 1b = I = I and therefore

C
1:2 _ .
WR - .8272? u(.I + 1) - hBJ(J + 1) (2-23)

where B = h/81TZI is called a rotational constant. The selection rule for

absorption is AI = + 1 so that the Bohr frequency condition gives

1): 213 (J + 1) (2-24)

A symmetric top molecule is one for which two moments of inertia
are equal. Symmetric rotors are further classified as oblate or prolate
rotors. The oblate type has Ia = Ib < Ic and the prolate Ia < Ib = IC.
This means that for the prolate rotor B = C, and for the oblate rotor

A = B, where

h h h
A 37.71:» B 8721—1," C tar; ‘ 5’

11

The energy levels of a prolate symmletric top are given by

w - —-z-—hz J(J+ 1) + —-—2—hz (—-1—- ——1-—-)K"‘
R‘ 8111b 8n 1,,L " 1b ‘
= h [BJ(J + 1) + (A - B)K’-]. (2-26)

The selection rules for absorption are AJ = + 1, AK = 0 so that the

transition frequencies are

1): 2B(J + 1) , (2s27)

the same as for linear molecules.
In the above treatment we have neglected the effects of centrifugal
distortion (or non-rigidity) which are quite pronounced for high values

of J. In the linear molecule the expression for the frequency becomes

1): 2B(J + 1) — 4DJ(J + 1)3, (Z-=28)
while in the symmetric top case

_. 3 2
'c)- ZB(J + 1) s 4DJ(J + 1) - ZDJKU +1)K . (2—29)

The D's represent distortion constants which depend on the various
molecular force constants and the moments of inertia and are usually
small compared to the rotational constants. The theory of centrifugal
distortion for symmetric rotors was first described by Slawsky and
Dennison (15).

For asymmetric rotors it is not possible to write down an explicit
energy expression as in the linear and symmetric top cases. It is
possible, however, to calculate precise values for the energy through
the use of published tables. In one particularly useful approach
introduced by Ray (16) and developed by King, Hainer, and Cross (17)

the rotational energy is written as

12

A+C A-C
2 )J(J+1)+( 2

 

 

W = ( )Eflm) <2-3o)

R

where J and ’r are quantum numbers and K is an asymmetry parameter
defined by
2B-A-C
= ._ - 1
K A .. c . (2 3 1
The reduced energy function E1 ( K ) has been tabulated at intervals of
0.01 in K between K: -1, the prolate top limit, and K = + 1, the
oblate top limit (18).
Another method of calculation is available for molecules which are
nearly symmetrical rotors. For a nearly prolate rotor (B N C), K~ —1,

and

B+C B+C
wR- 2 J(J+l)+(A- 2

 

 

J
) 01?, (bp). (2-32)

Here b is an asymmetry parameter given by

b_ C-B _\<+1
p" ZA-B-C -K-3

 

 

(2-33)

The reduced energy function 009'. (bp) may be obtained from systematic

application of perturbation theory as a power series in bp’

(.05: (bp) 2‘- K2 ‘1' Clbp + Csz2 + C3bp3 + . . . (2-34)

The values of K2 and C1 through C5 have been tabulated for all energy
levels with J i 40 (19).
The similar expression for the'case of a nearly oblate rotor (A N B),

K~+ 1, is

WR=

 

A+B A+B
2

J
J(J + 1) + (c - 2 )o," (be) , (2-35)

where
A-B K-l
o-2C-A-B K+3

 

 

(2-36)

13

The rotation absorption frequencies are computed from the Bohr frequency

c ondition

h-JR e w ._ w (2s37)

R R

The index ’1' is normally replaced by the index K_1K+1 (T = K_1-K+1)
where K_1 (32-) would be the angular momentum of the molecule about the
a axis in the case of a limiting prolate symmetric top, and K.“ (22;) would
be the angular momentum about the c axis in the case of a limiting oblate
symmetric top. The subscripts -1 and +1 refer to the value of the
asymmetry parameter K in the two limiting symmetric top cases. The
quantities K_1 and K,“ assume the values zero or positive integers less
than or equal to J.

The selection rule for J is AI = 0, or i 1 and as an aid to classify-
ing transitions the designations P, Q, and R- branches are used for
AI = -1, 0, and +1 respectively. ' In addition transitions are classified
as a, b, and c-type transitions according to the direction of the component
of the dipole moment which interacts with the incident radiation.

- Selection rules for a, b, and c-type transitions are as follows:

a-type: AK_1 = even AK+1 = odd
b-type: AK-1 = odd AK“ = odd (2-38)
c-type: AK_1 = odd AK“ = even

Before continuing to the "finer aspects" of rotational spectra a
short digression is necessary concerning the rotational constants. The
moments of inertia and hence rotational constants which are normally
measured are for the lowest vibrational state. The relation between the

measured rotational constant and the equilibrium value is given by

d.
Avl-Vz... = Ae — 2, (ii (vi + 31) , (2-39)

where A8 is the equilibrium value. _ The (US are small constants and Vi

. .th .
represents the vibrational quantum number of the 1— mode and di lts

14

degeneracy. Similar expressions can be written for B and C.

To determine the equilibrium value it is necessary to know the rotational
constants for each singly excited vibrational state in addition to the
ground state. Herein lies the center of the difficulty in the determination
of structures since equilibrium rotational constants have been obtainable

only for a few very simple polyatomic molecules (e. g. H20).

2. 4 Nuclear Quadrupole Hyperfine Structure

 

In microwave spectrosc0py one of the richest sources of interest
a and information is the hyperfine structure exhibited by many pure
rotation lines due to the coupling of nuclear Spin and molecular rotation
(20). The presence of extra lines constituting a hyperfine structure in
molecular rotational spectra was first reported by Good (21) for the
inversion spectrum of ammonia. The observed hyperfine structure
patterns have been interpreted as resulting from a splitting of the mole-
cular levels caused by an interaction between nuclear electric quadrupole
moments and the gradient of the molecular electric field at the position
of the nucleus. This interaction depends on the orientation of the
nucleus with respect to the rest of the molecule and therefore causes a
given level to Split into a series of levels corresponding to the different
possible values of the total (nuclear plus rotational) angular momentum
(22). t The splitting of rotational levels resulting from interaction (or
coupling) of nuclear Spin and molecular rotation is called the nuclear
quadrupole hyperfine structure. The other type of nuclear effect which
would be expected to lead to a Splitting of molecular rotational lines is
nuclear magnetic dipole interactions. However, these magnetic dipole
interactions are generally very small in most molecules since the mole-
cules are in '2 states.

Of great importance to chemists is the interpretation of this

nuclear quadrupole coupling in terms of chemical bond type. Townes and

15

Dailey (8) have shown that the gradient of the electric field at the quad-
rupolar nucleus arises mainly from the valence electrons associated with
the given atom. According to their interpretation the electrons in

closed shells about the nucleus contribute essentially nothing to the

electric field gradient due to their spherical symmetry. Distortion of

this symmetry due to other atoms in the molecule is of minor importance.
Furthermore, nuclei and electrons of other atoms are not assumed to
contribute due to their distance from the nucleus being considered. Thus
we are left with only the valence electrons as principal contributors to

the field gradient. The spherical symmetry of s orbitals and low penetrating
power of d or higher orbitals rules out any major contribution from these
sources. We are left then with the interpretation that the hyperfine splitting
is due mainly to the amount of puorhital character of the valence electrons
associated with the quadrupolar nucleus. Thus it is possible to obtain
information on the nature of the hybridization and the covalent or ionic
character of the bond.

The quantum mechanical treatment of the splitting due to a single
nucleus coupled to the molecular rotation of a linear molecule through
electric quadrupole effects was first worked out by Casimir (23). This
work was later expanded to include linear molecules with one or two
quadrupolar nuclei (24), symmetric tops with one quadrupolar nucleus
(25), (26), (27), (28), symmetric tops with two quadrupolar nuclei (28),
symmetric tops with three symmetrically located nuclei (29), and
asymmetric rotors with one or two quadrupolar nuclei (30), (31), (32).

The Hamiltonian which was found to describe the nuclear quadrupole
interactions to first order has the form:

HQ = 218s 33-: I “it’iififli‘ltt’ ' ’13in (2.40,

AV 1 1
where: e is the electronic charge
J represents the total angular momentum of the molecule

exclusive of nuclear spins

16

D

I‘ ~.

(

. . 0th
spresents the angular momentum of the 1-- nucleruso

l-4

i
Qi 15 the electric quadrupole moment of tne 1w nucleus, a

property of the nucleus and its energy stateo

2V g . , . s 5th
and ST A 15 “the average electric field gradlent at the 1-- nucleuso
2‘ v
Here v is the potential at the i: nucleus which results
lrom all the extranuclear charges, and z is a spacewfixed

axis.

For molecules with a single quadrupolar nucleus the Hamiltonian given

above leads to a quadrupole perturbatiOn energy of the fern

32v 3/4C(C+1) .. I(I+1)J(J+-1)

 

= . ——-z— a 1
W0 90 bz [ ZJ(ZJ~1}I(ZI-1) 1’ (Z 4 )
AV
where C = F(F+l) .. HIM-1} .. J(J+l)

and F J+I, 342-14, |J~I|.

Since WQ is different for each value of F, the total rotational energy
W = W + W 22.41

will depend on F also (normally however, W > > WQ).

R
The average field gradient is evaluated along a spaceufixed
direction and hence depends upon the electronic and molecular states of

the particular moleculeo Classically
e Zv>
Bz

. . th
where rj IS the radius vector between the nucleus and the k— charge

and 9. is the angle rj makes with the space-fixedZ axiso

3cos7'9'u1
<zie[ rj’ ]>A , (2-43)
v

AV

2
O 0 V I .
Conc1se expressmns for QT> A may be obtained for the cases
2
v

of the linear and symmetric t0p molecules. v However, for the case of

17

an asymmetric top this is no longer possible. Bragg (30}, (31) has

zv

evaluated <———z—>A by first order perturbation theory and finds it to be:
v

32
2 Ev BWR 32V hWR 32V BWR
qJ‘-"BZ<VAW‘>=B(J+1)(2J+3)[a BA +3132 313 + ac21’
(2-44)

where A, B, and C are the rotational constants and WR is the energy of
the rigid rotator. Thus qJ represents a molecular propertyr wrich depends
both on the geometry of the molecule and the distribution of charges within
the molecule. It is then possible to combine the equation for qJ with
Laplace's equation (VZV = O) and obtain several useful eXpressions for the

quadrupole energy W lf Laplace's equation is assumed to hold then only

Q.
two of the partial derivatives of the potential are independent. It is
customary to choose one of these as unique and use a linear combination
of the other two as the second parameter.

One expression which is useful for near symmetric rotors is

 

qJ: (J+lz))23+3) {'3sz (J+l) +3Z(l- n)Cn b n] qm _
n= 0
[Igo(n+l)cn+lbn]qm 77} (2-45)

where K, b, and the C's are given by Equation (2-34).

E 2v
Also qm = 32—2- (2-46)
m
2' second derivative of the potential along the molecule-
fixed principal axis which most nearly represents a

symmetry axis of the momental ellipsoid,

and n = ( Dav/3x1112 - gzv/BymZqu. (2-47)

The energy is written (stopping the sums at n = 2)

18

1
WO = J_('3+_'l) [(3K2-J(J+1)-3C2bz)qm+(C1+ZCzb+3C3b2)qmn]Y(F) (2-48)

where
i—C(C+1)-J(J+1)I(I+1)

(Y(F) E fflJF) = 2(2J-1)(2J+3)I(21-1)

 

(2-49)

The quantity Y(F), known as Casimir's function, has been tabulated for
values of rotational angular momentum J between 0 and 10, for the nuclear
spins 1 == 1, 3/2, 2, 5/2,‘ 3, 7/2, 4,. 9/2, or 11/2, and all possible values
of F (33). This table also includes relative intensities of the hyperfine
structure components.

. Using values of qm and qm n which may be approximated by reference
to known similar molecules, energy values for the hyperfine structure
components may be calculated. . Using the table mentioned in the previous
paragraph, energy differences of the appropriate hyperfine components
may be computed to give the frequency displacements from the hypothetical
unsplit frequency. Obviously once the transitions have been identified l
and the frequencies accurately measured a reverse calculation affords
accurate values of the coupling parameters qm and qm n.

Another approach is to express the average field gradient in terms

of the asymmetric top reduced energy function ELI]. (K) and SEE-Eli)- (34):
_ 1 -dE(K )
WQ ‘ J(J+1) {(yaa + 7(cc)[J(J+l) " 3 dx 1+ ()Laa " 7(cc”

dE(K)

E(K) - K-—d—E-—]} Y(F) (2-50)

where E( K ) is defined in Equation (2-30) and K by Equation (2-31).

The quantities 7( aa’ etc. are given by

2
7Laa = eQ E'T'av - (2-51)

In asymmetric top molecules the principal inertial axes seldom

coincide with any of the bonds in the molecule. ~ In these cases the coupling

19

constants (X's) must first be referred to bond axes before they can be
used for a discussion of the bonds. . If the off-diagonal elements 7(ab’
%ac’ and 7(bc of the coupling tensor were known the procedure would
be both simple and rigorous. Since in first order the off-diagonal
elements do not contribute and hence are not determined, the most
common procedure is to assume that these off-diagonal elements go to
zero for axes corresponding to bond axes.

If a and b represent axes in the principal axis system of a molecule
possessing a plane of symmetry (the ab plane), and z and x represent the
in-plane axes of the principal axis system of the quadrupole coupling
tensor, then immediately we may write down the expressions (all multi-

plied by a scale constant e0)

3 2v ) 2v 32v %

 

Ba: = aa 3b: - bb Sc: -
(2-52)
Bzv _ 33v _ E 2v __
Babb _ 7gb ba}c - bbBc _ O
3% _ tzv _ BZV _
3x2 _ %xx 5yz _ 7<yy Bzz _ 7(zz
(2-53)

32v )Zv : 32v
)X3y 3x32 3y3z

 

The two sets of second derivatives are related by an axis transformation

in the plane of symmetry. The equations for this transformation are

‘ _ x 2 - 2
%aa - zz cos Oz + Xxxs1n Gz
_ . 2 2
Xbb XZZ 8111 Oz + 'x cos Oz , (2-54)

20

where ez is the angle between the a and z axes. Alternatively

7 _ }aacoszez - 'Xbbsinzez
ZZ cosre

and
. z s
z - s1n 9z

(2—55)

7( _ xaasinzej } bbcoszfl
xx

sinze - coszez
z

The value of the angle Oz may be determined in several ways.
If it is assumed that the bond connecting the quadrupolar nucleus to an
adjacent atom (e.g. C-Cl) lies along the z axis of the quadrupole tensor,
then Oz may be computed from the structure of the molecule. On the
other hand if it is assumed that the quadrupole tensor represents a

cylindrical charge distribution about the z axis then

74w: yxx ‘1/2 x“
7 74.: 7hr 0.

