THE MICROWAVE SPECTRA OF
2-CHLOROPRGPAR5 AND
2 - EROMCF’ROFANE

Thesis {or “we Dear“ of DH. D.
MECHIGAN STATE UNIVERSITY
Frederick Lee Tobiason

196.3
4

   
    

  

LIBRARY

Michigan State
University

 

MICHIGAN STATE UNIVERSITY
DEPARTMENT OF CHEMISTRY
EAST LANSING, MICHIGAN

ABSTRACT

THE MICROWAVE SPECTRA OF Z—CHLOROPROPANE
AND 2-BROMOPROPANE

by Frederick Lee Tobiason

A presentation of the theory of rotational spectra
with the perturbations caused by nuclear quadrupole and inter—
nal rotation interactions is given. The development centers
around the asymmetric rotor with emphasis placed on the deter-
mination of molecular structure. Sections are included which
describe the microwave spectrometer and the preparation of
samples.

The microwave spectra of the isotopic species
(CH3)ZCHCl35, (CH3)20HC137, (CH3)2000135, (CH3)2013HCl35,
013H3CHC135CH3, CHZDCH0135CH3 (3 species), and CD3CDCl35CH3
have been examined, and from the rotational constants of
the first eight species, a complete structure has been obtained
by the substitution method. The parameters obtained are

as follows: r(CC) = 1.522 A, r(CCl) = 1.798 A, rCCHseC) =

1.091 A, r(CHmethyl) = 1.092 A; <:ccc = 112°42', <ICCCl
0 _ 0 y _ 0 t ._
109 ZA', <ICCHsec — 109 54 , <ICCHd — 110 51 , <:CCHB’Y —
109°40'.
The quadrupole coupling parameters along the principal

axes are :Kaa = —6l.49 Mc,‘;<£b = 3Q.81 Mo, and co = 26.68 Mc.

Frederick Lee Tobiason

This leads to values Ofi><bond = -69.61 Mc if cylindrical
charge distribution is assumed; and«><bond = —67.82 Mc and
“bond = 0.0275, assuming that the z axis and the C01 inter-
nuclear line coincide.

A study of the first excited torsional state transi-
tions of (CH3)20HC135 and CD3CDCl3SCH3 was made. A lower
limit of 3400 cal/mole was set on the potential barrier hin-
dering internal rotation by the frequency method, and an
estimate of 3800 cal/mole was made by the intensity method.

The microwave spectra of the (CH3)ZCHBr79, the
(CH3)ZCHBr81, and the (CH3)2C13HBr79 isotopic species of 2-
bromopropane were assigned. Using the substitution method
it was found that rCCBr) = 1.962 A.

The quadrupole coupling constants along the principal
inertial axes are ><éa = #77.9 MC’.:(bb = -262.9 Me, and
:(éc = -215.1 Mc for bromine—79. This leads to values of
Xbond = 525.7 Mc if cylindrical charge distribution is
assumed; and 3<bond = 512.1 Me and “bond = 0.0266, assuming
that the z axis of the quadrupole tensor and the CBr inter-

nuclear line coincide.

THE MICROWAVE SPECTRA OF 2-CHLOROPROPANE
AND 2-BROMOPROPANE

By

Frederick Lee Tobiason

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1963

 

To my mother
in memory of my father

[-1.
H-

ACKNOWLEDGMENTS

I am.greatly indebted to Professor R. H. Schwendeman
for his guidance, encouragement, and friendly counsel
throughout the course of this investigation and the pre-
paration of this thesis.

I wish to thank Professor M. T. Rogers, Mn Chester
Orzech, and Mn.Roy L. Foley for the labeled samples which
they generously donated.

Financial assistance in the form of Fellowships from
the Petroleum Research Fund of the American Chemical Society
and from the Research Corporation through a Frederick G.
Cottrell Grant are gratefully acknowledged.

Special thanks go to my wife for her steady encourage-
ment and for the typing of this thesis.

*******

iii

TABLE OF CONTENTS

Page
I. HISTORICAL BACKGROUND . . . . . . . . . 1
II. THEORY OF ROTATIONAL SPECTRA . . . . . . . 4
2.1 Introduction . . . . . . . 4
2.2 Angular Momentum and Rotational Energy. . . 4
2.3 Moments of Inertia . . . . . . . . . 9
2.4 Nuclear Electric Quadrupole Moments . . . . 17
2.5 Potential Barriers Hindering Internal

Rotation . . . . . . . . . . . . . . . . . 21

III. STARK MODULATED MICROWAVE SPECTROMETER . . . . . 31

3.1 Introduction . . . . . . . . . . . . . . . 31
3.2 Klystron Oscillators. . . . . . . . . . . 31
3.3 Waveguide Absorption Cells . . . . . . . . 36
3.4 Square-wave Generator . . . . . . . . . . . 37
3.5 Detection . . . . . . . . . . . . . . . . . 40
3.6 Frequency Measurements . . . . . . . . . . 41

IV. DETERMINATION OF THE MOLECULAR STRUCTURE OF
2-CHLOROPROPANE . . . . . . . . . . . . . . . . . 51

4.1 Introduction . . . . . . . . . . . 51
Preparation of Isotopic Species . . . . . 52
Preliminary Calculation of Transition
Frequencies . . . . . . . .
Examination of the Microwave Spectra

Molecular Structure . . . . . . . .
Discussion of the Structure . . . . .
Quadrupole Analysis . . . . . . . . .
Internal Rotation . . . . . . . . . . . . . 96

\l
(A

Introduction . . . . . . . . . 104
Preparation of Isotopic Samples . . . . . . 104
Prediction of the Transition Frequencies . 106
Examination of the Rotational Spectra . . . 108
Molecular Structure . . . . . . . . . . . . 110

2
3
u
5
6
7
8
V. THE MICROWAVE SPECTRUM OF 2-BROMOPROPANE . . . . 104
l
2
3
4
5
6 Quadrupole Analysis . . . . . . . . . . . . 112

iv

TABLE OF CONTENTS - Continued
Page
VI. SUMMARY . . . . . . . . . . . . . . . . . . . . . 116
REFERENCES . . . . . . . . . . . . . . . . . . . . . . 132

Table

I.

II.

III.

IV.

VIII.
IX.

XIII.

XIV.

LIST OF TABLES

List of Klystrons Now in Use at Michigan
State University . . . . . . . . . . .

Band Frequencies and Detectors Used .

Frequency Meters in Use at Michigan State Uni-
Versity O O O O O O C O C O O O O O C C O O

Computation of Hyperfine Splittings for the
220 ~ 321 Transition in 2— ~Chloropropane Using
the AF = 1 Components . . . . . . . . .

Hypothetical Unsplit Frequencies (Mc) in
2-Chloropropane . . . . . . . . . . . . . . .

Calculated and Observed Frequencies (Mc) for
the Hyperfine Components in (CH3)2CHC135 . . .

Rotational Constants (Mc) and Moments of
Inertia (amu A2) for 2-Chloropropane . .

Second Moments (amu A2) for 2-Chloropropane

Experimental Coordinates of Atoms in the
(CH3)2CHC135 Principal Axis System . . . .

Comparison of the Heavy Atom Coordinates Deter-
mined by Kraitchman' s Equations or by Assuming
2mici = 0 and Zmiaici = 0 . . . . . .

Structural Parameters for 2-Chloropropane . .

Change of Rotational Constants (Mc) in 2-Chlo-
ropropane Due to Reduction of Bond Length Upon
Isotopic Substitution . . . . . . . . . . . .

Coordinates Calculated from Kraitchman's Equa-
tions for Small Reductions in Bond Lengths upon
Isotopic Substitution . . . . . . . . . . . .

Changes in the Structural Parameters of 2-Chlo-

ropropane for the Corresponding Coordinates in
Table XIII . . . . . . . . . . . . . . . . . .

vi

Page
34

38

44

64

69

71

74
75

77

78
79

81

82

83

LIST OF TABLES — Continued

Table
XV.

XVI.

XVII.

XVIII.

XIX.

XXII.

XXIII.

XXIV.

Page

Variation of Pbb (amu A2) for 2—Chloropropane
Calculated by Assuming Various Reductions of
Bond Lengths upon Isotopic Substitution . . . 85

Comparison of the Molecular Parameters of
2-Chloropropane with Those of Similar Mole-
GUI-es I O O I O I O O O O C O O O O O I O O O 89

Quadrupole Coupling Constants for 2-Chloropro-
pane . . . . . . . . . . . . . . . . . . . . . 90

Comparison of Absolute Values of the Quadru-
pole Coupling Constantaand Bond Lengths in
Halogenated Hydrocarbons . . . . . . . . . . . 93

Hypothetical Unsplit Frequencies (Me) for
CD3CDC13SCH3 in v = 0 and v = l Torsional
States . . . . . . . . . . . . . . . . . . . . 98

Rotational Constants (Mo) and Moments of
Inertia (amu A2) of 2-Chloropropane Species
Used in Internal Rotation Study . . . . . . . 99

Parameters Used in the Calculation of the
Potential Barrier Hindering Internal Rotation
of the Methyl Group in 2-Chloropropane . . . . 100

Height of Potential Barrier Hindering Internal
Rotation in 2-Chloropropane . . . . . . . . . 101

A Comparison of the Height of Potential Bar-
riers Hindering Internal Rotation in Related
Molecules . . . . . . . . . . . . . . . . . . 103

Hypothetical Unsplit Frequencies (Mc) for
2-Bromopropane . . . . . . . . . . . . . . . . 109

Rotational Constants (Mo), Moments of Inertia
(amu A2), and Second Moments (amu A2) for
2-Bromopropane . . . . . . . . . . . . . . . . 111

Quadrupole Coupling Constants in 2-Bromopro-
pane . . . . . . . . . . . . . . . . . . . . . 113

vii

LIST OF TABLES - Continued
Table Page
XXVII. A Comparison of Quadrupole Coupling Constants

of 2-Bromopropane with Those of Similar Com-
pounds . . . . . . . . . . . . . . . . . . . . 115

viii

Figure

10.

ll.

12.

13.

14.
15.

LIST OF ILLUSTRATIONS

Page
Coordinate systems for a molecule in a center-
of-mass axis system and a translated axis sys-
tem . O I O I O O O O C O O O I I O O O O O 0 O 14

VCa) = V3 (1-cos 3a)/2 . . . . . . . . . . . . 24
Energy level diagram . . . . . . . . . . . . . 24
Block diagram of microwave spectrometer . . . . 32

A circuit schematic for a typical klystron

oscillator . . . . . . . . . . . . . . . . . . 33
Stark waveguide cross section . . . . . . . . . 36
Sample introduction system . . . . . . . . . . 39

A trace of a recording of the 514 d 615 transi-

tion in (CH3)2CHBr79 near 32600 Mo, and at a
Stark-field of 500 volts . . . . . . . . . . . 42
Reference frequency generator . . . . . . . . . 45

A model of a 2-chloropropane molecule depicting
the positions of the a, B, and y hydrogen atoms 53

A projection of 2-chloropropane in the ac plane
of symmetry . . . . . . . . . . . . . . . . . . 62

A recording trace of the 220 e 321 transition
in (CH3)2CHC13S and the 211 e 312 transition
in (CH3)2CHCl37 . . . . . . . . . . . . . . . . 66
A projection of 2-chloropropane in the ab plane 87

A plot of 22 versus CCl bond distance . . . . 95

A projection of 2-bromopropane in the ac plane
of symmetry . . . . . . . . . . . . . . . . . . 107

ix

LIST OF APPENDICES
Appendix Page

I. Measured Hyperfine Components (MC) for
Isotopic Species of 2-Chloropropane . . . . . 118

II. Measured Hyperfine Components (Mc) for
Isotopic Species of 2-Chloropropane . . . . . 123

III. Measured Hyperfine Transitions (Mc) for
CD3CDC135CH3 in vv' Torsional States . . . . . 127

IV. Measured Hyperfine Components (Mc) for
Isotopic Species of 2-Bromopropane . . . . . . 130

I. HISTORICAL BACKGROUND

Active experimentation in microwave spectroscopy began
only after the development of 1.25 centimeter radar equipment
during World War 11, even though the first experiments were
carried out in 1933 by Cleeton and Williams (1). The radar
equipment had been discarded for practical reasons and became
readily available to universities at the end of the war.

MDch of the early work in microwave spectroscopy was
devoted to the development of a more sensitive instrument and
to the theoretical and experimental study of the inversion
spectrum of ammonia. One of the reasons why ammonia was stu-
died was that its spectrum is very intense. High resolution
spectroscopy was first demonstrated in the experiments carried
out on ammonia by Bleaney and Penrose (2, 3) and by Coles
and Good (4).

The most significant instrumental advance was the result
of a suggestion by Hughes and Wilson (5) to apply a periodic
electric field (Stark-field) to the microwave absorption cell.
The resulting Stark-modulated spectrometer was much more
sensitive than any instrument previously available. With
the development of sensitive instruments, additional studies

were carried out on symmetric tops and linear molecules.

These molecules were studied first because of the simplicity
of their spectra.

The hyperfine structure that appeared in the ammonia
spectrum was accounted for by the existence of a quadrupole
moment in N14 (6). Under high resolution the complex hyper-
fine structure due to quadrupolar interactions provides a wealth
of information concerning the electronic distribution about
a nonspherical nucleus. From the treatment of Townes and
Dailey (7) it is possible to obtain information about hybridi—
zation and ionic character of chemical bonds from quadrupole
coupling constants.

Early theory predicted that the Stark effect would cause
a shift and splitting of the frequencies of the absorption
lines which would be proportional to the square of the elec—
tric field strength and to the square of the dipole moment
in linear molecules (8). This was verified by means of mea-
surements carried out on the Stark splittings of the 008
molecule (9), and the first of many dipole moments was deter-
mined by microwave spectroscopy.

In addition to the splittings caused by quadrupole
interaction and the Stark effect, hyperfine structure may
arise from internal rotations within the molecule. Poten-
tial barriers hindering internal rotation may be calculated
from the measured hyperfine splittings. The first barrier
determination by means of microwave spectroscopy was for

methyl alcohol (CH30H) (10). Later developments made by

Wilson's group at Harvard University (11, 12) produced a con-
venient method of analyzing barrier splittings. Now the most
accurate method for determining small barrier potentials is
by microwave spectroscopy.

The most important application of microwave spectros-
copy is the determination of molecular structure. Internuclear
distances and bond angles were first determined by varying
these parameters until the computed moments of inertia repro-
duced the experimental moments of inertia obtained from the
rotational constants for several isotopic species of the mole-
cule. A better method suggested by Kraitchman (13) makes
use of differences in the moments of inertia of two isotopi-
cally substituted molecules in order to determine the coor-
dinates of the substituted atom. This method requires
isotopic substitution of all the nonequivalent atoms in the
molecule and is insensitive to atoms located near a princi-
pal axis or the center of mass of the molecule. A workable
relationship between the substitution parameters and the
equilibrium parameters has not been established, and conse—
quently the effect of vibrations on the determined parameters
has not been determined. Even with these limitations, the
substitution method is one of the better methods for the

determination of bond distances and bond angles in molecules.

II. THEORY OF ROTATIONAL SPECTRA

2.1 Introduction

 

The microwave region of the electromagnetic spectrum
includes wavelengths from 0.06-30 cm (frequencies from 500-
l koI), or between the far infrared and the radio frequency
regions. In the microwave region one ordinarily observes pure
rotational spectra (absorption transitions between rotational
energy states with the same vibrational and electronic energies)
with vibration, nuclear quadrupole, and internal rotation
interactions as perturbations. 'Microwave spectra are usually
studied in the ground vibrational and electronic states
although the inversion spectrum of some molecules (such as
ammonia) and low energy vibrational states contribute richly
to the spectra.

-Since the rotational transitions arise from properties
of the angular momentum of rotating bodies, the theory will
begin with a discussion of angular momentum and energy of

rotation.

2.2 Angular Momentum and Rotational Energy

 

The Hamiltonian for a rigid asymmetric rotor is given

by the expression

 

I‘One ko = one kilomegacycle/second = one gigacycle/
second = 1000 megacycles (Mc)/second = 109 cycles/second.

4

where Pa’ Pb, and PC are the components of angular momentum
along the a, b, and c principal axes of the molecule respec-

tively, and I8 5 lb 5 IC are the principal moments of inertia

(2-1)

about the principal axes. Expressions for the eigenvalues

of HR (the energy levels) cannot be obtained in closed

form except for a few of the lowest energy levels.

In a general molecule-fixed Cartesian axis system,

a solution to the matrix equations for the commutation rela-

tions for the components of angular momentum,

PxPy - Pny = -1Pz,
Psz — PZPy = -iPx,
and P P - P P = -iP ,
z x X Z y
is
(P > - '(P > - l J(J+l) K(K+l)
y J,K;J,K+1 - ‘1 x J,K;J,K+1 ' 2 E ‘ J ’
P :
( Z)J,K;J,K K’
2 _ 2 _ l 2
(PY)J,K;J,K - (PX)J,K;J,K "' 5 [J(J+l) — K J,
(P2) = P2 + P2 + P2 = J(J+1).

J,K;J,K x y z

I
O
I"
N

The quantum number J -

K...

I
O
H.
I'"
H.
N

1.]

(2-2)

A.
2

(2-3)
(2-4)

(2-5)

(2-6)

and the quantum number

where J 22K. The x, y, z axes used here do not refer to

space-fixed axes, but to axes fixed in the rotating molecule.

The x, y, z axes may be identified with the a, b, c axes

in six ways, subject only to the restriction I8 5 Ib 5 Ic’
The Hamiltonian may be written in terms of the rota-

tional constants, A, B, C,

 

 

 

_ 2 2 2
HR(A,B,C) — hCAPa + BPb + CPC), (2-7)
where
A = h , B = 2 , c = 3 , and A 2 B 2 o. (2-8)
8n218 8n 1b 8n Ic

If a change of variables is made as proposed by Ray (14)

using two scalar quantities o and p,

A = qA + p
B' = oB + p (2-9)
0' = 00 + O,

the Hamiltonian can be written as

HR(A:B§C')/h [(sA+p)P§ + (oB+p)P% + (sc+p)P§], (2-10)
or

s<AP§ + Bpg + cpg) + p(P§ + Pi + Pi),

HR(A:B:C')/h
(2-11)
which by (2-6) and (2-7) reduces to

HR(A;B;C’)/h = oHR(ABC) + pJ(J+l). (2—12)

Ray's choice for o and p were

— 2 .. 15192.
C - A—C, p — (A-C), (2‘13)
so that
oA + p = 1, (2-14)
_ 2B—A-C _
GB + p — _A:C—— - n, (2-15)
and CC + p = -1. (2-16)

The dimensionless quantity n is called Ray's asymmetry para-
meter and is confined to -l 5 n f 1. The limit of u = -1
or B = C describes a prolate-symmetric rotor, while the
limit n = +1 or B = A defines an oblate-symmetric rotor.
Kappa equal to zero is the most asymmetric case.

Together with equations (2-13) through (2-16), equa-
tion (2-11) leads to the usual form for the energy expres-

sion of an asymmetric top

WR _ A+C A-C J
'H“ —.—E— J(J+l) + —E— E,(n) (2-17)

where the WR are the eigenvalues of HR(A,B,C), fhe Ei(n)

are the eigenvalues of the matrix,

HR(A',B',C')/h = Pg — Pg + “Pg, (2-18)
and the quantum number T =_J, J-l, J-2, . . . -J. In this
form

aim = sic-n). (2-19)

This approach was further developed by King, Hainer,
and Cross (15) who evaluated the reduced energies E(n),
classified the energy levels according to symmetry, and
listed the symmetry properties of the asymmetric rotor wave
functions. Tables of E(u) have since been given for J = 0
through 12 at intervals of 0.01 in u (16).

Once the energy for two levels is calculated, the

frequency is obtained from the Bohr condition,

w -w
i—i=Z/. (2-20)

h

Instead of labeling the energy levels with J and T
as is done above, it is sometimes useful to label them with
J, K_1, and K11. The quantum numbers K-l and K+1 are posi-
tive integers or zero and are related to the angular momen-
tum.about the a axis of the limiting prolate symmetric top
and the c axis of the limiting oblate symmetric top. The
relations between the sets of quantum numbers are T = K_1 -
K+1 and K_1 + K+1 = J or J + 1.

The allowed rotational transitions are classified
according to the change in J (AJ = -l, 0, and +1 label the
P, Q, and R branches respectively) and as a, b, or c accor-
ding to the direction of the component of the dipole moment
responsible for the transition. The selection rules for

a, b, and c-type transitions are

a type: AK_1
b type: AK_]_ = odd AK...1 = odd,

even AK+1 = odd,

c type: AK_]_ = odd AK+1 even.

The basic theory for the energy levels of a molecule
outlined above is for a rigid rotator. However, the atoms
in the molecule are forced away from an axis of rotation by a
centrifugal force which is different for every energy level.
The resulting small change in the moments of inertia will per-
turb the rigid rotator energy levels, causing a shift of the
transition frequencies. Centrifugal distortion may have an
enormous effect on the spectra of lighter asymmetric top mole-
cules (e.g., hundreds of megacycles in HDS) since the transi-
tions are usually between levels of very large rotational
energy. In heavier molecules where the moments of inertia
are large, the centrifugal distortion is usually small, and
accurate rotational constants may be obtained by neglecting
the complicated corrections which require six additional
parameters. A centrifugal distortion theory for asymmetric
rotators has been worked out by Kivelson and Wilson (17).

Experimental values of the rotational constants are
determined from the measured frequencies of the rotational
transitions. Experimental values of the moments of inertia

may then be obtained by means of equations (2-8).

2.3 Moments of Inertia

 

For a rigid molecule, the moment of inertia I about

any axis passing through the center of mass is given by

_ 2
I — ifimiri (2-21)

10

th

where m. is the mass of the 1 atom and ri is its perpen-

1

dicular distance from the axis.
The rotational constants and the moments of inertia

determined from microwave spectroscopy are called the effe-

tive rotational constants and the effective moments of

inertia. They are averaged over the vibrational state in

a peculiar way and include terms coupling rotation and vibra-

tion. They are consequently not equal to either the equili-

brium values or the average values of these quantities.

The relationship between the rotational constants in a given

vibrational state and the equilibrium values is

d.
Avl V = Ae - Zidi(Vi+ f). (2-22)
’ 2 . . .

Here Ae is the equilibrium value of A, the ai's are constants,
and vi is the quantum number of the ith vibrational mode
with di its degeneracy. Hence, to determine the equilibrium
values of the rotational constants it is necessary to know
the rotational constants for each singly excited vibrational
state in addition to the ground state.

The moments of inertia may be defined in terms of a
momental ellipsoid. The locus of I'% plotted along axes
passing through the center of mass is defined as the momental
ellipsoid. The center of the momental ellipsoid is at the

center of mass of the molecule, and the principal axes of

the ellipsoid are the principal axes referred to above

 

11

following equation (2-1). A molecule is classified as an
asymmetric top molecule if all three moments of inertia are
unequal, as a symmetric top molecule if two of the moments
of inertia are equal, or as a linear molecule if one of the
moments of inertia equals zero (18).

If the molecule has a plane of symmetry, then two of
the principal axes must lie in the plane and the third must
be perpendicular to it. The plane of symmetry is called
the principal plane. This is true of the most common iso-
topic species of both 2-chloropropane and 2-bromopropane.

The moments of inertia are related to the rotational

energies through the angular momentum,

P = 16. (2-23)

Here P is the angular momentum vector, E is the angular
velocity vector, and I is defined as the moment of inertia
dyadic or moment of inertia tensor. An expression for I

in dyadic notation is given by (19)

I = Zimi(r§I-Pi?i) (2-2’4)

.i+yij+zik is the radius vector from the center

1
of mass to the ith mass, mi’

where Pi = x
and l is the unit dyadic. In
tensor form,
I I I
xx xy xz
I = I I I (2-25)
Yx YY yz

I I
zx zy zz

12

where the elements in terms of rectangular Cartesian coor-

dinates measured from the center of mass are

_ 2 2 _ _
Ixx " Z:imi‘Yi " zi)’ xy ‘ Iyz ‘ ’Zimixiyi’
I = 'Z-m-(xg + 22) I = I = “i: m (2-26)
yy 1 1 1 1 ’ yz zy iyiz i’

H
I

II

II

2
22 _ 2-1_ mi (Xi +yi)’ IXZ IZX -::im ix iZ i

The diagonal elements are the moments of inertia and
the off-diagonal elements are called the products of inertia.

Inthe calculations and in the discussion of an asym-
metric top it is more convenient to use a planar dyadic P

defined in a center of mass system by
P = EiimiPiPi (2-27)

where mi and Pi are defined as before. The planar dyadic P

may also be written in tensor form (the second-moment tensor)

as
2
:EImixi Efimixiyi Eiimixizi
2
P = EEimixiyi :Eimiyi :Eimiyizi (2-28)
2
zimixz xi Zi Zimiyizi imizi

The tensors I and P may be formally regarded as sym-
metric matrices and hence may be diagonalized by an ortho-
gonal transformation. The diagonalization is equivalent to
a rotation of the x, y, z axis system in terms of which the

components of the two tensors were computed.

13

An S matrix which diagonalizes the I matrix also diagona-
lizes the P matrix; the eigenvalues of I are the principal
moments of inertia and those of P are the principal second

moments. The orthogonal transfonnation is given by

'Eis = I
abc
xv '_ (2-29)
SPS — Pabc
where the diagonal values of Iabc’ the principal 1's, and

the diagonal values of Pabc’ the principal P's, are related

by the expressions

Paa = (Ib+Ic-Ia)/2’
Pbb = (Ia+IC-Ib)/2, (2-30)
and PCC = (Ia+Ib-IC)/2.

If the mass of the 3th atom of a molecule is increased
by an amount Am (as in isotopic substitution), then in general
there will be a translation of the center of mass and a
rotation of the principal axes with respect to the principal
axis system of the original molecule.

The second moments of a molecule defined above in
terms of an axis system whose origin is at the center of
mass can be written in a translated axis system by making
use of the parallel axis theorem. The two systems of axes
are shown in Fig. l. The origin of the x, y, z system is

at the center of mass and x", y", z". are the parallel,

l4

 

H

 

 

 

%
x"

 

0
v

center x
of mass

1

 

 

 

Fig. 1. Coordinate systems for a molecule in a center-of-
mass axis system and a translated axis system.