(2—56)

In this case

 

3 2e -1
7Laa= 7L“ ( C032; ) (2'57)

and the values of 742,2 and 62 may be determined.

Still a third way to obtain Oz is from quadrupole coupling constants
for two isotopic species. In this case it is assumed that the potential in
the neighborhood of the quadrupolar nucleus is the same for the two
species. Combination of the coupling constants for the two isotopic
species enables the determination of 7(ab’ the non-zero off-diagonal

element in the a, b, c axis system. The equations are

7 = X33, " (‘YXQBLCOSZGZ + xbbSinzz 6 )
ab ’

2 sin6 chose

or 3' 12b” (ZaasinZGz + :Xhhcoszez ) (2’58)
-2 sine zzcose

 

21

where the primes refer to the isotopically substituted species. This
value of 73b along w1th values of yaa and 7bb allows calculation

of the angle Bz from

tan 29z = Z—Zab (2-59)
yaa‘%bb

It has been shown (35) that the quadrupole coupling constant in the
bond direction of a chlorine atom is related to the ionic character of
the bond (I), to the s and d character (52 and d2) of the chlorine bond
orbital, and to a quantity II which is determined by the double bond

character of the bond. The relation is as follows:

1 = (1 - sZ - d2 + 11) - ( "X“ / quatom). (2-60)

Here quatom = - 107. 74 Mc is the quadrupole coupling constant of a

free chlorine atom.

2. 5 Internal Rotation

 

Another type of motion which provides effects visible in the micro-

wave region is the rotation of one part of a molecule with respect to
the remainder, the so-called internal rotation. . The fine structure
observable in the spectrum as a result of this type of motion is a very
sensitive measure of the potential barrier hindering the internal rotation.

. The quantum mechanics of this problem was first treated by Nielson
(36) and later extensively by Dennison and his students (37) in their study
of methyl alcohol. Further extensive theoretical work was carried out
at Harvard University under Professor E. Bright Wilsonrlr. This work,
for the general case of molecules with a relatively high barrier, has
been presented by Herschbach (38, 39). A recent review article covering

the application of microwave spectroscopy to the study of internal

22

rotation has also been published (40). The following brief treatment of
this problem will be based largely on the paper by Herschbach (39).
The model comprises a rigid symmetric rotor attached to a rigid
asymmetric frame. The hindered motion involves rotation of the sym-
metric rotor about its axis (a). The kinetic energy of this system may

be expressed in the form

2T = 2,, 1%ng + 21c; zgigug + 10512 (2-61)
where g = a, b, c refers to principal axes of inertia fixed in the

framework part of the molecule
I represents the principal moments of inertia of the

entire molecule

Ic1 is the moment of inertia of the internal top about its
symmetry axis
)‘g is the direction cosine between the top axis and the
th
g— principal axes
“g is the component of angular velocity of the framework
th . .
along the g- pr1nc1pa1 axes
u is the angular velocity of the t0p relative to the

framework.
The first term on the right-hand side of Equation (2-61) may be recognized
as that used when there is no internal rotation present, while the last
term represents the kinetic energy of the top and the middle term is a
coupling between these two types of motion.
We now redefine the total angular momentum about the principal

axes
3T

Pg =
so as to include a contribution from the internal rotation, and the total

angular momentum of the internal top about its symmetry axis

23

3 T .

to include a contribution from overall rotation.

The kinetic energy may now be expressed as

P 2 _ 2
2T = z .5. + (EL—E.)— , -(2-64)
8 lg rIa

where (p - ‘9) is defined as the relative angular'momentum of the internal
top and the framework (§ = EéPgX'gIa/Ié) and r1.1 is a reduced moment
of inertia given by

x21
rIu=Ia[l-Z—g—Q-]:I

g I (Zn65)

The form of the potential barrier hindering the internal rotation of rotors

of threefold symmetry is taken to be

2V=V3(l-cos3o.), (2°66)

where u is the angle which gives the relative orientation of the rotor
and framework.

The classical Hamiltonian becomes

2 2
= _ Pg; (13 4?) 1; _ _
H . 2g 213 + ZrIQ + 2 (1 cos 3(1), (2 67)

or upon defining an inverse of the reduced moment of inertia

_ ‘52
F — —2—;-i:— , (2-68)
H=HR+F(p-p)~’-+ gin-c0530.) (2419)

where HR is the Hamiltonian for the ordinary rigid rotator problem.

In the treatment by Herschbach (39), the F P2 term is absorbed
into H-R since it is a quadratic form in Pg. The sz2 + 33-3- (1 - cos 3a)
terms are treated as torsional terms, the eigenvalue problem of which

leads to a form of the Mathieu equation, and the cross term -2FpF is

considered as a perturbation.

24

' If the barrier to internal rotation is very large, then each torsional
state v is essentially triply degenerate and the torsional motion is simply
an oscillation in one of the three equivalent potential wells. The spectrum
will be that of a rigid rotator. . However, as the barrier is lowered it
can be shown that the torsional levels of a symmetric rotor such as the
methyl group are split into two components by the quantum mechanical
tunneling effect and further that these levels have slightly different
moments of inertia for over-all rotation. As a result the rotational lines
are doubled. The separation is small for high barriers but increases with
J, torsional quantum state, and decreasing barrier height.

The two components are labeled by the letters A and E indicating
the period (211/3 and 217 respectively) and transformation characteristics
under the symmetry group C3. Thus each torsional level v Splits into
two sublevels, a nondegenerate level, vA(o'= o), and a doubly degenerate
level, vE (0’: i1).

. Herschbach (39) has shown that each torsional state may be treated
singly by perturbation theory after a Van Vleck transformation has been
applied to the Hamiltonian in matrix form. . This reduces the -2Fp'P
terms which are nondiagonal in v to higher order so that they may be

neglected. The transformed Hamiltonian is written

_ (n) n
H _HR+anwvc_ ‘8’

v0“ (2-70)

and is termed the effective rotational Hamiltonian for the torsional state
Specified by the quantum numbers v and O’. The terms chfn) are
dimensionless perturbation coefficients which depend only on the ratio
V3/F. The index n signifies the order to which the perturbation calcu-
lation is carried. The perturbation coefficients have been tabulated as

a function of a dimensionless parameter s

s = 4/9 (V3/F) , (2-71)

25

to fourth order for the v = 0, 1, and 2 torsional states. These pertur-
bation coefficients will differlin sign and magnitude for the A and E
levels of a given torsional level v. Since the selection rule is AU: 0,
each rotational transition will be a doublet consisting of a transition
between E levels (of frequency 'QE) and a transition between A levels
(of frequency “DAL

The remainder of the theory of internal rotational splitting will be
carried through in combination with an example--the determination (to
second order) of the barrier in Chloromethylsilane. A preliminary study
indicated that the barrier lay in the range 2. 4 - Z. 6 kcal. /mole so that
s values of 110, 113, and 116 were carried through in the calculations.
A plot of the calculated splittings, 'QE - "IJA, for these values of 3
allows the determination of the exact value of s from the location of the
experimentally measured 'JE - 7)A' The barrier height is then
determined from Equation (2-71). , Each split line allows an independent
evaluation of the barrier height.

The transitions 1029 —-> 936, 1028—9 937, 1129—>~ 1038 and
112, 10 —-> 1037 of the first excited torsional state showed resolvable
internal rotation Splittings. The first two will be carried through the
sample calculations.

If the calculation is to be carried to second order then from

Equation (2 - 70)

- (1) (2)
HVG, _ HR + vac l? + vaa ‘69 Z . (2-72)

Herschbach (39) has shown that the odd order terms in P vanish for
the A levels while those for the E levels are either negligible or can be
treated as perturbations. Substituting in Equation (2-72) expressions

for F it may be shown that the energies of the A and E levels are

 

26

EWR )W ‘BW

__ R R

WA—WR+ W AAA‘l' —I§—§-ABA+-—I§-&— ACA (2-73)
BWR BWR )WR (1)

WE ‘—" WR + W AAE+ —-3—B ABE+ T ACE+ AW ,

(2—74)

where AW“) represents the contribution to the E level from the term
first order in ‘6: and the terms in AAA, ABA, etc. represent the
contributions from the terms second order in F . The difference in
energy of the A and E levels for Chloromethylsilane becomes

_ BWR BWR (1)
wAawE .. ST (AAAuAAE) +—§—B- (ABA — ABE) .. AW . (2-75)

The quantities ACA and ACE are zero because the c axis of Chloromethyl-
silane is perpendicular to a plane of symmetry. . The partial derivatives are
obtained from Equation (2-32) or (2-35) while the A terms are replaced by

AAA - AAE 2‘- FQZ [W1A(2) - W1E(Z) ] (20°76)

(2) (Z) ]

ABA — ABE F@2[W1A - WIE

(32 (2-77)
:2- [AAA .. AAE]

The energy difference then becomes

_ 2 (1)
WAEWE— (W -:Z-—-3—B-)-z-Fa WIA -AW ,(2-78)

2
using W1E( )z - l/Z W1A(2) from Herschbach's table (39) for high 5 in

the first excited torsional state.

For the case of a near symmetric prolate rotor like Chloromethyl—
silane the first order correction to the E levels of the upper level of a
somcalled asymmetry doublet becomes

2
(K_,F aleh)
W — w'

 

AWN = leEMZ? = (2-79)

27

where (1 = kale/1a
W = rotational energy of upper level of asymmetry doublet
W' = rotational energy of lower level of asymmetry doublet

The value of Aw“)

for the lower level of the asymmetry doublet is the
negative of Equation (2»79).

The experimental parameters used for the barrier calculation in
Chloromethylsilane are shown in Table I. The first and second order
corrections to the energy levels are shown tabulated in Table II while
Figure 1 is a schematic representation of the splittings for the case of
s = 113 of the 10 ——> 9 transitions. A table of calculated versus observed
splittings for the four observed transitions is shown in Chapter IV,

Section 5.6-. The average value of the barrier heig .t found was 2. 55

kcal/mole.

2. 6 Stark Effect

 

A microwave spectrometer employing Stark modulation was first
described by Hughes and Wilson (5) . The basic principle is modulation
of the microwave absorption using a periodic (100 kc) Stark effect field.

The theory of the Stark effect of asymmetric rotators has been
described by Golden and Wilson (41). Only a brief introduction to the
theory will be presented here followed by a short discussion of’its use
in identification of spectra and in determining dipole moments.

. Rotational levels are ordinarily (2J+l)-fold degenerate correspond-
ing to the (2J+l) orientations of the total angular momentum with respect
to a space—fixed axis. The fundamental property of the Stark effect is
that it lifts this spatial (M) degeneracy. - In the usual. case the electric
field will produce an effect which is small compared to the rotational
energy so that the Stark splitting may be treated as a perturbation on

the total energy. As a result

28

Table 1. Parameters Used in the Analysis of Internal Rotation in

 

Chloromethylsilane.
A = 21666. 99 Mc(a)/sec
B = 3186. 19
c z: 2928. 36
1a = 23. 331852 amu A’-
1b = 158.663168
Ia = 5. 957 amu AZ
tam = 0.8287 xb = 0.5597 M: = 0
r = 0.81290
r1CL = 4.8424 amu A’-
F = 104.397 koM
62 = 0.044766
83 0.000441

 

(a)
(b)

from ground state

(C)ko = kilomegacycles

Mc = megacycles = 106sec"l

29

T A BLE II.
Chloromethylsilane.

Calculation of Corrections to A and E Levels of

 

First Order Correction to E Levels

 

 

(K-.Faw1,§")z/(w - w')

 

 

 

 

 

 

 

 

 

 

 

 

Asymmetry
doublet (W-W')Mc S. = 110 113 116
936~937 16.045 0.317 0.192 0.118
1039-1028 1304.767 0.002 0.001 0.000
Second Order Correction to A and E Levels
BWR 8" EWR z (z)
' ill—37 ”37’ W1 F ° WIA-
, BWR 132 2W _ T
Level 37:? 3247133) 3 -110 113 116
936 8.9921 0.4161 2.715 2.116 1.654
937 8.9939 0.4142 2.715 2.116 1.654
10?,8 3.9423 0.6185 1.316 1.026 0.802
1029 4.0102 0.5152 1.353 1.054 0.824
Level W(E) - W(A) 1) - 1)
E A
5:110 113 116 110 113 116
936 3.032 2.308 1.772 > 1.728 1.291 0.976
1029 1.304 1.017 0.796
1028 1.318 1.027 0.802

 

30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E
,’ ' 'T__—
I 936 ‘1‘— E I 0. 9O
, 0J9A\
I \ 1.41
I, \
Jig—r, 16 04 A
K = 3 \ . A1) = l. 29
\
\ E L
\ 937 --—-1—é—\// 0.52 —
‘ 0.19 E '\
\ 1.41
A __—
m): 0.90
LL 1
“If ‘I'
1028 E x E
I, A
J = 10 ’ 1304.78
K = \
\
‘\
\ 1029 E ’ E
A \ 0.68
L a l b l C ‘l d 1
a - Symmetric Rotor
b - Slightly Asymmetric Rotor (no internal rotation)
c - With Internal Rotation: First Order Correction f s __ 113
d - With Internal Rotation: Second Order Correction or _

Figure 1. Schematic Representation of Splittings (Mc) in 10 —-9 9
Transitions of Chloromethylsilane.

31

W=WR+WQ+WIR+WS (2-80)

where WR is the energy of a rigid rotator, WQ is the nuclear quadrupole

co t ib' t' W
n r 11 ion, AIR

correction due to the electric field.

is the contribution from internal rotation, and WS the

A uniform electric field is applied so that the field direction is
the space—fixed direction. The Stark effect then arises from the inter-
action of this field with the permanent electric dipole oriented within the
molecule and with a dipole induced in the molecule by the field. For
practical purposes the latter may be neglected.

From the theory of Golden and Wilson (41) a shift in the energy
levels is predicted which is proportional to the square of the component
of the dipole moment along a given axis and to the square of the field
strength. The direction cosines between the space-«fixed axis and rotating
molecule-fixed principal axes also enter into the calculation. . These have
been shown to be directly related to line strengths so that existing tables
may be conveniently used. , Therefore, by using a plot of the frequency
of a Stark component versus square-of-theuelectric field for several
transitions, the components of the dipole moment along the principal
axes of the molecule can be computed. . Certain transitions and Stark
components are more favorable depending upon. the particular molecule.