 

15

translated axes. The result of the application of the

parallel axis theorem is as follows:

. .".n . ."’,u
" (Ezlmlrl )(Pflmlrl )

 

P : P _ (2-31)
:Eimi
where
P = Eiimiririv
u _ "’ u" n
P — Efimiri ri ,
“"n = .117. + ’11-: + ."_. = ". _ "
rl x1 1 yl 3 21 k r1 r0,
A = 7 + 1 + r = . .
ro x01 yoj zok the vector connectlng
the origins of the two systems,
A r 7 r
. = . ' + . + .
rl x11 le zlk,
o o..." = _. o a —
andzlmlrl rozlml. (2 32)

If mass ms is increased by Am, the second moments of
this isotopic species can be calculated by means of an equa-
tion similar to equation (2-31) using coordinates in a
center-of-mass axis system of the parent molecule. The
moments of the substituted species will then be given with
respect to its own center of mass and to axes parallel to

the axes of the parent molecule. The second moment dyadic

for the substituted molecule in this system is

(AmFS)(AmFS)

 

: P + I: T: (2-33)
Eiimi+Am ’ft S S

where

16

M = the molecular weight of the original species,
M’ = the molecular weight of the isotopic species,
Am = M' I M,

and PS = xsi + ysj + zSR.

If the center—of—mass axis system of the parent mole-
cule is in addition the principal axis system of the parent,

the coordinates x-

1, Y1, zi are usually labeled ai, b

i, °i°

The substitution coordinates xS, ys, z become the a b

S 37 8’

CS coordinates of the substituted atom measured in the prin-

cipal axis system of the parent molecule.

The P' matrix is

2
Pee +7483 flasbs )Jfiscs
P, = )‘kaaS Pbb + )lbg PbSCS (2-34)
2
”(3838 )J‘Csbs Pcc + )Ics

If this matrix is diagonalized, the principal values of P'
(PAav Pbb’ Péc) for the substituted molecule will be found.
Kraitchman (13) has shown that
1 1
Ias| = Lu‘l [(Paa'Paa)(l + PEEEEEE)(1 + §§55;::)]I%.
(2-35)
Expressions for IbsI and IcSI may be obtained by cyclic
permutation of the subscripts.
The moments of inertia for different isotopic species

are obtained by analysis of the microwave spectra. The

unprimed P's and the primed P's then can be calculated,

 

 

 

 

 

 

 

l7

and hence the coordinates for any substituted atom may be
determined. If every nonequivalent site in the molecule

is substituted, the coordinates of every atom can be com-
puted. However, only the absolute values of the coordinates
will be obtained so the signs must be determined from prior
knowledge of the structure. Then by applying simple geometry
to these coordinates, all the bond angles and bond distances
of the molecule can be determined. More details on the use

of Kraitchman's equations will be given in Chapter IV.

2.4 Nuclear Electric Quadrupole Moments

The nonspherical distribution of charges in nuclei
such as chlorine and bromine gives rise to the so-called
quadrupole moment. These nuclei interact with the electrons
and other nuclei in a molecule to produce a variation in
the electrostatic energy of the system with nuclear orien-
tation. Every nuclear orientation leads to a different coup-
ling with the overall rotation of the molecule, and consequently
to different interaction energies. Transitions between
these perturbed energy levels give rise to quadrupole hyper-
fine structure.

The energy of interaction between a nucleus having
a quadrupole moment and the electric field in the molecule
depends on the value of the nuclear spin I, on the nuclear
quadrupole moment Q, and on the tensor quantity 33V, where

V is the electrostatic potential due to all charges external

18

to the nonspherical nucleus. This fundamental problem of
nuclear quadrupole interaction with molecular rotation was
first worked out for one quadrupolar nucleus by Casimir (20)
and has been extended to asymmetric tops with one or two
quadrupolar nuclei, including first and second order effects
(21, 22, 23). The part of the quadrupole interaction energy

dependent on rotational state is given by Casimir as

 

62v:>v (3/u)c(c+1) - I(I+1)J(J+l)

az2 2J(2J-1)I(21-l) (2-36)

”0:99

where
C = F(F+l) - I(I+l) - J(J+l),

F = J+I, J+I-1, . . .IJaII = the total angular momen-
tum quantum number,

J = the rotational angular momentum quantum number,
I = the nuclear spin quantum number,

Q = the quadrupole moment,
52V

2
BZ
space- -fixed direction. Classically,

2 [3 Zej -1
<:) V (2. . cg; .]> (2-37)
>3V. av.

th

and— —;> is the average gradient at the nucleus in a
av.

 

where Fj is the radius vector from the nucleus to the 1

electronic charge, and Gj is the angle Fj makes with the
space-fixed axis.
av2
For an asymmetric top the quantity (:L as
6Z2 av.

obtained by Bragg and Golden (22) using a first order

19

treatment, is expressed by

 

2 aw aw aw
q == 9—! = 2 [h -3 + q 1_B + q -5
J—- .522 av. h(2J+3)(J+l) 88 8A bb 6B CC BC

(2-38)
where

OWR _ h BE(K)

SK_ — 2 [J(J+l) + E(n) - (n+1) —§;——]

BWR ash.)

—— = h ————-— _

BB 6“ (2 39)

BWR h BE<K>

-—— = — J J+l - + -l -—-

BC 2 [ ( ) .E(n) (n ) an ]

82V 62V 62V

and , , and q are the field radients , , -
qaa qbb cc 8 aa2 abz 602’

 

respectively, along the principal axes.

Since Laplace's equation (VZV = 0) holds, only two
of the three constants qaa, qbbv and qCC are independent.
writing equation (2-38) in terms of the so-called quadrupole

coupling constants><aa = quaa’:y<bb = qubb’ and cc = eQqcc

and making use of Laplace's equation, one finds that
WQ = Y(F)[ aa fl(J,u) + (jxgb - CC) f2(J,n)]. (2-40)

The function

.g3/4)C(C+IQ - I(I+1)J(J+1)

f(I,J.F> = YIF) = 2(2J-l)I(21-l)(2J+3)

(2-41)

is known as Casimir's function and has been tabulated (16,
18). The functions fl(J,n) and f2(J,u) depend only upon the
rotational quantum number J and the asymmetry parameter a,

and can be derived from equation (2-38):

_ 2 BWR BWR
f1(J’”) ” J(J+1) (BA ' aB )
(2-42)
6W 6W
f (m) - —3-—— (J - —5>
2 J(J+l) 63 ac
aWP. . .
where the 33-, etc., are g1ven by equatlons (2-39).
. 62V 82V 2v
We now def1ne ——5 = qm' and ——7 - é—I/qm = n. The
Ba ab 60
first order perturbation correction then becomes
WQ = aqm + quT] (2‘43)
where
a = eQY(F) fl(J,u)
(2-44)
and B = eQY(F) f2(J,u).

One obtains values of W (where WQ << Wk) for every different

Q

value of F, and the total energy for the perturbed rotational

level is W’= WR + WQ. For I = 3/2 as in C135, 0137, Br79,
81

and Br , there are four values of F for each J (except
J = 0 or 1) and hence each rotational level is split into
four levels by the perturbation.

The useful chemical interpretation of quadrupole coup-
ling constants is obtained from these parameters in a mole-
cule-oriented axis system. In this thesis the axis system
is oriented approximately along the carbon-halogen bond,
and corresponds to the principal axes of the quadrupole coup-
ling tensor.

In general, only first order perturbation is used to

fit the quadrupole spectra, and only the diagonal elements

of the symmetric coupling constant tensor are obtained.

21

Even so, °n°e4><;a;;k<bb’ and cc are determined, they may

be transformed from the principal inertial axis system into
the principal quadrupolar axis system. This could be done
.exactly if the off-diagonal elements could be determined
from second order effects. However, by assuming a cylindrical
charge distribution about one of the principal quadrupolar
axes, or that a principal axis of the tensor and the carbon—
halogen internuclear line coincide, the transformation may
be carried out. Once the elements of this transformed ten-
sor are known, they may be related to the ionic character
of the bond and to the hybridization of the halogen bonding
orbital (7). Further details are given on these transfor-

mations and interpretations in Chapter IV.

2.5 Potential Barriers Hindering Internal Rotation

_A perturbation which gives rise to additional hyper-
fine splittings in the rotational spectra is due to internal
rotation (the rotation of one segment of a molecule with
respect to the remainder). From an analysis of these split-
tings one can determine accurately the height of the poten-
tial barrier hindering the internal rotation. The availability
of accurate values of the height of potential barriers hin-
dering internal rotation has given much information concerning
the influencing intramolecular forces even though the pre-
cise nature of the origin of potential barriers is still

somewhat a theoretical mystery.

22

The problem of determining the effect on the rotational
spectra of a symmetric rotor (a methyl group) attached to
an asymmetric frame (the rest of the molecule) has been stu-
died extensively by Wilson and his co-workers (11, 12).
Coupling between the angular momenta of internal and overall
rotation has been shown to be the most important mechanism
producing barrier-dependent splittings in the rotational
spectrum. In the principal axis method, as the theory developed
by these workers is named, the top-frame coupling is treated
by perturbation theory, and tables have been compiled giving
the perturbation coefficients which are needed for an analy-
sis of the spectra (24, 25).

In problems involving two equivalent symmetric rotors,
such as in 2-chloropropane, the possibility arises for
coupling between the tops as well as between the tops and
the frame. The analysis of such spectra is much more com-
plicated than the analysis of spectra in a one-top problem.
The first theoretical approach to the two-top problem was
by Swalen and Costain (26) in a study of acetone. The
most extensive work however has been and is being pursued
by Pierce and his co-workers (27, 28).

In the study of a two-top molecule such as CD CDClCH

3 3’

the internal rotation can be treated as a one-top problem.
This is because the tunneling of the heavier CD3 group is
very much less than that of the CH3 group. The method for

single top systems employed here is the one developed by

 

 

 

23

Herschbach (12). The model is that of a threefold symmetric
rotor attached to an asymmetric frame. The potential bar-
rier of the top is assumed to have a sinusoidal shape given
by the first term in a Fourier series expansion of the peri-
odic hindering potential. The expression for a top having

threefold symmetry (Fig. 2) is

V3
V(a) = 3— (l-cos 30) (2-45)

where V3 is the barrier height, and a is the angle of the
top with respect to the frame.

If the barrier height is large, the internal motion
will be small torsional oscillations in the three separate
potential wells (Fig. 2). This is equivalent to a harmonic
oscillator whose triply degenerate energy levels are depic-
ted in the right-hand side of Fig. 3. As the barrier height
is lowered, each torsional level v splits into two sublevels:
a nondegenerate level, VA (quantum number a = 0), and a
doubly degenerate level, VB (6 = i l). The splitting may
be regarded as arising from tunneling through the potential
barrier. The A and E classifications refer to the symmetry
of transformations under the C3 symmetry group.

The torsional energy levels are determined by the bar-

rier height V and by a reduced moment of inertia r10,

3
where

2
r=1_:1s_1_2

g 1g . (2-46)

24

_ \\ l/ \\ l/ \\ //

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A =
E v 2
E
x I x I . I V : 1
\/ \/ \/ A
O 211/3 411/3
OLA
V3
Fig. 20 V08) = 2_ (l~cos 3d)
Free Harmonic
Rotor Oscillator
m
:I: 6 3
i 5
E 2
:I: 4
A A
i 3 l
E
i 2
E V = 0
a: 1 ”if
A
0
V3 '3 0 V3 = 00

Fig. 3. Energy level diagram

 

 

25

I = the moment of inertia about the internal
rotor symmetry axis,

Ag = the direction cosine between the g principal
axis and the internal top symmetry axis,

the moment of inertia for the entire molecule

and I
g about the g principal axis.

Rotational spectra would not be affected by these
torsional splittings if it were not for the coupling of
angular momenta between the overall and the internal rota-
tion. Because there is no dipole moment change with tor-
sional motion, the A and E energy levels give separate
rotational spectra. Since the coupling has different effects
on the A and E sublevels of each torsional level v, the
rotational transitions from a torsional state v occur as
doublets instead of as a single line for a rigid rotator.
The frequency separations of the doublets depend on the
structural parameters and on the barrier height.

Molecules in torsional states with v > 0 have dif-
ferent moments of inertia which shift the energy levels
from those of the ground state, and therefore shift the
rotational spectra.

An effective Hamiltonian for each torsional state v

is given by

_ (n) n
Hvo — Hr + 1115?anvo Z? (2-47)

where Hr is the rigid rotator Hamiltonian,

26

F =-——E—-cn?F = §Q§;§§L in kilomegacycles,(2-48)

8n2rIa rIa

I
63: Zngg —3 = an + spy + yP

 

 

27
1g
0' = AXIQ, B " A 109 'Y : AZIO’,
Ix 1y 12
Pg = the g-axis component of the total angular
momentum,
(n) _ th . . .
and WVU — the n order perturbation coeff1c1ent.

The wig) depend only on the ratio V3/F, and have been tabu-
lated (24) against a dimensionless parameter 8 through fourth
order (n = 0 to 4) for the three lowest torsional levels

v = 0, l, 2. The parameter
s = 4.66139 (V3/F) (2-49)

where F is in ko and V3 is in cal/mole. The W(n) differ

vo

in sign and magnitude for the A and E levels of a given tor-
sional level V, and therefore the different rotational spectra
arising from HVE and HvA allow the barrier height to be deter-
mined. The selection rule is A0 = 0 so that transitions between
E levels (Z/g) and between A levels (1/;) are observed.

In carrying out a calculation to second order, Hvo

becomes

2
HVG = Hr + lamina? + hFWémt? . (2-50)

The odd order terms in C? vanish for the A levels, while those

for the E levels can be treated as a perturbation. The energies

 

27

for the A and E levels can be written as follows:

BWR ' BWR 1 OWR 1

WVA - WR + B—A_ AVA + 8—i— BVA + B—C_ CVA (2-51)
BWR , BWR , BWR , (1)

WVE = WR + B_-A_ AVE + ST BVE + 56— CVE 4' AW (2-52)

where the partial derivatives of WR are given by equation
(2-39) and AW(1) represents the contribution from the term
first order in (P and is negligible in asymmetric top cases
where there are large separations between energy levels.
The terms including AA, AE, etc. are the second order contri-
butions where AA, Aé, etc., are corrections to the effective
rotational constants.

The difference in energy between the A and E levels

(neglecting the first order term) is

awn . .
WA 7 WE - BA (AVA AVE)
aW12 . . awR . .
+ 53—.(BVA-BVE) + gE—'(CVA‘CVE) (2-53)
where

I 1 _ 2 (2) (2)

AvA ' AVE ‘ F3 Ewe. ‘ va 3

1 1 _ 2 (2) (2)
VA 7 VB _ F5 [W’A ‘ va 1 (2-54)

1 , _ 2 (2) (2)

VA ‘ vE ‘ FY [WvA ‘ vE 3

 

28

In the first excited torsional state v = l, substituting both

v = l and the high barrier equation WIA) = -2W{é) in the above

expressions, the equation can be rewritten as

aw aw aw
_ g Fw(2) 2 R + 2 R 2 R

E ‘ 2 1A I“ aA as + Y ac J (2‘55)

WA-W

and the difference in frequency of the A and E component is

(2)
3FW1A 2 8W 2 BWR 2 BWR
)jA - UE - T [a A(B—A$ 4‘ B A(a—E_)+ 'y [NEE—)3 (2-56)

where the differences in the partial derivative of WR are
between the two rigid rotator levels in question. These equa-
tions will be used in Chapter IV to set a lower limit on the

potential barrier for CD3CDCl35

CH3 as determined from the
absence of splittings in the first excited torsional state
rotational spectrum.

Use can be made of the foregoing equations and existing
tables to evaluate the potential barrier hindering internal
rotation by means of relative intensity measurements (29)
of rotational transitions in the excited torsional state and
in the ground state.

In the high barrier case, the motion of the top is essen-

tially one of a simple harmonic oscillator, and the purely

torsional energy is given by

_ (0)
EVC — thVO . (2-57)

29

The difference in energy between the ground and first excited

torsional state is

in) - 11(0))

00 (2-58)

E10 - E00, : hF(

which is equal to the torsional frequency multiplied by

h. The torsional frequency may be determined from the rela-
tive intensities of the first excited torsional state and

the ground state by use of the Boltzmann equation. The rela-

tive intensity R is given by

N 1 gV' -h UVV'
R,_ .2. z ___ _______ _
NV gv exp( kT ) (2 59)

where Nv' and NV are the populations of the upper and ground
states, gv: and gv are the statistical weights, and 1/;v,

is the torsional frequency of the top and is expressed by

-kT g
yvv. = T In (R if). (2-60)

After )/;v. is determined, it is used with expression (2-58)
to compute (WE- Wg). From the difference between these
perturbation coefficients, 8 and hence V3 can be evaluated.

The difficulty of making intensity measurements in
the microwave region lessens the accuracy of this method.
Some of the difficulties are wave reflections in the wave—
guide, noise interference, interfering transitions, small

splitting effects from internal rotation, and quadrupole

30

components not completely resolved. The last two decrease
the intensity from that of the unsplit transition. Even
with these problems, one can obtain fairly accurate values
if the intensity measurements are made a number of times

under varied conditions.

III. STARK MODULATED MICROWAVE SPECTROMETER

3.1 Introduction

 

The general microwave spectrometer consists of a
source for generating the electromagnetic radiation, a sample
absorption cell, a detection system, a means of displaying
or recording the detected signal, and finally a method for
measuring the frequency of the detected absorption signal.
To improve the sensitivity of the instrument, a periodic
Stark-field is applied by means of a square-wave generator
or a sinusoidal generator. The periodic Stark-field modu-
lates the absorption signal and provides a coherent AC sig-
nal for amplification and detection. In the Michigan State
University instrument, a 100 kc square—wave Stark-field
is applied.

A block diagram of the instrument in use at Michigan
State University is shown in Fig. 4. The main components
of this spectrometer will be described in the following

sections.

3.2 Klystron Oscillators

 

A schematic diagram for a typical klystron oscillator
is shown in Fig. 5, and in Table I is a list of klystrons

with their frequency range and operating voltages.

31

32

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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«acoua< ,
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mousse fl. sous: asses s1 _ _
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s. Q...
uo>«o»o& , h - --
as... s :3...
Houuwumn acuuumamu a oomofiafiumo “each
I: o>wuanaom nuoouaum anon Hung nouuuhHM
emphases . 1 6.6mm a _ _
cavsm w owns hamunm
kuum>mm usuauaum
we 11 novuoomm numam conunuam
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soggy neonaosou Houunoo
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. , . - , :oauwnauua neuusaouu<
usoanouuu< code as OOH opus muuuvm enemas 0H uauu> u
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mag _
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n auuuhm menu AHVnaxn umxnonm sucuuvuum
assuu> % w
e H
souufiaauno HostHAoeo a, nouuouon
-ueuufifieono.ll mm> .11 me: . . r11 mafia. inauuusuo
u: a vmfiaouuaoo voHHouuaou «my wsqasa espouse

 

 

 

 

 

 

 

 

 

 

 

 

 

 

33

 

 

 

 

 

 

 

 

 

 

 

Reflector

erutput Flange

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

W—uA
Cathode-—a
. Grid
VOltage f:
Supply
Beam I:
+ Voltage _ >‘/
Supply
:: Reflector
= Voltage _
Supply
Filament 1_
Voltage ?_
Sawtooth Voltage
Fig. 5. A circuit schematic for a typical klystron oscil-

lator.

 

34

.seaoe cos- use om- ssszuse messes mes use: mewsuao> souosamqmflsv
.mpumwflfiomwwmz .EmnuHmB .mcmano wcwhspomMSGmZ comnuhmonv
.mwchomwamo .Uoo3haaom cuuoz .sz cmELmsm mmNmH ..UpA mD\H2mAnw

.ssssomHHso .osas sass .sss assess Has .sssssoomss seeps>xso

 

 

w ommm assesses 0.0m - m.s~ mew so
m coma onsossussm o.m~ - o.- mm x N
N.ma ooom mp\Hzm m.sm - o.~m esmm m
N.NH ooom m:\Hzm m.~m - m.sm mama m
N.NH ooom m:\H2m o.e~ - m.mN moms m
w.HH ooom Aevmp\H2m m.- - o.ma mass m
mm oom msuswoomm< sesss> o.mH - :.~H NH-x
as .oo: Asvsssseoomms smess> s.~H - N.w ma-x
mwhmaamwaawe wwmuao> pmhfiuommficmz Aozxv mwcmh copumhax
mmvucohhso Emwm Emom bonusoopm

 

 

.Suwmum>wcs mumum cmwwsowz um mmD ca 302 machumhax mo umwA .H mHnt

35

An FXR Type Z815BT power supply is used to drive the
klystrons. The power supply includes two ranges of beam
voltage, 200-1800 volts and 1800-3600 volts, a reflector
voltage of 0 to -1000 volts (relative to the beam voltage),
0 to -300 volts (relative to the beam voltage) applied to
the grid, and 6.3V AC for the heater. In place of the heater
voltage from the FXR, a separate, regulated DC filament sup-
ply is used for heating the cathode.

A beam voltage up to 2000 volts is applied between
the anode and the cathode of the klystron tube, forcing
electrons off the heated cathode. The electrons pass by the
anode and through a cavity whose dimensions can be controlled
by an external screw-type plunger. A bunching of the elec-
trons is induced by an alternating electric field developed
within the cavity. That is, those electrons in phase with
the AC field are speeded up, and those out of phase are
slowed down. After the electrons pass through the cavity
they are repelled by the reflector plate which is at a high
negative potential, and are returned through the cavity,
giving up energy to the cavity in the form of pulses.
Depending upon the voltages and dimensions of the cavity,

a nearly monochromatic signal is directed from the outlet

of the cavity into the absorption cell. The frequency of
C

 

TManufactured by Electronics and X-Ray Division, F.R.
Machine WOrks, Inc., Wbodside 77, New Jersey.

36

the klystron can be changed by changing the reflector voltage

and/or the cavity size.

3.3 waveguide Absorption Cells

 

Two sample cells are in operation at Michigan State
University. Both are X-band waveguidesI and are approximately
ten feet long. One is made of brass with a silvered inside
surface, and the other is made of copper. A cross-section

of the brass waveguide is shown in Fig. 6.

 

 

'mr \\\\\\\ I
0.050” —*+-

0.900”

Stark
Electrode

 

 

 

 

 

 

 

 

LEMAM Ty

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'

Fig. 6. Stark waveguide cross section.

The X-band waveguide will conduct electromagnetic radiation

of a frequency from 8 ko to beyond 40 ko. A coin silver

 

IThe band type refers to the inside dimensions of the
waveguide and the wavelengths which can be conducted through
it.

37

septum for the Stark electrode, insulated on the top and

bottom by grooved Teflon strips, runs the length of the

rectangular waveguide. The sample cells are vacuum tight,

sealed by means of mica windows and O-rings. Transition

tapers are available for reducing the waveguide dimensions

to K, P, or R band, enabling different klystrons and fre-

quency meters to be connected. Table II gives a list of

the different bands, the frequency range of each band, and

the crystals used in the respective frequency regions.
Samples are introduced into the waveguide cell from

the vacuum line shown in Fig. 7. The vapor in sample bulb

A is solidified at -l96°C and the bulb is pumped on to insure

removal of non-condensable material. Then the bulb is allowed

to warm and a small amount of vapor is introduced into the

cell. The relative pressure of the sample in the waveguide

is determined by a thermocouple vacuum gauge, and the

usual operating pressure is approximately 10-2mm of mer-

cury. Any sample whiCh is condensable at -l96°C may be

returned from the waveguide to the sample bulb for future

use 0

3:4 Square-wave Generator

A modulating electric field may be put on the sample
by using a sinusoidal wave or square-wave form. At Michi-
gan State University a 100 kc square-wave generator designed

by Hedrick (30) is used. The square-wave voltage has

38

Table 11. Band Frequencies and Detectors Used.

 

*—

 

Frequency
Band range (ko) Crystals

X 8.2 - 12.4 1N23
12.4 - 18.0 1N23
1N78
K ' 18.0 - 26.5 1N26
1N78
R 26.5 - 40.0 1N26

1N53

 

39

aspm abnom> oH

l.

 

 

 

 

 

 

 

  

9:5 335.63
sec sooegwm

7 A)

 

 

 

 

 

m4

paumoam

N vvwswaemz oh
A

 

 

 

 

 

 

 

 

Ewummu cowuoacouucm uHQEmm .n .wwm

< pafim
«Haamm

.
I“

C
I;

 

 

 

H 32% WW
io>m3.0H #

 

\1

I? \

wane uamfiooofiumsa

 

40

a range in amplitude of 0-1250 volts on the Stark elec-
trode; however, voltages over 1000 volts have a tendency
to arc and burn the Teflon stripping. The square-wave
generator can be operated from the zero-based voltage
or from any positive or negative DC bias. A method for
supplying an exact DC bias for the base line of the square-
wave has been put into use. The bias voltage is measured
accurately using a potentiometer bridge. This method
allows precise measurement of the Stark voltage, and
hence enables accurate determination of dipole moments.
The electric field is introduced onto the Stark
electrode by means of a coaxial cable through a vacuumr
tight N-type coaxial connector which is connected to the
electrode by a spring loaded contact which fits through
a hole in the Teflon stripping. When the square-wave.
generator is on, the molecules are in the electric field
during alternate S-microsecond periods. This has the
effect of turning on and off absorption lines 100,000
times per second. Since the Stark transitions occur when
the field is on, the Stark spectra will be 180 degrees

out of phase with the zero-field absorption lines.

3.5 Detection
The most commonly used detector of microwave power
is the silicon crystal rectifier. A small wafer of sili-

con with a tungsten whisker contact imbedded in a metal

41

cartridge composes the rectifier where one electrode is
formed by the metal cartridge and the other by a pin contact.
The crystal diode rectifies the AC microwave power, producing
a signal which contains both AC and DC components. These
components are separated in a 100 kilocycle tuned preampli-
fier. The DC signal which is proportional to the microwave
power input is sent directly to the power meter, while the

AC signal which contains the modulated absorption signal

is sent to the phase-sensitive detector. The phase-sensi-
tive detector whose phase reference is the 100 kilocycle
square-wave selectively amplifies signals that are in phase
and 180 degrees out of phase. The signal is sent to the
oscilloscope orrecorder. 0n the oscilloscope a plot of
frequency versus microwave absorption is formed by sweeping
the klystron repeller voltage and the x axis of the oscil-
loscope simultaneously with a sawtooth voltage. On both

the recorder and the oscilloscope, the zero-field transitions
and the Stark-field transitions are recorded in opposite
directions. This is due to the action of the phase-sensi-
tive detector and the 180 degree phase difference between

the two signals. A trace of a recording is shown in Fig. 8.