. The identification of certain classes of absorption lines may be
carried out by observing the Stark effect. . For low J transitions of mole-
cules with no quadrupolar nucleus the Stark effect is very characteristic.
The presence of a quadrupolar nucleus within the molecule, as is true
of the cases studied here, leads to many more lines and tends to smear
out the Stark effect. However, if the molecule is a near symmetric
top then a characteristic Stark effect is still observable for certain
transitions, e. g. the erranch transitions in the molecules discussed

in this thesis .

III. DESCRIPTION OF THE MICROWAVE SPECTROMETER

3. 1 Introduction

 

In common with instruments used in other frequency regions a
microwave spectrometer consists basically of the following: 1) a source
of electromagnetic radiation of variable frequency, 2) a frequency
measuring device, 3) a sample absorption cell, 4) a detector of the
microwave radiation, and 5) a means of displaying the signal from the
detector, i. e. power output versus frequency. In addition the conventional
microwave spectrometer includes (a square wave generator to apply a
radiofrequency Stark:- effect field which modulates the absorption by the
sample.

Although the above lists the essential components a number of
variations are possible. The microwave spectrometer currently in use
at Michigan State University is shown in the schematic diagram of

Figure 2. 3 An explanation of the components is given below.

3. 2 Reflex Klystron Oscillators

 

Figure 3 is a schematic diagram of a reflex klystron oscillator
of the type commonly used for the production of microwave radiation.
A beam voltage (up to 2500 V) is applied to the cathode.. Electrons are
emitted which pass by the anode and through a deformable metal cavity
whose dimensions can be adjusted externally. A bunching of the electrons
occurs as the result of an alternating electric field existing within the
cavity. , Just beyond the cavity there appears a highly negative electrode
called the repeller or reflector which reverses the direction of the
electrons, sending them back through the cavity. These bunches of

electrons upon passing back through the cavity give up some of their

32

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34

Reflector
Electrode

 

 

Grid

 

 

‘_] Anode

Filament

 

 

Cathode

Figure 3. Schematic Diagram of a Reflex Klystron-Osci11ator..

0.050'

~0.900"

Stark
Electrode

 

 

 

.1

e—
0.400"
Teflon Tape: 0.062' x 0.400" with 0.032" groove 0.010" deep

Coin Silver Septum: 0. 032" x 0. 796"
‘ Length of Waveguide: 10'

‘ Figure 4. Stark-Waveguide Cross Section.

35

energy in the form of pulses provided they return with the proper phase.
The phase upon return and hence the oscillations in the cavity are
reinforced by adjustment of the reflector voltage and cavity dimensions.

The cavity is coupled out of the klystron into the waveguide through
a mica window. The result is practically monochromatic radiation which
is sent through the waveguide absorption cell.

. Table III is a list of the klystrons presently available in this
laboratory with the frequency ranges covered. . The frequency of each
individual klystron is variable over 40-60 Me by adjustment of the
reflector voltage or over 3-5 We by variation of the size of the cavity.

The power supply for the klystrons is an FXR Type 2815B) and is
designed specifically to provide the necessary voltages for powering
reflex klystron oscillators. The specifications include 200 to 3600 V in
two ranges for the beam voltage, 0 to -1000 V (relative to the beam)
reflector voltage, 0 to —300 V (relative to the beam) to the grid and 6. 3 V
A.C. for the heater. A separate regulated D. C. filament supply insures

stable heating for the klystron cathode.

3. 3 Waveguide Absorption Cell

 

The waveguide absorption cell consists of a ten foot piece of X-bandZ
waveguide made of brass and having a silvered inside surface. Figure 4
(page 34) is a cross section of the guide showing the dimensions; Along
the tOp and bottom of the guide is placed a strip of Teflon tape containing
slots for holding and insulating the Stark electrode. . Further details on the
Stark electrode system may be found in the section on the square wave

generator.) This X-band waveguide will conduct electromagnetic radiation

 

1Manufactured by Electronics and X-Ray Division, F. R- Machine
Works Inc. , Woodside 77, New Jersey.

ZX-band: 8.2-12.4 ko; P-band: 12.4 — 18.0 ko; Kuband: 18.0 -
26. 5 We; R-band: 26.5 - 40.0 ko.

36

Table IiI. - Klystrons Presently Available at Michigan State University.

 

 

Klystron Manufacturer Frequency Range
(ko)
X-13 Varian Associates(a) 8.2-12.4
X-12(d) Varian Associates 12.4-18.0
QK306 Raytheon(b) 18. 0-22. 0
2K33 Raytheon 22. 0-25. 0
QK289 Raytheon 27. 3-30. 0
R9518 EMI/US (C) 27. 2-32, 3
R9546 EMI/US 32. 3-37. 5

 

(a)
(b)

Varian Associates, Palo Alto,. California

Raytheon Manufacturing Company, Watham, Massachusetts

(C)
(d)

completed.

EMI/US Ltd. , 50 Swalm St. , Westbury, Long Island, New York

Purchased after work on ethyl chloride and Chloromethylsilane was

37

of frequency from 8. 2 to 40 ko. Tapered transitions are used to connect
the K- and R-band klystrons to the waveguide. The absorption cell is
sealed off from the rest of the system and madd vacuum tight by means

of mica windows. . Originally the mica windows were sealed to the wave-
guide by means of Apiezon W wax, but due to the low temperature

hardening of this wax the present system employs O- ring seals. - Most of
the length of the guide is contained in an aluminum-lined insulated box so
that the sample may be cooled to Dry-Ice temperature. A second waveguide
is now available which employs a liquid coolant and thus allows for a wider

range of temperature variation.

3. 4 Sample Introduction System

 

The absorption cell is coupled to the sample introduction system
through a tube soldered to the side of the waveguide. The vacuum system
is shown in Figure 5. ‘ Samples which are condensible at -19OOC may be
recovered unchanged after obtaining the spectra by freezing them back into
the sample bulb. The pressures used in microwave spectroscopy vary
from 10 mm to 10" mm. Hg but normally the sample is observed at from
0.1 mm to 0.01 mm Hg. ' Pressures are measured by means of thermo—
couple gauges, one attached to the absorption cell and another to the

sampling system.

3. 5 Detection

 

After passage through the region of low pressure gas in the wave-
guide absorption cell, the microwave power is measured by a detector.
"Crystal rectifiers are used almost exclusively for detectors of micro-
wave power in spectroscopy, although thermal detectors have been applied
in some special cases. The crystal detector consists of a fine wire in

contact with a block of semiconducting material (most often silicon but

38

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.8355

:0, Goowflm

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manna
Efifiom> o .H.

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appease/65>
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39

sometimes germanium). The contact resistance is greater in one direction
than in the reverse, and the current-voltage characteristic is very
nonlinear near the origin so that rectification occurs when an alternating
voltage is applied" (42). . The crystal types used were IN23 for X-band,
IN26 forK-band and R-band. 1 The D. C. portion of the output from the
crystal is sent through a current meter for indicating the power level at
the crystal. The A. C. portion of the output from the crystal is amplified
from its mic rovolt level by means of a high-gain tuned preamplifier.
From the preamplifier the signal is further amplified and sent to the
phases-sensitive detector. The reference signal for the phase detector is
the 100 kc signal from the square wave generator.

The output of the phase-sensitive detector is then sent either to the
oscilloscope or to the recorder. Signals from the detector, i. e. absorption
lines and Stark components, appear in the output with Opposite D. C.
polarity. The signal is applied to the y-axis of one trace of a dual-beam
Tektronix oscilloscope.Z On the x-axis of this trace is placed a slowly
varying sawtooth voltage . This same sawtooth voltage is applied to the
reflector electrode of the klystron, so that the horizontal axis of the
oscilloscope is a frequency scale, i. e. the oscillator frequency and
oscilloscope are being swept synchronously. The sawtooth voltage sweeps
the klystron uniformly over a mode which varies in general from 5 Me to
20 Mc in width. On the oscilloscope will appear a plot of microwave
absorption versus oscillator frequency.

1 An alternative way of displaying the spectrum is to send the output
of the phase-sensitive detector to a recorder. The klystron is driven

mechanically over the frequency range desired and now a permanent

 

1Obtainable from>Microwave Associates Inc. ,. Burlington,
Massachusetts.

zTektronix Inc. , Portland, Oregon.

40

record of microwave absorption versus frequency is obtained. Examples

of recorded spectra are shown in Figures 6 and 7.

3. 6 Square Wave Generator

The square wave generator was designed by L- C. Hedrick (43).
The specifications include 0-1250V zero-based square wave at 100 kc/sec.
However, the base of the square wave may be adjusted to other D. C.
levels if desired. . The output of the generator is connected to the Stark
electrode shown in place in the waveguide cross section of Figure 4.
At one end of the sample cell a spring loaded contact presses against the
top edge of the septum through a hole in the Teflon tape. The electrical
contact to the outside is through a. sealed N-type connector which is joined
with an O-ring seal.

The basic principle used is the modulation of the absorption of
the sample at a low radio-frequency (here 100 kc) by the application of
a square wave voltage to the electrode in the waveguide, thus creating an
alternating Stark effect. I This introduces a modulation of the microwave
energy at the low radio-frequency in the vicinity of absorptionlines.

. The function of the square wave generator then is to expose the
sample to this electric field for alternate five microsecond periods, thus
switching the absorption on and off 100, 000 times per second. . Therefore,
when the frequency of the klystron corresponds to an absorption frequency
of the sample, a portion of the microwave energy will be modulated due
to the varying absorption of the sample as the Stark-effect components
are moved back and forth in frequency. . This type of spectrometer was

first described by Hughes and Wilson (5).

 

lThe‘ Stark effect is discussedin Section 2. 6.

41

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43

3. 7 Frequency Measurements

The measurement of the frequency of an absorption line is usually
done in two steps. The steps consist of an approximate measurement
with a wavemeter followed by an "exact" measurement using a frequency
standard.

The absorption or cavity type wavemeters used throughout these
investigations are coupled to the waveguide by means of small holes.
As the klystron frequency sweeps through the frequency to which a wave-
meter is tuned, the wavemeter absorbs some of the energy. The resonance
curve of the wavemeter is traced out on the second beam of the dualubeam
oscillosc0pe and has the appearance of a weak absorption line. The wave-
meter is tuned by means of a micrometer screw and plunger arrangement
in the cavity.

There are four wavemeters currently available in this laboratory
and the one used will depend on the region of the spectrum being scanned.
The types and frequency range covered are shown in Table IV. Calibrations
were supplied by the manufacturer.

7 The arrangement for making precise frequency measurements is
shown in Figure 8. The Manson RD-140l is a proportional oven and
crystal oscillator which supplies a one megacycle sinusoidal output
frequency of high stability. The frequency stability is of the order of one
part in 108 per day. The Gertsch AM-lA VHF interpolatorZ is designed
to measure and generate frequencies from 20 Me to 1000 Mc using an
external 1 Mc standard. Accuracy of one part in 107 is reported and has
been verified in this laboratory. The frequency of the LFO (see Figure 8),
-OL.

m

is determined by using only those values of 'JL which give stable

lManson Laboratories Inc., 375 Fairfield Ave., Stamford,
Connecticut.

3 zGertsch Products Inc. , 3211 S. LaCienega Blvd. , Los Angeles
16, California. _

44

Table IV. Wavemeters in Use at Michigan State University.

 

 

 

Manufacturer Model Serial Frequency
Number Range (ko)

Narda(a) 810 128 8.2 - 12.4

Narda(b) 809 64 12.4 - 18.0

DeMornay-Bonardi(c) DBE-715-2 720 18. O - 26. 5

Microwave Associates(d) M1A518A 5 26.0 - 39.0

 

(a)The Narda Microwave Corporation, 118-160 Herricks Road, Mineola,

New York.
(b)

(C)

Not used for work on ethyl chloride or Chloromethylsilane.

DeMornay-Bonardi Corporation, 780 S. Arroyo Parkway, Pasadena,
California.

(d)

Microwave Associates Inc. , Burlington, Massachusetts.

45

 

 

 

 

     
    

  

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

   

  

 

 

 

 

 

 

 

 

 

 

 

 

 

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46

Lissajous figures when beat against the 1 Mc signal. If 1)L is such that

a stable Lissajous figure is obtained, then 11L = (p/q) where p and q are
integers which can be determined from the appearance of the figure.

The stability of the LFO is such that ‘QL may be set to better than one
cycle per second. The Gertsch FM-4A microwave frequency multiplier
will measure and generate frequencies 500 Mc to 30, 000 Mc. The equation

for the output frequency of the FM-4A is

-1)o= [n(k+-JL)i10],

where n and k are integers. The stability of the FM-4A is equal to that
of the AM-alA.

The frequencies of absorption lines in the microwave spectrum are
then measured by the difference in frequency between a harmonic of the

accurately known frequency of the FM-4A and the unknown frequency,

.. mflo _-. fidifference’

amicrowave

where m is an integer. This difference frequency is measured by means
of either the Hallicrafters SX—6Z-Al or collins 51.1—47- communications
receiver. The frequencies tof most lines can be easily measured to

i O. 05 Mc using these receivers and the uncertainty in the frequencies of
sharp lines is believed to be i O. 01 Mc.

The Collins receiver is used almost exclusively for frequency
measurements since the dial may be read directly to 0. 001 Mc. . The
Hallicrafters receiver may be tuned much more rapidly and is normally
used in the initial location of frequency markers and for measuring

approximate splittings and line widths. . The radio receivers are also

 

lThe Hallicrafters Company, 4401 w. Fifth Ave. ,. Chicago 24,
Illinois. -

zCollins Radio Company, Cedar Rapids, Iowa.

47

used for receiving the National Bureau of Standards radio station WWV.
The 10th harmonic of the 1 Mc oscillator is compared to the 10 Mc carrier
of WWV, whose accuracy at a receiver is generally better than one part
in 107. If the strength of the 10£111 harmonic of the oscillator and the
incoming WWV signal are approximately comparable and reasonably
close in frequency, the background noise will pulsate with a frequency
which is one-half the difference in frequency between the two signals.
' If the 1 Mc oscillator is adjusted so that the pulses occur at a rate of less
than one every two seconds the 1 Mc oscillator will be accurate to better
than one part in 107.

The difference frequencies are generated by means of the system

shown schematically in Figure 9.

Input

 

 

 

(Microwave —'3 '—I'— Mixer-=Multiplier
‘ Crystal
Power)
Tuning Slug
To Interpolation In
Receiver (r 3—__fi. 4 Input (Reference Signal)
O=5OO Mc
Low-pass
Filter

Figure 9. Difference Frequency Generator.