3.6 Freguency Measurement

 

An approximate measurement of the frequency of a transi-
tion may be made by means of a frequency meter. The fre-

quency meter contains a cavity whose dimensions can be

42

.Hmmc

on

 

 

~\mH 1 m\na

.suHoe com me easem-sssum s as use .6: ocean

N\mH 1 “\HH

I'll-W

\~

«\s .. «\k

hmmomAmmuv cw cowuwwcmpu mam 1 3am may no wcwopouoh m no woman <

m\HH 1 axe

 

.m .wsm

 

43

changed by a micrometer plunger. When the microwave radi-
ation is passing through the cavity, some of the energy will
be absorbed if the cavity dimensions are set properly.

This small absorption of energy by the frequency meter can
be displayed on one trace of the dual—beam oscilloscope.

The frequency meters are generally calibrated by the manu-
facturer, and charts are provided giving vernier scale readings
on the plunger versus frequency of absorption. Frequency
meter readings can be in error by 10-20 Mc unless the cali-
bration is exceedingly accurate. A list of the frequency
meters in use at Michigan State University is given in

Table III.

For more accurate measurements, use is made of the
instruments shown in Fig. 9. The fundamental standard fre—
quency source is a Manson Laboratories RD-l40 high-stability,
one-megacycle oscillator, which varies in frequency only
1 part in 108 per day. This crystal-controlled oscillator
is standardized to better than 1 part in 107 by beating
its tenth harmonic against the 10 Mc carrier of radio sta-
tion WWV from the National Bureau of Standards. This pro-
cedure is carried out by connecting a short antenna to a
1 Mc output which is rich in harmonics. A receiver tuned
to 10 Mc then receives and mixes the tenth harmonic and
the signal from WWV. If the tenth harmonic of the oscil-
lator and the WWV signal are comparable in intensity and

frequency, then the background noise will pulsate.

44

Table III. Frequency Meters in Use at Michigan State

 

 

 

University.
Frequency
Manufacturer Model range (ko)
Narda(a) 810 8.2 - 12.4
Narda 809 12.4 - 18.0
DeMornay-Bonardi(b) DBE-715-2 18.0 - 26.5
DeMornay—Bonardi DBD-715-2 26.0 - 39.0

 

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

(b)DeMornay-Bonardi Corporation, 780 S. Arroyo Park-
way, Pasadena, California.

45

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IN

poemhocow Roconvonm mocohomom

 

 

 

_
_
ex oooH-oon _

 

neuuaaaoao

 

 

esssosusoo

0: cog—coon

 

 

 

 

 

 

 

 

 

 

O m I wwm
632.502
3380 I 8H 5
huaosuoum “833:9:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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_ Houuuoo voaaouunoo oelou uoqfimwuHsz. ,
muaonvuum oz oeaou Heuuhuv
_ ,fll _
oz owloN _
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so; seesaw. N H mm ma “assesses: nz.H _
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AmmoonoHquno nauuaaauuo _
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HOU.HQQ.B°U OUV I U: um! _ RoadHHflO‘O II “08 508 _
Auoeeouom >3: ouv .ml, A: A 1 ex A guesses Assoeusoeoum _

 

 

 

 

_IIIII

 

 

 

 

II II_

acuqumnnu mm>
51E nuauuou

nauaaomhmuuH mmb
<Alz< aunuuou

acuqaaao-o
oaomouwmalmno

9W." a 69.3

46

When the 1 Mc oscillator is adjusted so that the pulsating
signal is less than once every two seconds, the two signals
differ in frequency by less than one cycle per second (1
part in 107). Another way of checking the frequency of the
1 Mc oscillator is to put the output of the receiver on the
y axis of an oscilloscope set for slow sweep time. The
frequency of the wave—form appearing on the face of the
oscilloscope will represent the difference in frequency
between the WWV signal and the tenth harmonic of the stan-
dard oscillator. By adjusting the oscillator crystal to
reduce the frequency of this wave-form to zero, the oscil-
lator is set to exactly one megacycle.

The 1 Mc output from the crystal oscillator is con-
nected to the input of a Gertsch AM-lA VHF interpolator where
the signal is amplified and selectively multiplied by any
number between 19 and 38. The output of the multiplier
is mixed with the output of a stable 1-2 Mc low-frequency
oscillator (LFO), and the added frequencies are used to con-
trol the frequency of a 20-40 Mc oscillator. To determine
the frequency of the LFO, a Lissajous figure is displayed
on a second oscilloscope by sending the LFO signal to the
x axis of the oscilloscope and the 1 Mc standard frequency
signal to the y axis. Only under rational ratios of x/y
will a figure appear, and from the shape of the figure the

LFO frequency can be set to better than i l cps.

47

The output signal from the Gertsch AM-lA is of some
frequency between 20 and 40 Mc plus harmonics. The output
signal and the 1 Mc standard signal are connected to the
Gertsch FM-4A microwave frequency multiplier. This instru-
ment contains a 500-1000 Mc variable-tuned oscillator which
may be locked to a frequency which is i 10 megacycles from
a harmonic in the signal from the AM-lA interpolator. Thus
generated frequencies in the range of 500-1000 Mc known to
one part in 107 are available at the output of the FM—4A
microwave multiplier.

The mathematical representation for a generated stan-

dard frequency is given by

y, = [m(K+ LFO) e 10] N Me <3-u)
where
m, K, and N are integers,
K = 19-38 Mc,
m = l, 2 . . .,
= l, 2 . . .,
and
ULFO = 1'2 Mcv
K+)/LFO = 20-40 Mc.

The output from the FM-4A is sent through a coaxial
cable to a crystal diode which is rectifying the microwave

signal. The two signals mix on this crystal and the sums

48

and differences between the microwave signal, the standard
generated signal, and the harmonics of both go back through
the coaxial cable to a low-pass filter which allows only

the first few harmonics of the smallest difference frequency
to pass to a receiver. When the receiver is tuned to the
difference signal, a sound can be heard through the speakers,
or the beat signal seen on the oscilloscope. This beating
sound arises from the effect of the sawtooth voltage on the
klystron electrode. That is, since the klystron frequency
is varied with the sawtooth voltage, its frequency will
correspond to the generated standard frequency only once
during each sawtooth sweep. The frequency of the receiver,
I/rec’ the standard frequency, l/é, and the frequency of

the microwave radiation, I/hi , are related as follows:
c

I/rec = lnI/g ‘ IAmicI (3-2)

OI‘

I[mic

n2]; 1 rec (3-3)

where n is an integer. To determine the exact frequency of
an absorption line, the frequency difference signal which
appears as a marker on the oscilloscope face is moved to
coincide with the center of the absorption line, and the
receiver reading is then added or subtracted to the stan-
dard frequency, depending upon whether it is a high frequency
marker (marker moves to a higher frequency as receiver is

turned to a higher frequency) or a low frequency marker

49

(marker moves to a lower frequency as receiver dial moves
to a higher frequency).

Frequency differences may be read off a Hallicrafters
SX-62-AI receiver to i 0.2 Mc, and measurements to i 0.02 Me

I receiver which can be read to

may be made with a Collins
1 kc. Because of a time delay between the 100 kc signal

and the beat marker reaching the scope, measurements must

be made while sweeping both directions to average out time
delay, and hence frequency discrepancies.

If, for an example, the absorption line and hence
microwave frequency was 21,750.50 Me, and if a high frequency
marker is desired, the Gertsch AM-lA frequency may be set
at 29.000000 Mc and the I/LFO at 0.200000 Mo, and the Gertsch
FM-4A locked in at 749.2000 Me. This will generate a fre-
quency of 21,726.80 Mc, which is 29 X 749.2000 Me, and the
difference, 23.70 Mc, is the frequency at which the receiver
will be set when the marker is right on the center of the
absorption line.

The Micro-Now* frequency multiplier can take the

place of all components shown in Fig. 9. Using a 5 Mc

base frequency which can be tuned to WWV, this instrument

 

IThe Hallicrafters Company, 4401 W. Fifth Avenue,
Chicago 24, Illinois.

*Collins Radio Company, Cedar Rapids, Iowa.

*Micro-Now Instrument Company, 6340 North Tripp Ave~
nue, Chicago 46, Illinois.

50

multiplies it to 25, 50, 150, and 450 Mc. These signals

and their harmonics are sent to the mixer crystal in place

of the output from the Gertsch FM-4A. All other principles

are the same, except that in using the Micro-Now many more

markers appear over a short range of microwave frequency.

IV. DETERMINATION OF THE MOLECULAR STRUCTURE
OF 2—CHLOROPROPANE

4.1 Introduction

The microwave study of 2-chloropropane was undertaken
at Michigan State University as part of a continuing study
of some halogenated hydrocarbons. The aim of this study
was to determine accurate structural parameters and quadru-
pole coupling constants for 2-chloropropane and to compare
them with those of methyl chloride (31), ethyl chloride (32),
and cyclopropyl chloride (33). As part of the study an
attempt was made to determine the potential barrier hin-
dering internal rotation of the two methyl groups.

The only previous determinations of the molecular
structure of 2-chloropropane were by electron diffraction
(34, 35). In 1939 Beach and Stevenson (34) reported the

following parameters:

r(CCl) = 1.75 e 0.02 A
<c001 = 109 3: 3°
<ccc = 110 at 3°.

Then in 1954 Yamaka (35) reported
r(CCl) = 1.76 i 0.02 A

r(CC) 1.55 i 0.02 A

<ccc x<0001 109.5 s 1.50.

51

52

By means of pure quadrupole resonance spectroscopy
on the solid, Livingston (36) reported IquI = 64.14 Me
at 20° Kelvin, and Scrocco, Bucci, and Maestro (37) reported
64.1 Mc at 800K.

The potential barrier hindering internal rotation of
either of the two methyl groups in 2-chloropropane as deter-
mined by the thermodynamic method was reported to be

2200 cal/mole (38).

4.2 Preparation of Isotopic Species

 

Since in the determination of molecular structure
using Kraitchman's method (13) every nonequivalent atomic
site must be isotopically substituted, at least eight dif-
ferent species of 2-chloropropane were needed for this study.

In most of the syntheses semi-micro vacuum line tech-
niques were used. The purity of the final products was
checked by infrared spectroscopy.

The species of 2-chloropropane studied were (CH3)20HC135
(in the ground and the first excited torsional states),
(0H3)20H0137 in natural abundance, (0H3)2013H0135,
013H30H01350H3, (0H3)2000135,'0H200H01350H3 (three species:
trans [a], gauchel [B], gauchez [y])J and CD3CDC1350H3

in the ground and two excited torsional states.

 

1..

ITrans and gauche refer to the relative positions
of deuterlum with respect to the adjacent CC bond. Fig. 10
illustrates the positions of the a, B, and y hydrogen
atoms.

53

 

Fig. 10. A model of a 2-chloropropane molecule depicting the
positions of the a, B, and y hydrogen atoms.

54

35 37
(CH3)ZCH01 and (CH3)ZCHC1

 

The (CH3)20HC135 and (CH3)2CHC137 spectra were examined
using a white label sample of 2-chloropropane obtained
from the Eastman Kodak Company. The 0137 species is present

in natural abundance to the extent of 24.6%.

(CH3)2013HCI

 

The preparation of (CH3)2013HCI35 was begun using a
modification of the method developed by Cox, Turner, and
Warne (39) for the preparation of Na(OOCI3CH3). The starting
material was 2.44 grams of 19% 013 enriched potassium cya-
nideI which was dissolved in 6 ml of water and added to
6.22 grams of methyl iodide in a small flask fitted with
a long, narrow neck and a standard taper ground joint.

The flask was sealed off in vacuo and shaken until the mix-
ture became homogeneous. The flask was cracked open and

the contents were distilled into a flask containing carbonate-
free sodium hydroxide (100% in excess). This flask was
evacuated, sealed, and heated for four hours at 8090 to
convert the methyl cyanide to sodium acetate. The mixture

was removed from the second flask and acidified with sul-
furic acid; silver sulfate was added, and the acetic acid-013
(91% yield) was removed by steam distillation. The acetic

acid was converted to barium acetate (89% yield) with an

 

IPurchased from the Oak Ridge National Laboratory,
Oak Ridge, Tennessee.