The reference signal is sent directly to the mixer-multiplier crystal whe’re
its harmonics are generated and mixed with the microwave signal. The
difference frequencies are fed back along the same coaxial cable and the

one that is less than 500 Mc passes through the low-pass filter to the

receiver.

 

C»

 

48

If the microwave signal is frequency modulated, the beat. signal
appearing at the input of the receiver will be varied also. For example,
if the klystron is varied from 24030 MC to 24040 Mc and the reference
signal is 800 Mc, the beat frequency will vary from 30 Mc to 40 Mc
(Z4030~30(800) = 30; the 3Oti1harmonic of the reference being used).

If the receiver is tuned to 36. 50 MC a sound will be heard in the speaker
each time the klystron frequency passes 24036. 50 MC. The variation

of the klystron frequency is accomplished by the sawtooth voltage placed
on the reflector electrode as explained previously. The second trace

of the dual-beam oscilloscope is used to display this frequency variation
and the beat frequency appears as a sharp "spike" on the trace. The
position of the "spike" is then governed by the setting of the interpolation
receiver. Both positive and negative beat notes are obtained so that if,
in the example mentioned above, the klystron is swept from 23975 Mc to
24025 MC, the reference frequency is 800 Mc, and the receiver is

tuned to 20' MC, two sounds will be heard in the speaker for each sweep
and two markers will appear on the oscilloscope, one at 23980. 00 Mc
and one at 24020. 00 MC.

Since the 100 kc signal and the frequency markers suffer unequal
time delays when being amplified, they may not reach the oscillosc0pe
simultaneously, so that we may have a slight displacement of identical
frequencies on the two traces. This is compensated for however, by
sweeping the klystron first from high to low frequency and then low to
high, making measurements both ways and taking the average of the two

measurements.

IV. MOLECULAR STRUCTURE OF ETHYL CHLORIDE

4 . 1 Introduction

 

Due to its importance as one of the simplest halogen- substituted
hydrocarbons ethyl chloride has been the subject of a number of reports
of microwave spectra. The a-type spectra of CH3CH2C135, CH3CH2C137,
and CHZDCHZCI” were first reported by Wagner and Dailey (44) who
also proposed a structure for the compound and determined the quadrupole
coupling parameters. The b-type Spectra of the CH3CH2C135 and CH3CHZC137
species were examined by Barchukov e_t 83.. (45) who determined the
projection of the dipole moment along the a axis in addition to proposing
a structure. The potential barrier hindering internal rotation of the
methyl group was evaluated by Lide (46) from an analysis of splittings
in transitions of the first excited torsional state using the structure
proposed by Wagner and Bailey.

Further interest in ethyl chloride at this laboratory stemmed from
a desire to provide a basis for comparison of the structure, barrier to
internal rotation, and quadrupole parameters with the corresponding
quantities in Chloromethylsilane (Chapter V), cyclopropyl chloride
(Chapter VI), and cyclobutyl chloride. The structure proposed by Wagner
and Bailey (44) included a value of 1. 5495A for the carbon-carbon bond
length which is longer than found in normal hydrocarbons (N1. 53A).

Since the barrier to internal rotation in ethyl chloride is considerably
larger than that generally accepted for ethane, a long carbon-carbon
bond would have been of interest for theories of internal rotation. ' In
order to obtain a complete set of molecular parameters by means of the
substitution method proposed by Kraitchman (9), several isotopic species

of ethyl chloride were prepared and their Spectra examined.

49

5O

4. 2 Preparation of Samples

 

In addition to the CH3CHZC135, CH3CHZC137, and CHZDCHZCI”
(gauche and m)‘ species which were re-examined, the species
CH3CDZC135, C13H3CHZC135, and CH3C13HZC135 were prepared and their
spectra examined. These compounds were made following for the most
part procedures given in the literature. * All preparations were done
in a vacuum system, with the purity of the final products determined by

examination of their infrared spectra.

CH3CHZC135 and CH3CHZC137

 

The CH3CHZC135 and CH3CH2C137 spectra were examined using a
sample of ethyl chloride obtained from the Eastman Kodak Company
(C137 - 24. 6% in natural abundance). The sample was used without

further purification.

CH3CDZC1

 

The CH3CD2C1 was prepared by a modification of a published
synthesis for labeled ethanol (47). The synthesis begins with the absorp-
tion of acetyl chloride vapor by a stirred solution of lithium aluminum
deuteride in diethylene glycol diethyl ether, followed by alcoholysis with
ethylene glycol monophenyl ether (Z-phenoxyethanol). The deuterated
ethanol (CH3CDZOH) which is evolved is trapped in a bulb cooled by
liquid air. The alcohol is distilled over onto-frozen phosphorus tri-
chloride and upon warming CH3CDZC1 is evolved. The equations

representing the reactions are:
ZCH3COC1 + LiAlD4 —% LiAlClz(OCDzCH3)z
LiAlClz(OCD2CH3)Z + ZHO-(CHz)z-O- Q —-—>
2CH3CDZOH + LiAlClz(O-(CHz)z-O- (p )2

3CH’CD20H + PC13 '—> 3CH2CH2C1 + H3PO3

A__4_

1Trans and gauche refer to the relative position of the deuterium
and Chlorine atoms.

51

CHZDCHZCI (trans and gauche)

 

The trans and gauche CHZDCHZCI were made by allowing a mixture
of ethylene and deuterium chloride to stand for several hours at Dry Ice
temperature in the presence of anhydrous aluminum chloride. The
deuterium chloride was made by adding phosphorus trichloride dropwise
to deuterium oxide (48). The equations involved in the preparation are:

PC13 + 3DZO ——> 3DCl + D3PO3

A

The final sample is an equilibrium mixture of one part trans isomer to

two parts gauche isomer.

C13H3CH2C1

 

The basic procedure used in the preparation of this isotope may
be divided into two parts, the first is the preparation of sodium acetate
from methyl iodide as given by Cox, Turner, and Warne (49), and the
second is the preparation of ethanol from sodium acetate as given by

Cox and Turner (47). The equations representing the overall preparation

 

are:
13 H20 13
C H31 + KCN ——--—>C H3CN+KI
1
C‘3H3CN )NaOH > C‘3H3coon fl C13H3C00Na
2) H230,

2C13H3COON3 + (C2115)ZSO4'A 2C13H3COOC2H5 + Nast4

C13H3COOCZH5 L‘MH“; C13H3CHZOH

 

C‘3H3CHZoH 391-9» C13H3CHZC1

A sealed flask containing labeled methyl iodide (approximately 45%
C13H3I), potassium cyanide, and water was shaken until the reaction
mixture became homogeneous. The flask was then cracked open and the

mixture of water, acetonitrile, and any unchanged methyl iodide was

52

vacuum distilled into a flask containing a sodium hydroxide solution.
This flask was sealed off and heated at 80°C for a period of four hours.
Following the addition of silver sulfate the mixture was acidified and
steamisdistilled. The pH of the distillate was adjusted to 8. 8 with
sodium hydroxide and labeled sodium acetate obtained by evaporation.
The finely powdered sodium acetate was heated with diethyl sulfate and
a slow stream of nitrogen gas was used to sweep out the ethyl acetate
formed. The preparation of the C13H3CHZC1 from the C13H3COOC2H5
followed closely the procedure given for the preparation of CH3CD2C1
from acetyl chloride, however, using C13H3COOCZH5 and LiAlH4 in place
of the CH3COCl and LiAlD4 respectively. A dilution of C-13 occurs in
the reduction such that the final sample contained 20-25% of C13H3CHZC1.

_ CH3C13H2C1

 

For the preparation of CH3C13HZC1 a sample of CH3COONa contain-
ing approximately 50% CH3C13OONa was obtained from the isotope
Specialties Company.1 The procedure for converting the sodium acetate
to ethyl chloride follows exactly the last three steps of the previous

synthesis. The equations are:
2CH3C‘300Na + (C2H5)zso,—> 2CH3C13OOCZH5 + Nazso4
CH3C‘3ooczH5 295% CH3C13HZOH

CH3C13HZOH 33—011» CH3C‘3HZC1

4. 3 Microwave Spectra

Once the isotopic species to be used in the structure determination
have been prepared the procedure for analyzing the spectrum of each

may be outlined as follows:

 

lIsotope Specialties Company, 170 W. Providentia, Burbank,
California. .

 

53

a) Computation of the principal moments of inertia of the species
based upon. an assumed structure. The rotational constants,
energy levels, and transition frequencies are then computed.

b) Search of the microwave spectrum of the compound for the
predicted absorption lines and careful measurement of the
frequencies of absorption lines in the regions of those predicted.

c) Assignment of absorption lines to the energy levels involved
and recalculation of the principal moments of inertia based

upon the experimentally measured frequencies.

Initial Computation of Moments of Inertia, Rotational
Constants and Transition Frequencies

The structure assumed for ethyl Chloride was that reported by
Wagner and Dailey (44). They gave accurate values for the rotational
constants B and C but were unable to determine A to any degree of
accuracy since the transitions they studied were insensitive to this con-
stant. The parameters they reported'included:

CC 1. 5495 4 0.0005A HCH 110°00' 4 30'

CH 1.1014 0.003A CCCl 110°3o' 4 2'

CCl 1.7785 :1: 0.0003A
The Russian workers (45) reported values of A for the Cl-35 and Cl-37
species. The moments of inertia and rotational constants for each
isotopic species were computed, assuming that isotopic substitution
does not affect the position coordinates of an atom. . The calculation was
performed using "MISTIC" the electronic digital computer at Michigan
State University.

The program used is one which transforms from a spherical polar
coordinate system with an arbitrarily chosen origin to a center of mass
Cartesian coordinate system from which the principal moments of

inertia and rotational constants are computed. A more detailed description

 

54

of this program may be found in the current literature (50). Preliminary
calculations showed that all the Species of ethyl chloride considered
were near-symmetric prolate rotors ( K = -0.940 to K :2 -O.965).

. From the rotational constants the desired energy levels and
transition frequencies are computed. The dipole moment of ethyl chloride
may be resolved into components along the a and b principal axes (see
Figure 10) so that both a and b-type transitions Should be observed.

The value of the component of the dipole moment along the a axis has
been measured by the Russian workers (pa = l. 745 D i l. 2%) (45) but
they report no value for the b component. Wagner and Dailey (44) report
that the a component would be about four times larger than the b com-
ponent and that they were unable to find any b-type transitions.
Substitution of the restrictions on J and K into Equation (2-32) and
using the Bohr frequency condition, Equation (2-37), gives for Rubranch

a—type transitions

B+C

2 )[bACI + bZACz + b3AC3 + no.1 (4-1)

 

'L)R=(13-;;9—)2J+(A-

This type of transition depends primarily on the values of B and C and
accounts for Wagner and Dailey (44) being unable to obtain an accurate
value of A. The other types of transitions in which we are interested

are R-branch b-type transitions JOJ —) (J+l)1, 3+1, for which

B+ B+
1) C C

R e (T) 2.] - (A - T) + (C—f’mc. + bACz +1 <4-2)

and the Q-branch b-type, JOJ —> J1, 51-1, for which

1)K = (A - B—gc) + (C—Z'B) [AC1 + bACz + b-’-AC3 + ] . (4-3)
The b-type transitions are very sensitive to the value of A as may be
seen from the frequency expressions. With these expressions for the

transition frequencies a whole series of absorption lines were computed.

55

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56

A perturbation of the energy levels occurs in the case of ethyl
chloride due to the quadrupole moment of the chlorine nucleus, so that
the single absorption line of a transition, whose frequency ( flR) is
computed as described above, is Split into several components (hyperfine

structure). . From Equation (2-37) and (2-42) we may write for the

frequency

1): 1)K + 2),, (4—4)

where ‘Z>R (called the hypothetical unsplit frequency) is a function only

of A, B, and C while ‘2)0
[Equation (2-33)] and the quadrupole coupling parameters qIn and qm n

is a function of the asymmetry parameter b

[Equations (2-46) and (2-47)]. The frequencies ‘UR and 1)Q are
computed separately since ‘U0 is only weakly dependent on the
asymmetry parameter b and using only approximate values of A, B, and

C one computes highly accurate values of 1) The value of ‘()R is

obtained from Equations (4—1, 4-2, 4—3) usinthhe assumed values of

A, B, and C while the calculation of --¢)Q is illustrated in Table v for
the Q-branch transition 404 —-> 413 of the parent Species (Cl-I3CH2C135).
The values of WQ/h for each level were calculated from Equation (2-48)
using the values of qrn and qm n given by Wagner and Dailey (44).1 The
differences, FOO, are found for the F—-—>. F' transitions of interest.
For Q-branch transitions the strongest components are those with

AF = O, i.e.-1_5_L ——> -i-l— , g- ——> 3., etc. The relative intensities govern
which transitions will predominate as Shown in the last line of the table.
The pattern predicted for this hyperfine multiplet is Shown in the lower
half of Table V. Comparison of the predicted appearance may be made

with the recorded spectrum of the 404 ——+ 413 transition of CHZDCHzCl35

(trans) as shown in Figure 6, Chapter III.

 

lqm = 48,855 MC; qmn e -2135 Mc; 1 = g- for C1-35 and C1-37.

57

Table V. Computation of Hyperfine Structure for the 404 -——>~ 413
Transition in CH3CHZC135.

 

C omputation of '1)

 

 

 

 

 

 

 

 

 

 

 

Q-
F = J + 3— J + 25 J - 3,1- J ., ~3-
(—‘z‘—) (i) (it) (‘3')
Egg (404) +4.53MC -7.92Mc -3.56Mc +8.89Mc
Wo
. (413) +2.82 ~4.93 -2.22 +5.52
n
1) AW
021—9 «1.71 +2.99 +1.34 -3.37
Relauv." (a) 31.5 23.6 18.1 14.9
Inten51ty
Appearance of the Spectrum
1 1 J 1IDR A A j
I l
~2- ass-
i— 9%-
ree iTi
L 1 1 I
1.66 Mc 3.05 MC 1.65 MC

 

(a)Reference 12, Appendix. I.

58

The calculation Shown in Table V is carried out for all of the
transitions of interest and accessibility, i. e. one must take into account
the regions covered by available klystrons. The calculation of hyperfine
Splittings may also be carried out using Equation (Zn-50) with a program

designed for use with "MISTIC. "

Examination of the Spectra and Assignment of Transitions

 

The Spectra of all the species were examined at Dry Ice temperature
using the conventional Hughes-Wilson microwave Spectrometer described
in Chapter III. Both oscilloscope display and pen—anduink recording
were used. Normally a recording of the region several hundred megacycles
on either side of the predicted frequency was made and lines within the
region having the predicted quadrupole patterns measured.