55

equivalent amount of barium hydroxide. After drying in
vacuo over P205, the barium acetate was pyrolysed in vacuum
at 500°C (40, 41), yielding 0.8 cc of acetone. The ace-
tone was purified by bulb-to-bulb distillation, and was
dried over magnesium sulfate. A lithium aluminum hydride
reduction was carried out on the acetone in diethylene
glycol-diethyl ether (42) using 2-phenoxyethanol as the
substituting alcohol. The 2-propanol was distilled from
the reaction mixture and was converted to 2-chloropropane
by reacting it with phosphorus pentachloride.. The chlori-
nation was completed by letting (CH3)ZCHOH react with PClS
at the lowest possible temperature. A small flask con~
taining 2 grams of PC15 was attached to the vacuum line

and evacuated. The (CH3)2CHOH (0.3 cc) was distilled into
the reaction bulb. The liquid air dewar was then removed
from the reaction bulb to allow the bulb to warm. As the
alcohol started to move down the sides of the flask onto
the P015, the liquid air was applied again to cool the
reaction flask. Upon wanming slowly, the reaction occurred
instantaneously and the reaction products were trapped at
-l96°C as they left the reaction mixture. The volatile
components were removed by distillation at -78°C. The
2-chloropropane was distilled at -10°C into a bulb containing
potassium carbonate to remove any acidic by-products.

The 002 formed was removed at -78°C and the 2-chloropro-

pane (0.2 cc) was distilled into the sample bulb.

56

The infrared spectrum showed no impurities. The equations
for the overall preparation are as follows:

H 0
CH3I + K013N —3—+ CH3013N + KI

Ba(OH)
CH 013N + l) 5295» CH 01300H -————£+ (OH 01300) Ba
3 2) H2301 3 3 2

o
(CH3Cl3OO)2Ba -§99—9+ (CH3) 0130 + Bacl30
vacuum 2 3

 

(diethylene g1ycol:4

13 °
“(933)20 O * LlAlfih diethyl ether)

LiAl [0H(cl3u3)214

. 13
LlAl .[OH(C H3)2]4 + 4H0—(0H2)2-0—q)———————+
4(CH3)2013HOH + LiAl ‘.[0-(0H2)2-0-q>]q
(CH3)2013HOH + P015 ————-+ (CH3)2013HC1 + P0013 + HCl.

13
c H3CHCICH3

 

A sample of propionic acid containing 15% CH3CHZCI3OOHI
was reduced by lithium aluminum hydride in diethylene
glycol-diethyl ether, using 2-phenoxyethanol to release
the n-propyl alcohol. The alcohol was pumped from the
reaction mixture and trapped in liquid air (42). The
n-propyl alcohol was allowed to react with phosphorus
pentachloride using the same technique as described in the

preparation of (CH3)2013HC1. The resulting l-chloropropane

 

IThe sample was obtained from Mn.Roy Foley of Kedzie
Chemical Laboratory, Michigan State University.

57

was rearranged over anhydrous A1013 (43) to yield 2-chloro-

propane. The overall reactions are as follows:

(diethylene glycol-\
diethyl ether)

 

ucu3cuzcl300H +3LiA1H4

(CH3CH2013H20)QLiAl + 2LiA102 + 4H2

LiAl(OH2Cl3CHZCH3)4 + “HO-(CH2)2'0‘47““'9

acu3cnzcl3H20H + LiA1[0-(0H2)2-0-q?ln

CH30H2013H20H + 9015 —————+ 0H30H2013H201 + P0013 + H01

AlCl .
0H3CH2013H201 ————§e»013H303010H3 + H01 + A1013 (polymer).

(CH3)2CDC1

 

Approximately 0.003 moles of 2—deuteropropeneI and
a slight excess of hydrogen chloride were allowed to react
over anhydrous aluminum chloride at -78°C to form 2-chloro-
propane. The resulting product was purified by distillation.
The reaction is

A1C13
CH2 = CD-CH3 4’ HCl ___-9 (CH3)2CDC1.

CHZDCHCICH3

 

This compound was prepared in two steps. Deuterium

chloride was prepared by a reaction of 98% D20 with

 

1'The sample was a commercial preparation from Merck
Chemicals, and was obtained from Dr M.T. Rogers of Kedzie
Chemical Laboratory, Michigan State University.

58

phosphorus trichloride. The deuterium chloride was reacted
with propene at -78°C over anhydrous aluminum chloride.

The compound was purified by bulb-to-bulb distillation.

The use of AlCl3 in this reaction caused deuterium exchange,
giving other deuterated species and also (CH3)ZCHC1. The
reaction steps are given by:

3020 + P01 —————9 3001 + D3PO3

3

A1C13

CD3CDClCH3

 

A sample of deuterated 2-propanol (CD3CDOHCH3)I
with small impurities of tetramethylsilane and carbontetra-
chloride was obtained.

To purify the sample, vacuum line distillations were
used but were not wholly successful. Since these two
impurities would not interfere with either the chlorination
or the rotational spectra, a direct reaction was carried
out using phosphorus pentachloride as previously described.

The reaction is
CD3CDOHCH3 + P015 ————-a CD3CDClCH3 + P0013 + HCl.

4.3 Preliminary Calculation of Transition Frequencies
The first step in the preliminary calculations of

transition frequencies is to assume a structural model for

 

TThe sample was obtained from.Mn.Chester Orzech of
the Kedzie Chemical Laboratory, Michigan State University.

59

the molecule. The following values for the molecular

parameters were assumed:

all r(CH) = 1.09 A
r(CC) = 1.53 A
r(CCl) = 1.785 A
<000 = 110°
all other angles = 109.50.

A general right-handed Cartesian coordinate system
with the z axis perpendicular to the plane of symmetry was
located in the molecule. Spherical polar coordinates were
then determined for every atom. Punched paper tape containing
the polar coordinates and atomic masses in a systematic
form was prepared for input into the ”MISTIC" digital com-
puter at Michigan State University. The structure program
(44) which was stored in the computer then acted upon the
input data in a sequential manner to compute first the
general rectangular Cartesian coordinates (x", y", and z")
and then the second moment tensor in the general coordinate
system. Next, the center-of-mass coordinates and the
second moments in the center-of-mass coordinate system .
were computed using equation (2-31).

The second-moment matrix in the center-of—mass axis
system with the z axis perpendicular to the plane of sym-

metry is

60

Pxx ny 0
P = ny Pyy 0 (4-1)
0 0 P22

The principal P's may be found by diagonalizing this

matrix as shown by equation (2-29), where

cos 0 -sin 0 0
s = sin 0 cos 9 0 (4-2)
0 O 1

The angle 0 is between the a and x axes, and is given by
the expression

2P
tan 20 —'—-¥§X- (4-3)

Pyy-Pxx

After the principal P's are determined, the principal
moments of inertia are computed from expressions obtained

from equation (2-30),

H
II

Pbb + P

a 00’
Ib = Paa + Pcc’ (4‘4)
Ic = Paa + Pbb’

and the rotational constants are obtained by use of equation
(2-8). The asymmetric top rigid rotator energy levels can
now be computed from equation (2-17). Kappa is given by

equation (2-15), and the E(n)'s are determined by fourth

61

order interpolation from the E(n) table in Townes and
Schawlow (16, Appendix IV). The transition 1/ is deter-
mined from equation (2-20).

The class or type of transition looked for is governed
by the direction of the dipole moment with respect to the
principal axes. In asymmetric tops, the dipole moment
seldom lies along a principal axis. In the case of 2-chloro-
propane, where the z axis is perpendicular to the plane of
symmetry, P would remain the same in the similarity trans-

ZZ

formation. Then by examining the transformation of Pxx

and P by using equations (4-4) along with the corres-

YY
ponding equations in the x, y, z axes system, one can deduce
that the axes correspondence is x ~ a, y d c, and z e b.
Since the a axis is roughly parallel to the C01 bond and
since the dipole moment of the molecule is probably nearly
parallel to the CC1 internuclear line, a-type transitions
should be observed. Figure 11 shows a projection of 2-chloro-
propane in the ac plane of symmetry.

Before examining the rotational spectra, the hyper-
fine splittings due to the chlorine quadrupole moment must
be estimated. Preliminary calculations are made by assuming
that the quadrupole coupling constant along the C01 bond
(qu22 = 22) is equal to that determined experimentally
for a compound such as methyl chloride or ethyl chloride,

and then transforming this quantity into the principal axis

system of 2—chloropropane. Assuming a cylindrically symmetric

62

a case

A.owoa mop ou hoafiowocoohoo ow mwxm
.huuoashm no woman on mop cw mamaounopoasOlN mo cowuomnona < .HH .wwm

 

Aoomvme

 

\\\ Acvm

Amvm

 

HO

 

33m

 

 

 

63

charge distribution about the C01 bond, for which -%:X;z =

><TY =:><%x, the quadrupole tensor is written as

X22 0 0
Xond = 0 ny 0 (4-5)

0 0><XX.

This tensor is transformed by use of the following expres—

X... = Ohms a-..

where S is given by equation (4-2) with 0 = 02, the angle

sion:

between the a axis and the C01 internuclear line.

For 2-chloropropane with an ac plane of symmetry,

.3KFY is unchanged in the transformation and equals :(hb'

while_:K;a and cc are given by

:><;a =;:Xéz c0520Z +_:X;X sin20z
:Xéc = :ng Sinzez +I:X;X 008292.

Once the quadrupole coupling constants (:Xga, ><bb1 cc)

(4-7)

are computed, use is made of equation (2-43) to calculate
the corrections to the energy levels due to the quadrupole
coupling. After these energies are computed, the hyperfine
structure is constructed as shown in Table IV for the 220 a
321 transition. The selection rules governing these transi-
tions are AJ = 0, i 1; AF = 0, i l; and AI = 0. The fre-

quency of an observed hyperfine component is equal to

64

Table IV. Computation of Hyperfine Splittings for the
220..321 Transition in 2-Chloropropane Using

the AF = 1 Components.

 

Computation of l/b

 

 

 

 

 

 

 

 

F = J'+ 3/2 J'+ 1/2 J'- 1/2 J'- 3/2
HQ .
h (321) 0.63Mc -l.26Mc -0.38Mc 1.51Mc
‘19
h (220) -u.14 10.34 0 -14.47
aw
l/' = —39(M°) 4.77 -ll.6O -0.38 15.98
Relative
intensitya 35.7 2n.5 16.0 10.0
Appearance of the Spectrum
MR
_ l_
{ l
l a 2
2 2 3...;
2 2
2.1
2 2
Z._.9
2 2
I L 1 1
11.21 Mc 5.15 Mc 11.22 Mc
2L

 

8Reference 16, Appendix I.

65

3/0 = I/R + UQ (4-7)

where 1/6 and )jk are given by the Bohr frequency condition.
The calculated hyperfine pattern in Table IV may be

compared to the observed pattern in Fig. 12.

4.4 Examination of the Microwave Spectra

 

The spectra of all the species were examined at Dry
Ice temperature using the conventional Hughes-Wilson spec-
trometer described in Chapter III.

The 000 e 101 transition was predicted to be below
the range of our klystrons, so a search was made for the
J = l r 2 transitions predicted to fall in the 12.4-17.5 ko
region. Unfortunately, the crystal detector mount used at
that time was not a good one for this region and consequently
the signal to noise ratio and resolution were poor. It there-
fore seemed best to look for the J = 2 d 3 transitions pre-
dicted to lie in the 20-25 ko region. Recordings were made
over much of this region, and transitions having the hyper-
fine structure with the expected intensity pattern and the
approximate splittings were measured. An assignment was assumed
correct when five transitions could be computed with the rigid
rotator expression. For final fits of the rotational con-
stants to the experimentally observed frequencies, use was

made of the expression

aWR
2/0-1/C=A )(AA)+1()(Ba)+a(—55—c)(coc)
(4-8)

66

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67

where the subscript ”0” stands for "observed" and the sub—
script "0" stands for "calculated." The partial derivatives

of the rigid rotator energy with respect to the rotational con-
stants A, B, and C are given by equation (2-39).

With a correct assignment assured, an experimental evalu-
ation of the quadrupole coupling parameters was made using
differences in equation (2-43) for low J transitions. The
frequency difference of the hyperfine components within a

transition are given by
6(AU) = 6(Acr)qm + 6(A8)qm11. (4-9)

The constants 6(Ao) and 6(AB) were computed using the observed
rotational constants, and qm and qmn were fit by least squares.
The standard deviations of the parameters qm and qmn were

used in conjunction with Snedecor's F tests for the equality
of variance to set the experimental error within a 95% confi-
dence interval. Once the quadrupole coupling parameters

are determined accurately, a reverse procedure to that shown

in Table IV will give more precise rigid rotator frequencies
(EAR = 2/0 - 1/6). With more precise rigid rotator frequen—
cies, the rotational constants A, B, and C can be redeter-
mined using a least squares fit on equation (4-8). Transitions
were included that had high dependence on all three rotational
constants. The asymmetry (n = -.34 to -.47) is sufficient

to allow an accurate determination of the least moment of

inertia. Centrifugal distortion, which seemed to be small,

68

was not taken into account. The standard deviation of the
parameters 6A, 5B, and 60 determined by the least squares
analysis were used with the F tests for the equality of vari-
ances to estimate the error within a 95% confidence interval.I

The quadrupole coupling constants for the other iso-
topic species were obtained by transforming :Kga, :XPP’ and
:Kéé from the (CH3)ZCHC135 principal axis system into the
principal axis system of the substituted species, with the
exception of (CH3)ZCH0137 where in addition use was made of
the nuclear quadrupole moment ratio, Q(Cl3EVQ(Cl37) = 1.2688,
(16), to find the C137 coupling constants. These transformed
coupling constants fit the hyperfine splittings within the
experimental error.