Both autype and butype transitions were observed for all the isot0pic
species and with the exception of the R-branch b-type all transitions
showed resolvable hyperfine structure. An assignment of transitions
was considered to "fit" when at least two R-branch autype and two Q-branch
b—type transitions were consistent to within one tenth of a megacycle with
a set of A, B, and C values. _ The Rabranch bmtype lines were used as a
final confirmation of the assignment in all but two cases. Traces of the
In --> 212 transition in CHZDCHZC135 (gauche) and the 404,—)- 413
transition in. CHZDCHzCl35 (trans) are Shown in Figures 6 and 7 in
Chapter III. The frequencies of the l —-> 2‘a-type transitions reported by
Wagner and Dailey (44) for the species CH3CHZC135, CH3CH2C137, and
CHZDCHZCF‘5 were remeasured and found to vary by as much as :0. 5 MC
from their reported values. Table V1 is a list of the frequencies of all
the assigned hyperfine component transitions used in the determination
of the quadrupole coupling parameters and rotation constants. Table VII
is a list of other measured frequencies together with their probable

assignment in certain cases. Blanks exist in these tables either because

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63

a region was inaccessible with present klystrons or because the lines
were too weak for accurate measurement. The uncertainty in the
absolute frequency measurements of transitions is believed to be no
greater than :I: 0.05 Mc while the differences in frequencies within
multiplets is probably less than i O. 02* MC.

The average frequencies of the hyperfine multiplets is used to
obtain approximate values of the rotational constants. Differences in
the frequencies of the components of a multiplet will depend only on 110,
and hence may be used with the approximate values of A, B, and C to
compute precise values of qm and qm n . ' Selected differences within the
O ”9* l and l ->- 2 transitions were used to determine the values of qIn
and qm n by means of least squares. The precise values of qm and qmn
were then used to compute '1) R for the various transitions from which
precise values of A, B, and C are determined. A comparison of the
calculated and observed frequencies obtained after a least squares
determination of qm and qmn is shown in Table VIII for the CH3CHzCl35
species. Similar computations were carried out for each isotopic species.

With accurate values of qm and qmn the hypothetical unsplit
frequencies (flR) may be computed. These are given in Table IX.
From the hypothetical unsplit frequencies the values of A, B, and C
are computed. . For the determination of B and C the following transitions

were used (obtained from Equation (4-1)

130009101=1J0 : B+C
film->212: fll = B+3C (4-5)
- =3B+C.

‘1)110 "'> 211 _ 1)?-

A least squares analysis shows that in fact

B

3,2—(4 1)., -10-r.)1+ 26 1);) and
(4-6)

‘172"(4")0+ 26-01-10-02)

O
n

64

Table VIII. Comparison of Calculated and Observed Frequencies of
Hyperfine Components in CH3CHZC135.

 

Calculated Observed
Transition F —->- F' Frequency Frequency
000—). 101 3/2——>3/2 10446.15 10446.11
3/2 -> 5/2 10458.45 10458.46
3/2 -->1/2 10468.29 10468.37
111-3 212 3/2—>5/2 20371.50 20371.50
5/2-9 5/2 20374.90 20374.88
3/2 —-> 3/2 20377.86 20377.89
5/2 —-> 7/2 20383.80 20383.79
1/2 _->1/2 20392.88 20392.86
Ila—>2ll 3/2—->5/2 21433.83 21433.79
3/2—> 3/2 21436.25 21436.27
5/2—> 5/2 21442.73 21442.73
5/2->- 7/2 21446.13 21446.21
1/2—> 3/2 21452.28 21452.27
1/2—> 1/2 21455.68 21455.62
161 —> 202 1/2 —> 3/2 20891. 57 20891.45
5/2—-> 5/2 20892.58 20892.41
3/2 —;~ 5/2 20904.88 }
5/2 —> 7/2 20904.94 20904°87
3/2—-> 3/2 20913.71 20913.69
303 —> 312 3/2 —-> 3/2 27734. 23 27734. 22
9/2—> 9/2 27737.01 27737.03
5/2—> 5/2 27740.18 27740.18
7/2 -—> 7/2 17742.95 27742.95
404-434l3 5/2—-> 5/2 28862.90 28862.92
11/2—> 11/2 28864.58 28864.73
7/2 —-> 7/2 28867.70 28867.92
9/2 —> 9/2 28869. 38 28869.63

 

65

 

 

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66

The value of A was then obtained from the frequency of the lowest
J Q-branch line observed. The rotational constants, moments of inertia,
and second moments are shown in Table X.

The B and C rotational constants for the Cl-35 and C1~37 species
are essentially the same as found by Wagner and Dailey (44) and the A
constant in both cases is within 0. 5 MC of that reported by the Russian
workers (45). The B and C constants should be nearly free from un-
certainty due to centrifugal distortion effects while a small uncertainty
from this cause may remain in A. The effect of this uncertainty on the
structure determination should be negligible both because the value of
A is quite largemaking the percentage error relatively small, and
because differences in corresponding moments of inertia of the various
species are used in the coordinate evaluations. The last step is an
analysis of the molecular structure based upon these experimentally

determined parameters .

4. 4 Molecular Structure

 

The data of the present work combined with those previously
reported are sufficient to determine the coordinates of all the atoms in
ethyl chloride by the substitution method described in section 2. 2. For
this purpose the second moments were computed for all the species and
are given at the bottom of Table X. The CH3CI'.HZC135 species was chosen
as the parent species for use in Equation (2-14). The second moments of
the parent species combined with those of CH3CHZC137 determined the
coordinates of the Cl atom, those of the two C-13 species determined
the coordinates of the two carbon atoms and the trans and gauche
deuterium species served to locate the methyl hydrogens. The doubly
deuterated species was used with-Equations (2-15) and (Zulé) to determine

the methylene hydrogen coordinates.

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68

For an atom substituted in the plane of symmetry (the ab plane in
this case) Pcc and Pcc' should be the same if the molecule is rigid.
However, the zero point motions and hence the effective coordinates
of the atoms are always changed by isotopic substitution, causing
differences between Pcc and Pcc' to occur. .The values of FCC for the
various species of ethyl chloride are shown on the bottom line of Table X.
It may be seen that PCC decreases slightly upon substitution of a heavier
isotOpe for the chlorine atom or either carbon atom, whereas there is
a much larger increase in PCC upon substitution of deuterium for
hydrogen. The reasons for this difference have been described quali-
tatively for propane (51) and are probably very similar for ethyl chloride.

Examination of Kraitchman's equations (Equation (2—14)) show

that if PCC'-P is assumed to bezero, the term including this quantity

cc

will vanish. Furthermore it is then possible to compute Paa"Paa and

PL, ('“Pbb using only two of the three experimentally determined moments
L- . ,

of inertia. Since Peck-PCC is not zero, the values of the coordinates

obtained will depend upon which two moments of inertia are chosen.

That this is true may be seen from the expressions for as and b5

-- 1 APbb
a 4:: — AP. 1+ ——-——
I 3' H aa( Pbb-Paa
(41"?)
1 AP
b 2 = — AP 1 +
| 5' H bb( Paa-Pbb

which are obtained from Equation (2-14), dropping the term in APCC.

The evaluation of APaa and APbb in terms of moment of inertia differences
is now possible for three different cases. If we do not know Ala (the
difference in the a moments of inertia for the parent and isotOpic species)
then it may be shown that

Ala = AIC — AIb and (4--8)

APaa = Alb

(4-9)

[I

APbb AIC - Alb.

69

If we do not know Alb, then
APaa : AIC - Ala

(£1le)
Apbb = Ala .
Finally, if we do not know AIC, then
Apaa == Alb
(4-11)
Apbb = AIa.

- In Table XI the variations of certain of the molecular parameters with
choice of moments of inertia is shown.

The values of the CC and CCl distances and the CCCl angle are
nearly independent of the choice of moments of inertia. However, the
CH(t) distances and CCH(t) angle show large variations reflecting the
large difference in FCC shown in Table X for CHZDCH2C135(t) and
CH3CH2C135. The large changes in the H(t) parameters are magnified
by the small value (N 0. l A) of the b coordinate of H(t). The coordi-
nates listed in Table XII are averages of those used to compute the
entries in Table XI. The molecular parameters shown in Table XIII
were computed from the coordinates in Table XII with the exception of
the methyl group parameters. Because of the small b coordinate of
H(t), and because of the large change in inertial defect upon deuterium
substitution mentioned above, the methyl group was as sumed to have
trigonal symmetry about the CC bond with parameters determined by
the positions of the out-of-plane hydrogen atoms. Even though examples
of ”tilted" methyl groups have been described, the molecules most
closely resembling ethyl chloride do not appear to have-tilted axes (52).
The uncertainty in the coordinates of the in—plane hydrogen atom in
ethyl chloride is too large for a meaningful analysis of the tilt of the

methyl group axis .

70

Table XI. Variation of Parameters in Ethyl Chloride with Choice of
Moments of Inertia.

 

 

— =
Parameter Ia’Ib’Ic 1b, IC Ia’ Ic Ia’ Ib

cc 1.5205A 1.5233A 1.5175A 1.5198A

cc1 1.7888 1.7880 1.7895 1.7861

CH (t) 1.0854 1.0610 1.1017 1.1053

ccc1 111.00° 110.88° 111. 12° 108.31O

CCH (t) 109.93° 112.92° 108. 12° 108.31o

Emiai 0.1095 amu A 0.1292 amu A 0.0898 amu A 0.1292 amu A
2mibi 0.0433 0.1180 -0.0077 .1 . -0.0074

Zmaib, —o.0430 amu A2 -0.2117 amu AZ 0.0625 amu AZ 0.0353 amu AZ

 

Table XII. Coordinates of the Atoms in the CH3CI-IzCl35 Principal Axis

System.

 

 

'Atom a b c

Cl 1.00635 A 0.11978A 0

c (methyl) -1. 71313 0. 37440 0

C (methylene) -0.60147 -0.66Z65 0

H (methylene) -0. 64078 -1. 29220 i 0. 88759 A

H (t) «2.68055 -0.12279 0

H (g) -1.64130 1.00982 i 0.88445
23mia1 = 0.1144 amu A
Emibi = 0.0366 amu A

2m,a,b, = -0.0390 amu AZ
1 1 1

 

72

Table XIII. - Molecular Parameters for Ethyl Chloride.

 

=8
cc 1.520 4: .003 A CCCl 1110214 8'

cc1 1-788 8. .002 A HCH (methyl) 108030' 4 30'
CH (methyl) 1.091 :I: .010 A HCH (methylene) 109012' :I: 30'

CH (methylene) 1.089 :t .010 A CCH (methylene) 111036' 1 30'

 

 

 

CH3CH2C135 Experimental Calculated
Ia 16.1319 amu AZ 16.0519 amu AZ
Ib 92.0202 91.7030

I 101.8744 101.4160

 

73

The uncertainties reported in Table XIII reflect only an estimate
of the inconsistency of the substitution. method as applied to ethyl
chloride. The precise meaning of the substitution coordinates has been
the subject of some discussion (53), but certainly needs further clarifi-
cation. The tests of internal consistency represented in Tables X and
XI have been discussed previously. A further test of consistency is
shown in. Table XII with the values of the first moments and cross product,
all of which should be zero since the a, b, c axes are assumed to be
principal axes.

. The moments of inertia calculated from the final parameters are
slightly smaller than the observed moments which appears to be typical

for substitution parameters .

4. 5 Discussion of the Structure

 

Examination of the parameters in Table XIII reveals a number of
interesting points. First the carbon-carbon distance in ethyl chloride
is not longer than the carbon-carbon distance in saturated hydrocarbons.
Comparison of the value found in this investigation with those reported
for propane (51) and isobutane (54) shows that in fact it is slightly smaller
(1. 520A vs. 1. 526A). These values have all been determined by the
substitution method. - In addition, an estimate of what the CC distance
in ethane would be by a substitution method has been made by Lide (54)
and also gives a value of 1.526 A. The CC distance reported for ethyl
fluoride (55), l. 533 A, is somewhat longer than in ethyl chloride. The
disagreement in the carbon-carbon bond length of ethyl chloride as
reported by Wagner and Dailey (1. 5495 A, (44)) appears to be a
consequence of attempting to calculate a structure without isotopically
substituting all, or nearly all positions within a molecule. Wagner and

Dailey substituted neither carbon atom nor the methylene hydrogens,

74

so that the positions of these atoms would be questionable.

The CCl bond length in Table XIII is slightly longer than in methyl
chloride (1.781 A, (56)) and the ccc1 included angle is 1.5° larger
than tetrahedral. However, the nearness of the chlorine atom (0. 1 A)
to the a axis prompts one to question the uncertainty in these numbers.
Calculations by Laurie (57, 58) indicate that the substitution method
tends to give coordinates which are too small when an atom is near an
axis. A larger b coordinate would increase the CC1 distance 0. 004A/.0.01A
and the CCCl angle 17'/0. 01A. In such cases it is common to use the
requirement that the first moments and product of inertia vanish to
locate the atom. ' In ethyl chloride over half the mass of the molecule
resides at the chlorine nucleus so that the small values of Emiai and
2miaibi shown in Table XII can be made to vanish by changing the b
coordinate of the chlorine atom by less than 0.001 A. In addition,
chlorine substitution results in an extremely small difference in Pccupcc’
as shown in Table X. This is reflected as a very small variation in the
CC1 distance and CCCl angle with choice of moments of inertia in
Table XI.

The CH distances and HCH angles in the methylene and methyl
groups are not unusual. However, the larger than tetrahedral CCH angle
together with the large CCCl angle lead to a very small value for the
ClCH angle. _ The uncertainty in the value of this angle may be rather
large owing to the large change in inertial defects obtained upon substi-
tution of deuterium for hydrogen. . However, all of the coordinates of
the methylene hydrogen atoms are large (greater than 0. 6 A in absolute
value) which should reduce the effect of such changes. The uncertainties
listed for the hydrogen atom parameters are based on a 0. 01 amu A2
change in the inertial defects upon deuterium substitution. - Even though

the combined effects of inaccurate location of the various atoms may

be somewhat larger than the listed uncertainties, it seems probable

75
that the ClCH angle is of the order of 20 or so less than tetrahedral.
Table XIV shows a comparison of some of the molecular parameters in

ethyl chloride with similar molecules.

4. 6 Quadrupole Analysis

 

The parameters qm and ann were determined by least squares as
explained in section 2.4. An error analysis showed the splittings to be
approximately equally sensitive to qm and qmn. The quadrupole coupling

constants 7Q , x , and were then determined from the
aa bb cc

. . + + 7( _
values of qm and qmn together w1th the relation 7(aa ’xbb cc - 0.
Table xv gives 7L , 7L , and , the diagonal values of
aa bb cc

the quadrupole coupling constant tensor in the principal inertial axis
system of the molecule. Since ethyl chloride has a plane of symmetry
perpendicular to the c axis, the coupling constant 7cc is equal to one
of the diagonal values, say 'XYY. The relations between the other
components are given by Equation (2-54).

Assuming that the direction of the z axis coincides with the C-Cl
internuclear line allows the determination of the angleIBz from the
structure, and the parameters computed on this basis are listed in
Table XV in the column headed I. Assuming that a principal axis of
the tensor lies along the C-Cl bond apparently leads to a non-cylindrical
charge distribution about the bond.

- If it is assumed that the tensor represents a cylindrical charge
distribution, then 0z and 7c zz are determined from Equation (2-57),
giving the parameters in the column labeled II in Table XV. The angle
02 is now 270, one degree larger than the value determined from the
structure. The assumption of a cylindrical charge distribution
apparently leads to an angle of 10 between the C-Cl internuclear line

and the principal axis of the quadrupole tensor.

76

Table XIV. Comparison of Ethyl Chloride with Similar Molecules.

“—
-—

 

Molecule . CC Distance ' ‘CCX Angle CCl Distance
CH,CH,_c1(a) 1. 520 A 111°2' 1.788 A
(b) 0
CH3CHZCH3 1. 526 112 24'
CH3CHZF(C) 1. 533 109°27'
CH3C1(d) 1. 781

 

(a)
(b)
(C)
(d)

This thesis
Reference 51
Reference 55

Reference 56

77

Table XV. Quadrupole Coupling Constants for Ethyl Chloride.

 

 

Principal Axes

 

 

 

 

Isotope qum (MC) 77
CH3CHZC135 -49. 20 :t 0.10 0.4479 :1: 0.0034
c‘3H3CHzc135 -48 . 48 0. 4641
CH3C13HZC135 -49. 51 0. 4224
CH3CD2C135 -5.1.07 0. 3957
CHZDCHZC135(t) -49. 32 0. 4428
CHZDCH2C135(g) -47. 36 0. 5053
CH3CHZC137 -38.65 0.4204
CCl Bond Axes

I(a) II(b)
yzz -68.8oio.15 Mc -71.24:t0.19MC
nbond“) 0.035 4 0.003 0
ez 2600' 27%! :1: 5'
I 22% 20%

 

(a)

(b)Assuming a cyclindrical charge distribution.

(dnbond = (Xxx - 7833/7sz

Assuming z axis and C-Cl internuclear line to coincide.

78

The value of the angle Bz was also determined from an evaluation
of FXab’ the non-zero off-diagonal element in the tensor in the a, b, c
axis system. Using data for CH3CHZC135 and CH3CDZC135 and Equation
(2-59) the angle 02 is calculated to be 27° i. 2°. Unfortunately the
uncertainty is large enough to include both of the previous assumptions.

It is clear that the electrostatic potential in the neighborhood of
the chlorine nucleus is approximately cylindrically symmetric in the
direction of the C-Cl internuclear line. , However, a small amount of
asymmetry, or a slightly "bent" bond, or some combination of the two,
cannot be ruled out by the present rotational spectra.

The magnitude of the quadrupole coupling constant in the bond
direction has been shown (35, 59, 60, 61) to be related to the ionic
character of the carbon-chlorine bond by means of Equation (2-60).
Assuming s2 = o. 15 and d-2 and 11 to be negligible the ionicity of the
carbon—chlorine bond in ethyl chloride is found to be 20-22% depending
upon whether assumption I or II is used as shown inTable XV. This
may be compared with 20. 8% ionic character in the CC1 bond in methyl
chloride (35).

4. 7 Barrier to Internal Rotation

 

Lide (46) has determined the height of the potential barrier
hindering internal rotation in ethyl chloride by analysis of the fine
structure of the 220 —-> 321 and 221 -> 3;; transitions in the first excited
torsional state. The computations required the moment of inertia of
the methyl group)“ 0.) and the angle between the a axis and the CC bond
(am). For this‘purpose the structural parameters of Wagner and Dailey
(44) were used. The barrier height has been recomputed using the
structure proposed above.

The calculations have been performed using Herschbach's (39)

formulation of the theory develOped by Wilson and his co-workers (62),

79

discussed in section 2. 5. In this formulation the quantity 3 k referred

to by Lide is given to highapproximation for ethyl chloride by

Sk : FaKW1E(1) + Fa3K3W1E(3) . (4-12)

The numerical values of all the parameters needed in the calculation
are given in Table XVI.

The barrier height computed using the present structure is
3685 cal/mole. This may be compared to the value 3560 cal/mole given
previously (46). The principal reason for the difference is the much
smaller moment of inertia of the methyl group used here (3. 16 amu A2 vs.
3. 28 amu A2). It should be pointed out that this value is still subject
to revision due to possible differences between the ground state structure
used here and the structure in the first excited torsional state for which

the barrier dependent frequency differences were recorded.

80

Table XVI. Internal Rotation in Ethyl Chloride.

 

8k 2 6.35 i 0.20 M68

6m = 42058'

10. = 3.1613 amu A2

r = 1- (I.L COSzem/Ia) - (IQ sinzem/Ib) = 0.87913
F =inZ/2rlz 181.9 ko

s = 4V3/9F = 94.43

V. = 3685 i 12 cal/mole

 

(axReference 46.

V. MOLECULAR STRUCTURE OF CHLOROMETHYLSILANE

5 . 1 Introduction

 

The determination of the structures of derivatives of silane and
methyl silane has afforded the opportunity for many interesting com-
parisons with derivatives of methane and ethane. The work reported
in this thesis allows direct comparison of one case, ethyl chloride and
Chloromethylsilane, while further comparisons may be drawn from
previously reported work. .The work reported here on Chloromethyl-
silane is believed to be the first determination of the molecular structure
of a derivative of methylsilane containing halogen substitution in the
methyl group.

The assignments of rotational transitions in the species CH2C13SSiI-I3,
CHZC1378iH3, CH2C135SiD3, Cch1358iH3, and CHDc1355iH, were made at '
Harvard University by Dr. R. H. Schwendeman while the assignments
for C13H3Cl3SSiH3 and CHZC135Si29H3 were made at Michigan State University
by the author. The determination of the structure and the internal

rotation analysis was also carried out at Michigan State University.

5. 2 Preparation of Samples

 

The following isotopic Species were used in the microwave study

of Chloromethylsilane

CH2C13SSiH3 ground and ls—t excited torsional states
CHZC137SiH3 ground state
CHZC13SSiD3 ground and lei-texcited torsional states
CDzCl3SSiH3 ground and ls—t excited torsional states
CHDCl3SSiH3 ground state
C13HZC13SSiH3 ground state
CHZC13SSi29H3 ground state.

81

82

The initial sample of CHzClSng was a gift from Dr. Herbert Kaesz.

The preparation of the various isotopic species of Chloromethylsilane
followed for the most part procedures which are available in the
literature. The deuterated samples were prepared at Harvard University
by Dr.- Schwendeman while the C-13 sample was synthesized in this
laboratory. The CHZC137SiH3 and CH2C13SSi7‘9H3 species were observed

in natural abundance (24. 6% and 4. 68% respectively).

c‘3'H,3c1gsiH3

 

The equations representing the synthesis are

,co- co-
13 13 /
CH,1+KNC ————>CH3\N +KI
\—co

0 — , COOH
c13H3N + Hc1+ ZHZO ——~—-> C13H3NH39HC1+

\co - A \COOH

C13H3NHz-HC1+ HZNCONHz—9 C1°H3NHCONHZ + Nl—l.c1

c13H3NHCONHZ + NaNoZ ——-> C13H3N(NO)CONHZ+ NaOH

C13H3N(NO)CONHZ + KOH 3331-31; CBHZNZ + KCNO + ZHZO

c13H2NZ+Sicn podelei c‘3H2c18ic13 + N2

 

4C13H2CISiCl3 + 3LiAlH4 ——-> 4C13HZC1SiH3 + 3LiCl + 3AlCl3

The method of Cox and Warne (63) was used directly in the
synthesis of N—Methyl.c‘3-phthalimide. Dry methyl-'Cl3-iodide was
vacuum distilled with liquid air cooling into the side arm of a flask
which contained potassium phthalimide previously dried by heating
under vacuum. The flask was sealed off, then heated at 1800C until

no liquid remained in the side arm, which was maintained at room

83

temperature. The product sublimed to the neck of the flask and was
washed out with chloroform after completion of the reaction.

. The NwMethyloCB-phthalimide was refluxed gently for several
hours with constant-boiling hydrochloric acid followed by liberation
of the methyle-CU-amine with sodium hydroxide in the standard Kjeldahl
procedure. The product was trapped in standardized hydrochloric acid.

. The method of Arndt (64) was used in the preparation of N-Nitroso-
methyl-Cmuurea. The methyl-Cl3-amine hydrochloride was refluxed
with urea for several hours followed by the addition of sodium nitrite.
This solution was added slowly to a mixture of ice and sulfuric acid
cooled in an ice-salt bath. The NeNitrosomethyl-Cmnurea rises to the
tOp as a crystalline foamy precipitate which is filtered, washed with
ice water and dried.

Diazon'iethane-=C13 was prepared by adding the NwNitrosomethyl—
Cl3wurea to a mixture of 40% KOH and ether. .The deep yellow etheral
solution of diazomethane was dried over potassium hydroxide pellets
(65).

The solution of diazometl‘ianemCl3 in diethyl ether was added at
-780C to an ether solution of silicon tetrachloride in the presence of a
small amount of c0pper powder to yield ChloromethylaC13-trichloro-
silane (66).

. The final step in the synthesis was the reduction of the chloro-
methyl-C13-trichlorosilane with a diethylene glycol diethyl ether solution
of lithium aluminum hydride to give the desired product, Chloromethyl-

C‘s-silane.

. CHJClSiDg

 

The synthesis follows exactly that of the C-13 sample up to the
final step where lithium aluminum deuteride is substituted for the

hydride in the reduction of the trichlorosilane compound.

84

 

The preparation was again very similar to that described for the
C-13 compound. . The difference lies in. the use of CDZNZ for the prepara-
tion of the chloromethyl trichlorosilane. . The CDZNZ was prepared by
converting CD3COOD to CD3CONHZ (67) and then to CD3NHZ (68). The
deuterated methylamine was then used to prepare deuterated N-Nitroso-
-methylurea from which the CDZNZ was generated with base as described
previously. The sample of CDZCISiH3 was found to contain enough
CHDClSiH3 to allow its spectrum to be recorded also.

. The spectrometers used were both conventional Hughes-Wilson
type using 100 kc Stark modulation. The spectrometer used at Michigan
State University has been described previously (Chapter III). At Harvard
the frequencies of the absorption lines were measured by comparison
with the harmonics of a crystal-controlled oscillator operating at 5 Me
which was compared with the 5 Mc carrier of radio station WWV.

Since oscilloscope display with a unidirectional sweep circuit was used
in all the work at Harvard, the absolute precision in frequency is
probably not greater thanwj; 0. 2 Mc. . However, for most of the multiplets
the frequency separations should be accurate to j; 0. 05 MC. . Frequency
measurements of transitions in the C-13 and Si-29 Species, which were
studied at Michigan State University, are believed accurate to :.I-. 0. 1 Mc
in all cases and i O. 05 Mc in favorable cases. , The rotational transi-
tions of the C- 13 species were measured for the most part using the
oscilloscope with bidirectional sweep circuit and are believed accurate
to :1: 0. 05‘Mc in most cases. The Si-29 transitions were measured from
a recorder trace using frequency markers every 1» Me and are probably
only accurate to :1; 0. 1 Mc.

The spectra were all observed with the sample cell cooled with
Dry Ice. Since Chloromethylsilane slowly decomposed in the sample

cell, occasional changes of sample were necessary.

85

5. 3 Microwave Spectra

 

Figure 11 is a projection of Chloromethylsilane in the plane of
symmetry (the ab plane). The molecule is a near prolate symmetric top
with the asymmetry parameter K varying from approximately -0. 95 to
-0. 97 for the various species (bpfv -0.007). . Both a-type and b-type
transitions were observed.

. Most of the observed lines were of two general classes: the R-
branch parallel transitions with K_1 = 0 or 1; and the Q-branch perpen-
dicular transitions with K.1 changing from 0 to l. The multiplet
structure of the parallel transitions was either unresolved or only
partially resolved, while under favorable conditions the perpendicular
transitions consisted of two pairs of clearly resolved lines, the members
of each pair being separated by 0.8 to 1.7 Me, the centers of gravity of
the pairs having a separation of approximately 5 Mc. The measured
hyperfine component frequencies of the C-13 and Si-29 species are
shown in Table XVII. The hypothetical unsplit frequencies of the species
measured at Harvard University as well as the C-13 and Si-29 species
measured at Michigan State University are shown in Tables XVIII and
XIX.

Rough values of the rotational constants were determined by fitting
the hypothetical unsplit frequencies of the observed transitions with
lowest J to the rigid rotator expression for the energy levels. Since all
the species are near symmetric prolate tops the combinations of rotational
constants which prove most convenient as fitting parameters are i— (B+C),
é—(C-B), and (A - 342$). ‘ If the frequencies of the remaining transitions
for a given species were computed using the fitting parameters selected
for the lowest J transitions, small discrepancies outside of experimental
error appeared between the calculated and observed frequencies.

In particular the value of i—(B+C) required to fit the J = 3 —> 4 a-type

transitions was somewhat different from that required to fit the

86

 

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Table'XIX. . Hypothetical Unsplit Frequencies (Mc)(a) of Observed
Transitions in First Excited Torsional State Species of

 

 

Chloromethylsilane.

Transition CH2C13SSiH3 c1«1.._c13-‘351D3 CD2C13SSiH3
303.41o4 22435.80 23992.05
313-414 23429.48
3.24413 24631.06
40......505 30517. 53 28028.14 29954.65
414:515 29915.57 27534.57 29277.72
4.3-5.4 31203.74 28592.69 30779.07
70.,.-7l6 22477.10
808-1817 23674. 57 20397. 79
909.918 20003.13

100, 10.101, 9 26672. 38 21330.46

110,“.111,lo 28501.29 22844.72

120,12....121,11 29142.97

 

(a)Uncertainty estimated to be :1; O. 2 Mc.