In Appendices I and II the measured frequencies of the
hyperfine components for the various isotopic species are
listed. The frequencies in most cases were measured to
i 0.02 Mc, although with weaker transitions as in the CHZD
sample which was a mixture of three species, measurements
of i 0.05 M0 were not uncommon.

The hypothetical unsplit frequencies (I/fi's) for tran—
sitions in (CH3)2CHCl35 (ground and first excited torsional
states) and various isotopic species are given in Table V.

A comparison of the calculated and the observed fre-
quencies of the hyperfine components for selected transitions

from (CH3)ZCHCl35 is shown in Table VI.

 

I'This error analysis assumes a random error which is
not strictly true here because of centrifugal distortion.

69

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71

 

 

 

Table VI. Calculated and Observed Frequencies (M0) for '
the Hyperfine Components in (CH3)2CHCI35

Observed Calculated

Transition F 4 F' Frequency Frequency
1 2 5/2 4 7/2 14197.18 14197.18
11 12 3/2 4 5/2 14181.84 14181.81
1/2 ~ 3/2 14202.20 14202.22

5/2 4 5/2 14190.49 14190.50

3/2 ~ 3/2 14186.96a 14186.57

1/2 4 1/2 14208.94 14208.90

1 2 5/2 4 7/2 15230.70 15230.70
01 02 3/2 4 5/2 15231.64 15231.60
1/2 4 3/2 15214.27 15214.27

5/2 4 5/2 15216.24 15216.23

3/2 4 3/2 15241.94 15241.94

1/2 4 1/2 15228.70 15228.74

1 2 5/2 4 7/2 16923.94 16923.84
10 11 3/2 4 5/2 16908.53 16908.47
1/2 d 3/2 16926.80 16926.70

5/2 4 5/2 16915.19 16915.15

3/2 4 3/2 16914.71 16914.68

1/2 4 1/2 16935.51 16935.39

2 3 7/2 4 9/2 21106.94 21106.98
12 13 1/2 4 3/2' 21107.01
5/2 4 7/2 21103.34 21103.37

3/2 4 5/2 21103.40

2 3 7/9 4 9/2 22134.57 22134.64
02 03 5/2 4 7/2 22135.60 22135.63
3/2 4 5/2 22131.55 22131.58

1/2 4 3/2 22130.50 22130.60

2 3 7/2 4 9/2 23339.55 23339.55
21 22 5/2 * 7/2 23324.20 23324.18
3/2 4 5/2 23335.15 23324.16

1/2 ~ 3/2 23350.60 23350.53

2 3 7/2 4 9/2 24540.77 24540.80
20 21 5/2 4 7/2 24524.35 24524.45
3/2 4 5/2 24535.57 24535.66

1/2 4 3/2 24551.92 24552.02

72

Table VI.--Continued

 

 

 

Observed Calculated

Transition F ~ F' Frequency Frequency
4 4 4 11 2 ~ 11/2 20516.14 20516.04

04 23

9 2 4 9/2 20523.00 20522.92
7/2 4 7/2 20520.51 20520.51
5/2 - 5/2 20513.65 20513.62
505 4 524 13/2 ~ 13/2 23818.64 23818.81
11 2 4 11/2 23821.61 23821.59
9 2 5 9/2 23822.69 23822.68
7/2 ~ 7/2 23817.66 23817.72

 

aInterfering transition.

73

4.5 Molecular Structure

 

In this study every nonequivalent atomic site in 2-chloro-
propane was isotopically substituted. This allows the coordi-
nates of every atom to be determined by the use of Kraitchman's
equations (2-35).

The experimental rotational constants and the moments
of inertia are given in Table VII. The principal second
moments are given in Table VIII.

For an atom substituted in the plane of symmetry (the
ac plane in this case), Pbb and Pbb should be the same for
a rigid molecule. The changes observed in Pbb upon isotopic
substitution can be attributed to changes in the zero-point
vibrations. The largest change in Pbb usually occurs upon
deuterium substitution. In 2-chloropropane the largest change

013 substitution where APbb = 0.0065 amu A2.

occurs in the
By comparing second moments of molecules having a similar
plane of symmetry, it is found that in propane APaa = 0.0054
amu A2 for C13 substitution, and APaa for deuterium substi-
tution is 0.0001 (45). The change in Paa for dimethyl sulfide

30 is 0.0005

and dimethyl silane in substituting S3“ and Si
and -0.0012 amu A2 respectively (27, 28).
Since Kraitchman's equations are derived for a rigid

molecule, the coordinates for an atom substituted in an

ac plane of symmetry are given by

1
2

AP
{/4:1[Apaa(1 +.___22__)]}

PCC-Paa

m
02
ll

0‘
m
u
<3

(4-10)

74

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0000.004 0000.044 0444.00 40.0040 00.4000 4.0 4 04.0004 4400000040000000
0004.004 0040.044 0004.00 00.0400 04.0400 0.0 4 00.0404 4000000040000000
0000.004 0004.444 0000.40 04.4040 00.0000 0.0 4 40.0404 64000000040000000
0400.004 0040.044 0440.00 04.0040 00.0400 0.0 4 04.0404 00000400000040
0000.404 0000.444 0440.00 00.0000 00.0000 0.0 4 40.0000 00400040040000
4000.404 0000.044 4000.00 04.4000 40.0400 4.0 4 00.0044 004000040000
4000.004 0000.044 4400.00 00.0040 00.0000 4.0 4 00.4000 404000040000
0000.404 4000.044 0000.00 40.4000 00.0400 00.0 4 00.0000 004000040000

64 04 04 o 00 < 0046000

 

 

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75

Table VIII. Second Moments (amu A2) for 2-Chloropropane.

 

 

 

Species Paa Pbb Pcc_
(CH3)2CH0135 102.7736 54.8319 7.8261
(CH3)2CH0137 105.7137 54.8324 7.8293
(0H3)2000135 103.0597 54.8350 10.0341
(0H3)2013Hc135 103.0346 54.8254 7.9859
013H30H01350H3 104.1744 56.3771 7.8402
CH2DCHC135CH3(a)a 103.2644 59.4015 7.8841
0H200H01350H3(0) 107.82313 56.3269 7.8556
CHZDCHC13SCH3(y) 104.0690 56.4749 9.2367

 

8Position of D with respect to the CC bond.

76

1
2

AP
_ _ -1 aa
1C3} _ {/u' [AP°°(1 + Paa‘Pcc)]} .

These expressions are obtained from the full Kraitchman
equations (equation 2-35) by setting APbb = 0. Since the
experimental APbb is not zero a question arises as to whether
equations (2-35) or (4-10) should be used. The difference
between the coordinates calculated in the two ways is found
to be less than 0.0001 A which has a negligible effect on
the computed bond distances and bond angles. When atoms
are substituted near a principal axis or the center of mass,
the coordinates computed from Kraitchman's equations tend to
be small (46). In such cases the atom may be located by
using the conditions that in the principal axis system
2miFi = O (center—of-mass condition) and Zmiaici = 0 (pro-
duct of inertia vanishes).

Table IX gives the coordinates determined from the

experimental rotational constants after a direct application

of Kraitchman's equations. Table X shows the change in the

coordinates when the c coordinates of the heavy atoms lying

near a principal axis have been corrected by setting :Emici
and Ermiaici equal to zero. The corresponding structures
for these sets of coordinates and an average structure are
given in Table XI.

Recent calculations of the vibrational effects on

structure determination indicate that bond lengths between

heavy atoms may shorten by as much as 0.0001 A upon isotopic

77

Table IX. Experimental Coordinates of Atoms in the
' (CH3)2CHC135 Principal Axis System.

 

 

 

Atom a b c

C1 1.2286 A 0 0.0409 A
C (center) -0.5128 0 —0.4021
C (end) -l.l695 0 1.2666 A 0.1222
H (secondary) —O.5303 0 -1.4929
H (a) -O.6664 i 2.1546 —0.2588
H (3) 02.2184 i 1.2891 -O.1796
H (y) -1.1136 i 1.2833 1.2203

:Efniai = —O.1473 amu A

2.0.6. = —0.3902 amu A

1 1 1

20.3...

2
1 1 1 1 —0.0ll8 amu A

 

78

Table X. Comparison of the Heavy Atom Coordinates
Determined by Kraitchman's Equations or by
Assuming Zmici = 0 and Emiaici = 0.

 

 

c Coordinate

 

Assuming
Kraitchman's Emici = 0
Atom Equations Zmiaici = 0
Cl 0.0409 A 0.0462 A
C (center) -0.4021 -O.4021

C (end) 0.1222 0.1308

 

79

Table XI. Structural Parameters for 2-Chloropropane.

 

 

 

18 11b 111C

r(CCl) 1.7968 A 1.7982 A 1.798 0 0.005 A
r(CC) 1.5200 1.5230 1.522 0 0.002
r(cnsec) 1.0909 1.0909 1.091 0 0.005
r(CHmethyl) 1.0920 1.0920 1.092 0 0.01
<000 112°53' 112°32' 112°42' 0 25'
<ccc1 109°30* 109°17' 109°24' 0 21'
<00Hsec 109°45' 110°3' 109°54' 4 30'
<010Hsec 105°12' 105°21' 105°16' 0 30'
<CCHad 111°3' 110°39' 110°51' 4 30'
<00HB and Y 109°38' 109°42' 109°40' 4 30'
<HaCI-IB

= 4:18.011Y 10906' 10904' 10905' 0 30'
<HaCHY 108°16' 108°40' 108°27' 4 30'
I8 62.3516 amu A2 62.4219 amu A2
1b 110.2004 110.2707
1 156.9412 156.9412

 

aTaken directly from coordinates determined by Kraitch-
man's equations.

Z: bCorrecting the coordinates of the heavy atoms with
imici = O and Zimiaici = 0.

CAverage structure.

dH is trans and H

are gauche with respect to
the CC. gond.

Bandy

80

substitution, and 0.003 A between a heavy atom and hydrogen
upon deuterium substitution (47, 48).

Calculations made by reducing the bond lengths of
heavy atoms that are attached to the atom substituted indi—
cate that such reductions could have a great effect on struc-
ture determination as computed from Kraitchman's equations.
The procedure is to first assume a structure for the mole-
cule (here use was made of the determined coordinates for
2-chloropropane), and to compute the rotational constants.
Then the rotational constants are computed for the isotopic
species where each of the heavy atoms is isotopically substi-
tuted without changing the bond distances. These rotational
constants will allow computation of a reference set of heavy
atom coordinates. Now the previous step is repeated with
the bond lengths to heavy atoms from the atom isotopically
substituted reduced by a consistent amount. Table XII gives
the rotational constants computed for different shortenings
of bond lengths. Table XIII shows the coordinates as calcu-
lated from Kraitchman's equations, and Table XIV gives the
corresponding structural parameters for a series of changes
in the bond lengths. Examination of these tables shows
that if small changes occur in the bond lengths upon isotopic
substitution, there may be a considerable error in some of
the structural parameters deduced by means of Kraitchman's
equations. The only coordinates that are greatly changed

here are those of the central carbon atom where a larger

81

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03.0003 00.0003 30.4033 0
40.3404 00.3000 00.0440 < 0000.0
00.0040 00.4000 44.0040 0
00.0003 00.4003 40.0033 0
44.0404 03.0000 30.0440 < 4000.0
03.0040 30.4000 00.0040 0
40.0003 40.4003 03.0033 0
00.0404 30.0000 00.0440 < 000000.0
03.0040 00.0000 00.0040 40.0300 0
44.0003 04.0003 00.0033 30.3403 0
00.0404 00.0000 00.0440 00.0440 0 040040440
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82

 

 

 

Table XIII. Coordinates Calculated from Kraitchman's
Equations for Small Reductions in Bond
Lengths upon Isotopic Substitution.
Coordinate Set 01 0 (middle) C (end)
Originala a 1.2219 A -0.5176 A -1.1663 A
b O 0 1.2659
c 0.0466 -0.4084 0.1329
0.00005b a 1.2210 40.5119 -1.1660
b O 0 1.2652
c 0.0463 -0.4082 0.1330
0.0001 a 1.2201 —0.5064 —1.1658
b O 0 1.2649.
c 0.0462 -0.4077 0.1325
b O 0 1.2605
c 0.0443 -0.4054 0.1306

 

aNo bonds reduced in length when the atom was sub-
stituted.

bReduction of bond lengths in angstroms to atom sub-
stituted.

83

Table XIV. Changes in the Structural Parameters of
2-Chloropropane for the Corresponding
Coordinates in Table XIII.

 

 

Bond Reduction

 

Parameter 08 0.00005 Ab 0.0001 A 0.0005 A
r(CCl) 1.7980 A 1.7915 A 1.7852 A 1.7313 A
r(CC) 1.5220 1.5236 1.5253 1.5403
<(000) 112034' 112017' 11203' 109°50'
<(0001) 108°48' 108°59' 109°9' 110°34'

 

aNo bond lengths reduced when the atom was substituted.

bReduction of bond lengths in angstroms to atom sub—
stituted.

84

change is expected since three bonds are affected. It is

13 substitution) cal-

interesting that the APbb (for center C
culated assuming a 0.0001 A bond reduction reproduced the
experimental difference (Table XV). This illustrates one
of the problems in using substitution parameters (i.e.,
vibrational effects), and indicates the need to take vibra—

tion into account in order to obtain extremely precise struc-

tural parameters.