91

J z 4 —> 5 transitions. In addition a term in J2 (J + 1)‘2 was required to
fit the Q-branch b-type transitions. 3 Examination of the expressions
given by Polo (69) for the first order approximation to the energy of a
non-rigid near symmetric rotator showed that contributions from the

centrifugal distortion constants D and S 1 would remove the discrep-

J J
ancies. It was found that the values

DJ = 4kc and SJ 2 0.5 kc

could be used for all the ground state species. The first excited torsional

state species were fit separately using the values

D : 3kc and SJ = 0.4 kc.

J
The rotational constants in Tables XX and XXI were obtained from the
hypothetical unsplit frequencies after the above centrifugal distortion

corrections were applied.

5. 4 Molecular Structure

 

The moments of inertia of a sufficient variety of isotopic species
are available to use the substitution method of Kraitchman (9) to
determine the coordinates of every atomin the molecule except the
silicon hydrogen atoms. Table XXII lists the values of the second
moments for all the isotopic species. The last column of Table XXII

provides a comparison of the values of P

cc» which should be unaltered

for substitution of an atom in the plane of symmetry of a rigid molecule.

The coordinates of the chlorine, silicon, and carbon atoms listed in

 

1For an asymmetric rotator such as Chloromethylsilane a first
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description of the nature of these constants is reasonable for only the
simplest molecules; consequently they are ordinarily treated as adjust-
able parameters and varied to fit the discrepancies between the experi-
mental frequencies and those calculated using the rigid rotator
expressions for the energy.

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Table XXI. Rotational Constants (MC) and Moments of Inertia (amu. AZ)(a)
for First Excited Torsional State‘Species of Chloromethyl-

 

 

silane .

01120135511513 CHZC13ssiD3 CDZC13SSiH3
.A 21666.99 17484.26 17253.46
B 3186.19 -2913.42 3155.30
0 2928.36 2701.62 2854.83
1a 23.3319 -28.9135 29.3003
1b 158.6632 173.5181 160.2165
I 172.6328 187.1214 177.0792

 

(a)

Conversion factor used: 5. 05531 x 105 Mc-amu Az

94

Table XXII. Second Moments (amu A2)(a) for Ground State Species of

 

 

Chloromethylsilane.
Paa, . Pbb PCC
CHAC3135$iH3 153. 3027 18.7585 4.4745
0115137851113 157. 2886 18.8301 4. 4739
C13H2C13SSiH3 153. 2926 19. 5107 4.4704
01120355129113 155. 7366 18.7933 4. 4743
cnzcfissm3 153. 2968 23. 2028 6. 0478
CHDCl3SSiH3 153. 2949 21. 1200 5. 1400
CHZC13SSiD3 165. 3301 21. 3843 7. 4437

 

(a)

-Computed using Equation (2-17) and the moments of inertia given in
Table XX.

95

Table XXIII are averages of the coordinates obtained using the three
possible combinations of two moments of inertia or all three moments

of inertia in the Kraitchman equations (previously discussed in section
4.4). The determination of the a coordinate of the carbon atom con-
sistently gave imaginary results which characteristically occurs when

an atom lies very close to an axis. This effect is apparently due to the
difference in the intramolecular motion in the parent and C- 13 substituted
molecules. The a coordinate of the carbon atom was therefore set

equal to zero in Table XXIII.

The b coordinate of the methylene hydrogen atoms was determined
in two ways. . Equations (2-14) were used for CHDCI3SSiH3 as the sub-
stituted molecule or alternatively the moments 'of inertia of CDZC’1355iH3
were used with Equation (2-15). . The two procedures give essentially
the same results for the b coordinates of the hydrogen atoms. - Imaginary
results were again obtained for the a coordinates and consequently these
were set equal to zero in Table XXIII. The out-of-plane coordinates
of the hydrogen atoms were obtained using Equation (2-16). An essentially
equivalent value for the out-of-plane coordinates of the methylene hydrogen
atoms was obtained from the Kraitchman expression (Equation 2-14) for
Icil using CHDC13SSiH3 as the substituted molecule.

The ins-plane coordinates of the silicon hydrogen atoms were
determined by assuming the Si-C line to be the symmetry axis of the
silyl group, assuming the H-H distance to be that given by twice the
c (outuoprlane) coordinate of either atom, and fitting the difference in
moments of inertia of CHZC13SSiD3 and CHzc135SiH3.

The bond distances and bond angles obtained from the coordinates
in Table XXIII are shown as Structure I in Table XXIV.

When atoms lie too close to an axis to give meaningful values of
the coordinates using Kraitchman's equations, it is customary to try

to obtain better values of the coordinates by using the requirement that

96

Table XXIII. Coordinates of the Atoms (A) in the Principal Axis System
of CH2C13SSiI-I3.

 

 

 

Atom a b c
C1 1.4297 0.1943 0
Si -1.5697 0.1893 0
C 0 -0.8705 0
H(C) 0 -1.5191 10.8840
H(Si, in plane) -2.7377 -0.7141 0
H(Si, out of plane) -1. 5607 1. 0292 i1. 2144

 

0.1742 amu A
0.0645 amu A

M
.3
0:

M
.3
0..
H

2miaibi 0. 1340 amu A2

97

Table XXIV. Bond Distances (A) and Bond Angles (degrees) in
Chloromethylsilane.

 

1 ‘—=

(a) (b) (C)

 

Structure I Structure'II "Best" Structure

 

SiC 1.894 1.884 1.889 :1: 0.01
CCl 1.783 1.793 1.788 t 0.01
CH 1.096 1.096 1.096 3:0.01
SiH 1.477 1.477 1.477 :t 0.005
SiCCl 109.3 109.3 109.3 :t 0.3
HSiH 110.6 110.6 110.6 :1: 0.5
HCH 107.5 107.5 107.5 :1: 0.5
SiCH 109.3 109.4 109.3 :1: 0.5

 

(a)

Assuming a coordinate of C atom and two methylene H atoms to be
zero.

(‘0)

Assuming a coordinate of C atom and two methylene H atoms to be
such that Emiai = 0.

( )

c
Average of structure I and structure 11.

98

the first moments and in-plane product of inertia must vanish.
Unfortunately here the a coordinates of both the carbon atom and the
methylene hydrogen atoms need to be improved. ' Moreover the b
coordinates of the chlorine and silicon atoms are not very large.
Consequently the product of inertia was not used but instead the entire
CH2 triangle was moved enough to reduce the value of Emiai in Table
XXIII to zero. The result of this computation gives the bond distance
and bond angles shown as Structure'II in Table XXIV.

The principal differences between the two structures given in
Table XXIV are the values for the C-Si and C-Cl distances. . The SiCCl
angle is the same in the two structures and of course the hydrogen
parameters are virtually unaffected. The "best" structure in Table XXIV
is simply the average of structures I and II. The uncertainties given
arean estimate of the combined effect of inconsistencies in the substi-
tution method and the inaccurate location of the near axis atoms.

No contribution to the uncertainties has been included for possible dif-s

ferences between substitution parameters and equilibrium values.

5. :5 Quadrupole Hyperfine Structure

 

Analysis of the hyperfine splitting of the Q-branch transitions of
CHZC135SiH3 yielded the diagonal values of the quadrupole coupling
constant tensor in the principal moment of inertia axis system. . The
splittings in the R-branchlines were too small to be resolved clearly
and consequently were not used. . The splittings in the Q-branch
transitions are not greatly dependent on 12m = e0 3;];- and conse-
quently the analysis was carried out only for the parent species where
a large number of carefully measured Q-branch frequencies were
available.

Since the Q-branchmultiplets consist of two pairs of closely

spaced lines, a single experimental quantity was obtainedfor each

99

transition by differencing the average frequency of each pair. ’ If we

represent this difference by A1.) we have:

A1) 2 617% + 62(7(bb- 7(a) (5-1)

where (:1 and c; are quantities which depend only on the degree of
asymmetry of the molecule and the transition in question. The relevant
data for the Q-branch multiplets of CH2C1358iH3 are given in Table xxv.
The values of %aa and (ybb - 'XCC) were obtained by least squares
and also from the slope and intercept respectively of a plot of A‘J/cl vs.
cl/cz. The values of qum = yaa and n = (’Xbb - yea/yea are
given in Table XXVI.

The individual coupling constants may be obtained from the para-
meters chosen and the additional requirement that the sum of the coupling
constants is equal to zero. . The coupling constants so obtained are the
diagonal values of the quadrupole tensor in the principal inertial axis
system. No offs-diagonal elements are obtained but if an assumption is
made concerning the principal axis system of the quadrupole coupling
tensor, the diagonal coupling constants may be obtained in this system.

Assuming that the CC1 bond direction is a principal axis of the
coupling constant tensor allows the determination of Bz (angle between
a and z axes) from the structure. The values of 7 zz and n =
('Xxx' nyV ‘Xzz are then computed from~Equations (2-55) and
appear in the column headed I in Table XXVI (the x axis is perpendicular
to the z. axis in the plane of symmetry). - Assuming that the quadrupole
coupling constant tensor is oriented in the direction of the CC1 bond
requires that the electrostatic potential in the neighborhood of the
chlorine nucleus be slightly elliptical about the C-Cl bond.

Alternatively it may be assumed that the coupling constant tensor
is cylindrical in which case Equation (2-56) is used to compute the

results shown in the column headed II in. Table XXVI. ‘ It may be seen

100

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3

101

Table XXVI. Quadrupole Coupling Constants in CH2C13SSiH3.

Principal Axes

 

 

qum= -3Z.51_-l:.0.56 Me n =1.215i0.021

Bond Axes

I 11“”)

7(zz -68.7J-.1.6Mc ~72.0_1-_0.6Mc
92. 36.70 37.23; 0.2°
nzm 0.048.t0.016 0
1+ szudz 0.37 0.34
I 0.22 0.19

 

(a)Assuming 9z from structure I.

(b)Assuming yxx = 'ny = ’XCC.

(C)

"‘2 : (xxx ‘ $ny/xzz'

102

that the two values of 92. in the table differ by 0. 50 whichis greater
than the uncertainty in this angle as determined from the structure.
Using the values of the coupling constants obtained for CHZC13SSiH3,
the known relation between the Cl-35 and C1-37 coupling constants (70),
and the relative orientations of the principal axes of the various species
computed from the structure, it is found that the multiplet splittings of
all the species can be predicted within experimental error.
Applying the interpretation of quadrupole coupling constants of
terminally bonded atoms by'I‘ownes and Dailey (59, 60), the ionicity I
of the CuCl bond is approximately 19—22% depending upon which assump-
tion is used to compute I} zz in Equation (2-60). For this calculation

it was assumed that sZ = O. 15 and that (El2 and II are negligible.

5. 6 Barrier to Internal Rotation

 

Rotational transitions in the first excited torsional state of
CH2C13SSiH3, CD2C13SSiH3, and CH2C13SSiD3 have been observed and
rotational constants assigned (Tables XIX and XXI). Four of the observed
transitions in the parent compound show fine structure in addition to
that due to quadrupole coupling. . These splittings, which are due to
internal rotation, have been analyzed according to the method deve10ped
by Wilson and his co-workers (62) using the formulation of Herschbach
(39). . The analysis of these internal rotation splittings was presented
in the theory section (2. 5). Table XXVVII lists the frequencies 1) ,
the frequency difference -‘)A - —')E’ and the calculated values of V3
for the four transitions in CHZC13SSiH3. . Two sets of numbers are given
for two of the transitions and are the result of the partially resolved
hyperfine structure due to quadrupole coupling. The interaction between
internal rotation and the quadrupole coupling is negligible in this case.

' It is also possible to use the average value of V3 to compute the

splittings -7)A - —-(_>E. The results of this calculation-are given. in the

103

Table XXVII. ' Internal Rotation in Chloromethylsilane.

 

 

 

Transition VIA ’ (VIE-VIA)exp (VIE-lekalc V3
10;,9-93’6 32235.62 Me 1.20 Me 1.21 Mc 2.55 kcal/
32233. 43 1. 22 mole
102,843,, 30914.77 0.75 0.86 2.59
112, 10.103, 7 26284.7 1.1 1.13 2.. 53
26282.6 1..
112,9“103,8 24383.97 0.96 0.94 2.54
In = 5. 957 amu AZ
9 = 3402'
m
r = 1 .- (cosZBmIa/la) - (sinZQmIQ/Ib) = 0.8129
F z‘l‘iz/ZrIu = 104.4 mm:

Average 3 = 113.7
V3 = 9Fs/4 = 2.55 i 0.05 kcal/mole

 

104

next to the last column of Table XXVII. . The calculations in Table
XXVII required values of the perturbation coefficients at an 3 value
which is higher than that tabulated by Herschbach (39). ‘ In order to
obtain these values the entries for 72 E s i 100 were used to obtain the
coefficients of an equation of the form proposed by Swalen (71). The

equations are:

2 1
()x106)]= 7.53280 + 1.74940 log s -0.904790 Sr

.(5-2)

log I “ (WI-A

1
log [W1E(l)x 106] = 7.42187 + 1.77560 log 8 -0.907184 s?-

where the W's are the perturbation coefficients discussed by
Herschbach (39) and s is given by Equation (2-71). . The second order
correction to the E level can be obtained by use of the relation
WIE = - ~2- WIA . An extrapolation to s = 113. 7 was done by means
of these equations.

The potential barrier is determined to be 2. 55 d: 0. 05 kcal/mole.
The estimated uncertainty is believed to be large enough to include
the uncertainty in the measurement of the splittings as well as a
contribution from uncertainty in the structure. The structural para-
meters of the ground state were used with the exception of 10. which
was obtained from the moments of inertia of the first excited torsional
state Species of CH2C135SiH3 and CH2C13SSiD3. The value of v3

determined is very sensitive to 10. but not to 9 the other structural

m’

parameter needed.

5. 7 Discussion

 

The most unusual feature of the proposed structure for chloro-
methylsilane is the long 510 distance (1. 889 A). While the uncertainty
in this value is large owing to the insensitivity of the data to the a

coordinate of the carbon atom, it seems probable that the SiC distance

105

is approximately 0.02 A longer than the corresponding distance in
methylsilane (1. 867 A, (72)‘. ' In contrast fluorine substitution on the
silicon atom of methylsilane has been shown to decrease the SiC
distance (73). - A comparison of the structures of ethane (74), ethyl
chloride (this thesis), and ethyl fluoride (55) shows that the CC distance
is relatively insensitive to halogen substitution. Table XXVIII sum-
marizes the heavy atom geometry and barriers to internal rotation of
Chloromethylsilane and a number of related molecules.

On the basis of bond distance and quadrupole coupling parameters
the CC1 bonds in Chloromethylsilane and ethyl chloride seem very
similar. However, the SiCCl angle in CHZClsiI-I3 is near tetrahedral,
whereas the CCCl angle in CH3CH2C1 is 1110 (Chapter IV).

The CH and SiH distances appear to be normal. . The HCH angle
is smaller than expected, particularly since the SiCCl angle is near the
tetrahedral value. Small HCH angles in methylene groups have been
reported (51), but accompanied by larger than tetrahedral angles
between the other two bonds to the carbon. The HSiH angle (110. 60)
is approximately 20 larger than in. methylsilane (108. 30, (72)), but
only slightly larger than in SiH3F (110. 2°, (73)).

The potential barrier hindering internal rotation of the silyl
group in Chloromethylsilane is approximately 0. 9 kcal. higher than
the barrier in methylsilane (72), Table XXVIII. ‘ A similar increase in
the barrier in ethane is noted upon substitution of chlorine for hydrogen
(46). Substitution of fluorine for hydrogen in ethane is approximately
twouthirds as effective as chlorine substitution in raising the barrier
(75). . Conversely, fluorination of the silicon atom in methylsilane
reduces the barrier (76). . These data and those above clearly indicate
a striking difference in the behavior of carbon and silicon towards
halogen substitution. - It will be interesting to see if these trends are

corroborated in subsequent structure determinations of similar molecules.

T able XX VIII.

106

Comparison of Chloromethylsilane with Similar Molecules.

 

w

Bond distances (A) and bond angles (degrees).

 

 

SiC cc ' CCl SiCCl ccc1
SiH3CH2C1 1. 889 1. 788 109. 3
SiH3CH3(a) 1.867
CH3SiH2F(b) 1. 849
CH3CHZC1(C) 1. 520 1. 788 111.0
d
CH3CH3( ) 1.525
CH3CH3F (e) 1. 533
Barriers to internal rotation (kcal/mole).
V3 V3
SiH3CHZC1 2. 55 CH3CH2C1(g) 3. 56
SiH3CH3(a) 1. 67 CH3CH3(h) 2. 88
. (f) (i)
CH381HZF 1. 56 CH3CHZF 3. 25

 

(a)
(b)
(C)
(d)
(e)
(f)
(g)
(h)

(1)

Reference 72.

Reference 73.

This thesis.

Reference 74.

Reference 55.

Reference 76.

Reference 46.

K- S. Pitzer, Discussions Faraday Soc. 19, 66 (1951).

Reference 75.

VI. MICROWAVE SPECTRA OF CYCLOPROPYLCHLORIDE

6 . 1 Introduction

 

A determination of. the structure and the nature of the bonding
orbitals in cyclopropyl chloride would be of considerable interest and
importance due to its bearing on the theory of "strain" in small- ring
compounds. Numerous theoretical treatments (77, 78, 79, 80) of
the structure of cyclopropane have been presented and a great deal of
controversy appears over the direction of the orbitals in the C-C bonds,
the HCH angles, and the ability of the ring to conjugate with unsaturated
groups. ~ It is hoped that the determination of the structure of cyclo-
propyl chloride including an evaluation of the quadrupole coupling
constants by microwave Spectrosc0py will help to resolve some of the
controversy.

The study of cyclopropyl chloride is the first in a proposed
series of structure determinations on small-ring compounds. The
preparative work on the second molecule of the series, cyclobutyl
chloride, has already been started. In addition, work on 1, l-dichloro-
cyclOpropane, cyclobutyl bromide, cyclopentene, and cis-Z, 3-epoxy-
butane is being carried on at other universities.

Prior to the work reported here on cyclopropyl chloride the
microwave spectra of the C1-35 and Cl-37 species had been examined
(81) and R-branch a-type transitions assigned. . However, no transitions
sensitive to the smallest moment of inertia were reported so that the
value of the rotational constant A remained largely undetermined.

The R-branch a-type transitions of the C1-35 and Cl-37 species have
been remeasured and in addition a series of Q-branch c-type transitions
were identified and measured so that all three rotational constants

B, C, and A could be calculated accurately. A further check on A and B

107

108

was possible when the 000 ——> 110 transition, R-branch c~type (1): A + B)
was identified and measured.

. An attempt to prepare a deuterated derivative of cyclopropyl
chloride failed due to difficulty in the photochlorination of deuterated
cyclopropane. ~ A unique method of preparing a C-13 isotope was found
(82) but the first attempt (using C-12) was unsuccessful. Further work

in the preparation of these isotopes is now underway.

6. 2 Preparation of Samples

 

The initial sample of cyclopropyl chloride was obtained from
Dr.. Harold Hart and used without further purification. . The Cl-37
isotopic species was observed in natural abundance in this sample.

The following equations show the synthesis route which was used
in the preparation of deuterated cyclopropane and attempted synthesis
of deuterated cyc10propy1 chloride. It is felt that the photochlorination
step failed mainly because of the small amount (N0. 2 cc) of deuterated
cyc10propane available. The main products of the photochlorination
apparently are polychlorinated derivatives.

Br—CHZCHZuCOOH + soc1Z —> Br-CHZCHzg-COCl + so2 + HCl
ZBr-CHZCHz-uCOCl + LiA1D4 é-l—g—léérLiAmMoCDZ-CHZCHZ-Be),
LiA1C12(OCDz-CHZCHz-Br); 3%?»- Br-CHZCHz-CDZOH
Br~CHzCHz-CDZOH + 1413;: (48% aq.) —> Br-CHZCHZ-CDZBr + H20

D
Br -CH2CHz-CD2Br + Zn —-> >< + ZnBrz
D

D I
h.
2 >( +C12 —2—> VCR + .P— C1 + DCl
D D D .

A new method for preparing,mono-deuterated cycloprOpane utilizing
deuterium oxide is now under consideration as a way of obtaining a

larger amount of the isotOpic Species for use in the photochlorination.

109

A unique preparation of cyclopropane appeared in the recent
literature (82) in which diazomethane is added to ethylene in the
presence of diethylaluminum iodide as a catalyst. ' An attempt at this
synthesis was made using dimethylaluminumiodide (83) but the only
product obtained was a polymeric material, presumably polymethylene
formed from the diazomethane. . The synthesis appears attractive since
a process for synthesizing C-l3 diazomethane has already been worked

out (section 5. 2).

6. 3 Microwave Spectra

 

Figure 12 is a projection of cyclopropyl chloride in the plane of
symmetry (the ac plane). . The molecule is a near prolate symmetric top
with the asymmetry parameter K equal to approximately -0. 97 for
the Cl-35 and Cl-37 species. . The spectra were observed with the
microwave spectrometer described in Chapter III of this thesis.

. Using the rotational constants and quadrupole data given by Friend
and Dailey (81) calculations indicated that in the region 8-12 ko there
should appear a series of Q-branch c-type transitions for J=~ 5 to J = 8.
Furthermore the quadrupole interaction should split each line into two,
giving rise to a series of doublets. . However, a long and thorough
search of the spectrum from 8-12 We showed mainly quartets.

The Q-branch transitions were found only after the quadrupole
coupling constants from 1, ladichlorocyclopropane (84) were used to
predict the hyperfine splittings. The new quadrupole constants correctly
predicted quartets for these transitions and an assignment was made
easily. The values of the observed hyperfine component frequencies
for the Qubranch and R-branch c-type transitions appear in Table
. XXIX along with the calculated and observed hypothetical unsplit
frequency. The value of the rotational constant A was determined by

fitting the 0 —> 1 transition (‘J = A + B) after a good value of B had

110

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112

been calculated from the R-branch a-«type transitions. The 0 -—>- 1
transition should be almost free of centrifugal distortion effects while
the anranch lines are of higher J and could be uncertain by a few mega-
cycles due to this effect.

The R-brancha-type transitions reported by Friend and Dailey (81)
were remeasured and the frequencies of the hyperfine components appear
in Table XXX. Table XXXI is a comparison of the calculated and
observed hypothetical unsplit frequencies. ~ Agreement with the published
values is within: 0. 2 Mc for the Cl-35 species and 1; 0.4 Mc for the
Cl-37 species. Slightly worse agreement is obtained with some of the

individual members of the hyperfine components.

6.4 Molecular Structure

 

A calculation of the molecular structure of cycloprOpyl chloride
will not be attempted until more isotopic species have been studied.
With only the data presented here on the C1-35 and C1-=37 species the
structure should not differ significantly from that of Friend and Dailey
(81). However, using the structure reported by them we have been
unable to reproduce their reported calculated rotational constants.
Before the substitution method (9) can be used in a structure determin-
ation more isotopic species need to be studied.

. Table XXXII gives the rotational constants, moments of inertia,
and second moments for the C1-35 and Cl-37 species. From the second
moments and also the coordinates of the chlorine atom (a = 1'. 2861, c =
0. 0698), computed using Kraitchman's equations (9), it is seen that the

chlorine atom lies very close to the a axis.

6. 5 Quadrupole Analysis and Discussion

 

The quadrupole parameters qm and qrnn were determined from

hyperfine splittings using the method of least squares as explained

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114

Table XXXI. Hypothetical Unsplit Frequencies (Mc) of the RuBranch
.a—Type Transitions in C3H5Cl35 and c3H5c137.

 

 

Hypothetical Unsplit Frequency

 

 

Species Transition Observed Calculated

031150135 211-» 312 23005.31 23005.08
212—9 313 22156.42 22156.45
202-—> 303 22565.04 22564.90
221—2» 32.2 22583.68 22583.70
220+ 32.1 22602.45 22602.50
322» 423 30107.94 30107.95
32,,1 —> 422 30154.74 30155.01

(33115037 211.9 312 22454.72 22454. 95
212—9 313 21646.29 21646.06
202» 303 22036.13 22036.18
221 —>- 322 22053.40 22053.15
220—> 321 22069.84 22070.12

 

T able XXXII .

 

115

for C 3H5C

Rotational Constantsg (£5110), Moments of Inertia (amu AZ),

and Second Moments( C135 and C3 H5 Cl”.

(a)

 

 

C3H5Cl35 03115037
.A 16536.20 16528.92
B 3905.40 3810.35
c 3622.50 3540.70
1a 30.5712 30.5846
1b 129.4441 132.6731
1C 139.5531 142.7771
1paa 119.2130 122.4328
:pbb 20.3401 20.3443
‘pcc 10.2311 10.2403

 

(a‘
(5)

From Equation (2.. 17).

'Conversion factor used: 5. 05531 x 105 Mc-amu AZ.

116

previously (section 2.4). The 212 ——> 313 transition of the Cl-35 species
could not be fit with the present quadrupole parameters and consequently
was not used in the least squares analysis. The other K = 1 transitions
also show rather large deviations (~1 Mc) between calculated and
observed frequencies for which no explanation is known. . Similar difficulty
in fitting K = 1 transitions has been noted in other compounds (e. g. ethyl
bromide (85)). _ The difficulty, which seems certainly to be outside of
experimental error, may be due to second-lorder effects which are not
considered here. However, a preliminary estimate of second-order
effects using published equations (86) showed a frequency change of only
j; 0.01 Mc.

The quadrupole parameters Clm and qm n were also calculated using

Equation (24-48). From Equation (2-48) we may write

A1) =c1qm+czqmn

where A‘J is a difference in frequency of two hyperfine components

and c1 and c2 depend on the degree of asymmetry. A plot of AU/cl vs.
cl/cz for the various pairs of hyperfine components will give values of
qm and qmn as intercept and slope respectively. The values obtained
for qm and qmn by this method were in good agreement with the values
obtained by least squares. . The quadrupole coupling constants 7( aa’
7Lbb’ and, 7“: were then determined from the values of qm and qmn

together with the relationship

7&3 + xbb + 7cc: O

The values of the quadrupole parameters and coupling constants appear
in Table XXXIII. '

Without a knowledge of 7 ac it is impossible to calculate the
direction of the principal axes of 7‘ in the Cl-C-H plane and the value

of 7L along these axes. However, if it is assumed that the tensor

117

Table XXXIII. Quadrupole Parameters and Coupling Constants in
03145035 and C3H5Cl37.

 

 

 

031150135 c3115c137
qum -56.639 Mc =44. 373 Mc
qmn 16.808 13.009
7C... -56.639 -44.373
7065 36.724 28.691

19.916 15.682

118

represents a cylindrical charge distribution about the C-Cl bond
direction, then the direction (82) of this axis can be calculated. From
Equation (2-57), with ')L M = —2 7L bb, 02 is found to be 23.00.

Friend and Dailey (81) calculate a value of 23. 2° but as mentioned
previously we could not reproduce their rotational constants from their
reported structure. . Using their published values of bond distances and
bond angles the value we compute is 22.850.

~ A calculation of Gz was also performed using the CC, CH, and CCl
distances and HCH and ClCCl angles reported for 1, l-dichlorocyclo-
propane (84) as the structural parameters for cyclopropyl chloride.

This gave a value of 22.520 for Oz.

Finally Gz was calculated by assuming that the difference between
the in-plane and out-of—plane quadrupole coupling constants is the same
in cyclopropyl chloride and l, l-dichlorocyclopropane. , This difference
is 2.45 Mc for the dichloro compound and leads to a value of 21. 70
for Gz.

The most that may be concluded from the above series of calcu-
lations is that the angle Bz lies in the range 21. 5-23. 50. A further
evaluation of the angle will be possible when data for the C- 13 (carbon
attached to the chlorine) species is available.

- It is interesting to note that the coupling constants for l, l-dichloro-
cyc10propane (84) and methylene chloride (87) differ by only about 0. 5 Mc
and those for cyclopr0pyl chloride and methyl chloride differ by about
1. 3 Mc. The values of the coupling constant in the CC1 bond direction
are shown in Table XXXIV. The coupling constant xbond is consider-
ably less (N 5 Mc) in the mono-chloro compounds so that it appears
that the ionic character of the CC1 bond is greater for the mono-chloro

c ompound s .

119

Table XXXIV. Values of the Coupling Constant in the Bond Direction
for CycloprOpyl Chloride and Some Related Compounds.

 

 

 

Molecule FXbond
1,1-Dichlorocyclopropane 78. 89
Methylene chloride 78. 4

Cyclopropyl chloride 73.. 45

Methyl chloride 74. 74

 

F’
03400

12.

13.

14.
15.
16.
17.

18.
19.
20.
21.
22.

9‘9"???
“989.9900

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CHEMISTRY LIBRARY

 

 

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