4.6 Discussion of the Structure

 

The parameters shown in Table XI are quite different
from those first determined by electron diffraction. Many
comparisons of bond distances obtained by recent electron
diffraction and microwave spectroscopy show that it was not
uncommon for the early workers in electron diffraction to
underestimate the uncertainties in their numbers. Comparing
the present structural parameters of 2-chloropropane with
those of related molecules that were determined by the sub-
stitution method one observes that the C01 bond distance of
1.798 A is 0.01 A longer than the bond distance in ethyl
chloride which, in turn, is 0.007 A longer than the bond
distance in methyl chloride; but it is 0.0005 A shorter than
the CC1 bond distance in tertiary butyl chloride (49).
Uncertainties in the C01 bond distance may be large for
two reasons; first, the proximity of the chlorine atom to the
c principal axis (0.0462 A), and, second, the vibrational

effects. The errors estimated for the parameters in Table XI

85

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0000.00 0400.00 0000.00 4000.0
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0 0 0 0 0 0 0 0
00004000 0040 00400040 4 000 404000 4 000 004000 4 000 400

 

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86

are based in part on how the zero-point vibrational effects
affect bond length change upon isotopic substitution.

The CC bond distance of 1.522 A can be compared with
1.526 A in propane (45), 1.526 A in ethane (50), 1.520 A
in ethyl chloride (32), and 1.530 A in tertiary butyl chlo-
ride (49). These distances are all between carbon atoms of
approximately the same hybridization. An example of the
effect of change in hybridization on a CC bond distance is
the value of 1.501 A obtained for the CC single bond in pro—
pylene (52). The CCC angle in 2-chloropropane is 112°42',
the CCC1 angle is nearly tetrahedral, and the CCHsec angle
is 109°54'. This set of angles cannot be explained in terms
of a simple hybridization calculation. The small ClCHsec
angle of 105°l6' is comparable with the XCH angle in ethyl
chloride and in ethyl bromide (51).

Upon examining the methyl group parameters, an unsym-
metrical methyl group is evident. The HBCHY triangle seems
to be in a plane parallel to the plane of symmetry. A com-
plete study of the unsymmetrical nature of the methyl group
was not attempted since the hydrogen coordinates may be
uncertain because of the small c coordinates and the large
vibrational effects upon deuterium substitution. However,
there is no question that the equilibrium configuration of
the methyl groups is staggered with respect to the 001 bond.

Figure 13 shows a projection of 2-chloropropane in the ab plane.

87

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88

Table XVI shows a comparison of the structural parameters

of 2-chloropropane with those of related molecules.

4.7 pguadrupole Analysis

 

The parameters qm and qmn were determined as described
in section 4.3. The parent species [(CH3)ZCH0135] was fit
by least squares and the values for qm and qmn are given within
a 95% confidence interval. Since only a-type transitions
were observed, qmn was less sensitive to the hyperfine split-
tings than qm. The quadrupole coupling constants ><éa’
.;Xéb’ and :X;0 were determined from the values of qm and
qmn and the relation :Xga + :Xéb +:><0c = 0. The values
for the parent species are :Kéa = -61.49 0 0.11 Mc, :(bb =
34.81 0 0.25 Mo, and )(CC = 26.68 0 0.25 Mc. The quantities
qm, qm , and n given in Table XVII represent the diagonal
values of the quadrupole coupling tensor in the principal
axis system of the molecule. The off-diagonal elements could
not be determined since second order effects were negligible.
Consequently, when the quadrupole coupling constant tensor
is diagonalized to find the charge distribution along the
001 bond at the chlorine nucleus, it must be transformed
using either of two assumptions.

If it is assumed that the principal axis (the z axis)
of the quadrupole tensor and the C01 internuclear line coin-
cide, the tensor can be diagonalized because the off-diagonal

elements are zero in the principal axis system and the required

 

89

 

 

 

Table XVI. Comparison of the Molecular Parameters of
2-Ch1oropropane with Those of Similar
Molecules.

Molecule r(CC) r(CCl) <CCC <CCX

(033)3001a 1.530 A 1.803 A 110°56' 107°59'

(CH3)20H01b 1.522 1.798 112°42' 109°24'

CH30H201° 1.520 1.788 111°2'

cn3c1d 1.781

(CH3)3CHe 1.525 111°9'

(CH3)20H2f 1.526 112°24' 109°32'

 

8Reference 50.

bThis

thesis.

cReference 32.

dReference 31.

eReference #9.

fReference 45.

90

Table XVII. Quadrupole Coupling Constants for
2-Chloropropane.

 

 

Principal Inertial Axis System

 

 

Isotopic Species qum(Mc) qumfl(Mc) n
(0H3)20Hc135 -61.09 0 0.11 8.13 0 0.49 —0.1322 0 0.0082
(CH3)2CHC137 -48.46 6.40 -0.1322
(CH3)2CDC135 -61.89 7.64 —0.1234
(CH3)2C13HC135 —61.56 7.96 -0.1294
013113010135013 -61.37 8.15 -0.l328
0H200H01350H3(a) -61.53 7.92 -0.1288
CHZDCHC135CH3(B) -61.65 7.80 —0.1264
CHZDCHC135CH3(Y) -60.61 8.80 -0.1053
CD3CDC135CH3 -60.22 6.94 -o.1152

 

 

CCl Bond Axis System

 

 

 

1b 20
L><02 CMc) -67.82 0 0.12 -59,51 0 0.50
nbondd 0.028 0 0.003 0
62e 14°26' l6012' 0 301
I 23% 22%

 

an =(:<bb - :XO0VJKOa-

bAssuming the z axis of quadrupole tensor and the CC1
internuclear line coincide.

CAssuming cylindrical charge distribution.

d'nbond = (Xx ' XrQ/Xzz

eAngle between the a and z axes.

9l

transformation angle may be obtained from the structure.

The relationships for this transformation are given by

:Xf 2 :)<: . 2
cos 9 - s1n 0
:><;z 0 aa 2 cc 2 (Q-ll)

c0820z — sin20z

. 2 2
2X: Sln 0 -:></ cos 0
XXX - 88 2 CC 2 0-12)

_ . - 2
Slnzez cos 02

where 02 is the angle between the 3 axis and the z axis
and is determined from the geometry of the molecule. In
2-chloropropane where there is an ac plane of symmetry,

’><yy = :KLb. The parameters computed using this assumption

are listed at the bottom of Table XVII under column 1.
The significance of the non-zero value for n is not clear.
It has been interpreted in terms of double bond character,

but could possibly arise from the assumption used to obtain

Secondly, if the charge distribution about the C01

bond is considered to be cylindrically symmetric,

>(22 = 4)ch = 4x}, = '2va (0-13)

and 92 may be determined from the relation

3 00320 -1
:Kéa = :X02 < 2 z ). (4-10)

The values determined using this assumption are listed in

 

Table XVII under column 2.

92

The magnitude of the quadrupole coupling constants in
the bond direction has been shown to be related to the ionic
character of the bond (6, 53, Sh, 55). The ionic character

is given by the relationship

1 = <1- 52 + 02 — 11) — qzz/qat (0-15)

2 and d2 are the s and the d character of the chlorine

where s
atomic orbital involved in the CC1 bond, II is related to
the double-bond character of the CC1 bond, and quat =
-lO9.74 Me is the quadrupole coupling constant of atomic
chlorine. By assuming that s2 = 0.15 and that d2 and II
are negligible, the ionic character in the CC1 bond is found
to be 22-23%. This is greater than in ethyl chloride and
smaller than in tertiary butyl chloride, which is the expected
order based on the inductive effect of methyl group addition.
Table XVIII is a comparison of the quadrupole coupling
constants and the bond distances of a sequence of chlori—
nated compounds. The consistent increase in the CC1 bond
distance and decrease in the quadrupole coupling constant
is noted. This can be explained qualitatively by considering
inductive effects from the electropositive methyl group and
competition for the electrons between the chlorine and carbon
atoms in multihalogenated compounds (56). As the electro-
positive methyl group is added, the electrons will be pulled
away from the chlorine, thus tending to increase the bond

2
length and to decrease <32; (equation 2-37).
av.

Table XVIII.

 

93

Comparison of Absolute Values of the
Quadrupole Coupling Constanusand Bond Lengths

in Halogenated Hydrocarbons.

 

 

Molecule r(CCl) quzz(Mc)a quzz(Mc)b quzz(Mc)c Ref.
(CH3)3CCl- 1.803 62.3 66.9 66.9 50
(CH3)2CH01 1.798 64.1 69.12 67.82 this
thesis
CH3CH2C1 1.788 66.0 71.24 68.80 32
CH301 1.781 68.40 74.74 74.74 31
C3H5Cl 73.45 59
0112012 1.775 72.47 79.66 78.40 60
C013H 1.758 76.98 80.39 80.39d 61
0014 1.766e 81.85 86f 86f 62
SiH3CH2C1 1.788 72 68.70 63
SiH3C1 2.050 40 40 64
SiF3C1 1.989 43 43 65

 

aSolid at 200 (References 57 and 58).
bAssuming cylindrical symmetric charge distribution.

CAssuming that the z axis of the quadrupole tensor
and the CC1 internuclear line coincide.

dReference 66.

eDetermined by electron diffraction.

fEstimated from the solid value.

94

In multichlorinated compounds the chlorine atoms compete for
the carbon atom electrons, causing a decrease in ionic charac-

ter of the CC1 bonds, reducing the CC1 bond length, and increasing
< 02V
822

One may note that the change in:)<

av.’

zz going from CH3Cl
to CH3CH2C1 is only 2.4 Mc in the solid state‘" and only;
3.50 Me in the gas phase assuming cylindrical charge distri-
bution, but is 5.94 Mc when the z axis and CCl internuclear
line are assumed to coincide. It would seem that if one is
to compare coupling constants, the assumption of cylindrical
symmetry should be used unless the principal coupling con-
stants could be determined exactly. One argument for this
is from the recent work on ethyl bromide where:><;z, deter-
mined by using cylindrical charge distribution, was within
1% of 22 obtained from the fully known coupling tensor.

In comparing molecules of approximately the same hybridi-
zation,$ the :x:bonds may be directly correlated to bond
distances. Figure 14 shows a plot of‘)<;z (gas values)

versus r(CCl). The plot of 22 (determined from the coup-

ling tensor transformation) versus r(CCl) shows a significant

 

22 for nuclei of spin I = 3/2, obtained from nuclear
quadrupole resonance on the solid, represent only average
values which are essentially those of a symmetrical charge
distribution. For these values, n is assumed equal to zero.

*It is known that there must be a change in hybridi-
zation for compounds such as methylene chloride having angles
HCH = 112° and C1CC1 = 112°, which cannot be explained by
the usual hybridization theory.

.00004040 0004 400 04040> um 40 4040 < .04 .w4m
TH

dow.4 25.4 0000.4 Non...” mm.n.4 dmu.4 own.4

 

_ 4 4 4 _ 4 _

00400400 0044
400405040404 400 004 000 04X0 N 008 mu

     

004494444040 0w4000 40044004400 AU
400040000

0040000

 

95

 

 

 

00
00
40
00
00
04
44
04
04
04

mm

 

 

96

break in the curve between ethyl chloride and methyl chloride
which would suggest an abrupt change in chemical properties.

2 plot along with known induc-

Based on the r(CCl) versus;)<é

tive effects of methyl group addition, one might expect that
the longer straight chain chlorinated hydrocarbons (such as
n-propyl chloride) would have CCl bond lengths (based on
substitution parameters) that fall between those of ethyl
chloride and isopropyl chloride.

If one examines the change in going from 2-chloropro-
pane to cyclopropyl chloride (essentially closing the ring),
the large increase in.:<bond may be due to loss of an effec-
tive methyl group and to a partial change in hybridization

2),

(sp3 0 sp both which increase the quadrupole coupling

constant (56).

4.8 Internal Rotation

 

The first excited torsional state of (CH3)2CHC135,
and the ground (0, 0 state), the CD3 (1, 0 state), and the
CH3 (0, 1 state) torsional states of CD3CDC135CH3 were examined.
The attempt to determine the potential barrier hindering
internal rotation was carried out using CD3CDC1350H3 since
it could be treated as a one-top problem (section 2.5).
Assignments were made based on the relative intensity
of torsional state transitions compared to ground state tran-
sitions and on the hyperfine splitting. Computation of the

Boltzmann factor using reasonable estimates of the torsional

97

energy indicated that the intensity ratio of the (l,O)/(O,l)
state should be 1.5. Observed ratios were 1.3 to 1.7.

The measured hyperfine components for CD3CDCl35

CH3

in the (0, O), (l, O), and (O, l) torsional states are given
in Appendix III. The hypothetical unsplit frequencies are
listed in Table XIX. Table XX lists the rotational constants
for the CD3CDC1350H3 species and for (CH3)ZCHC135 in the
first excited torsional state.

By applying the methods given in section 2.5, a lower
limit was put on the height of the barrier hindering internal
rotation of the methyl group in CD3CDC13SCH3. The calculation
is based on the observation of no splitting in the 1249 ~
1248 transition in the (0, l) torsional state. Parameters
used in the internal rotation calculation are listed in
Table XXI. Splittings greater than 0.5 Mb would have been
detectable, and since no splitting was observed, the poten-
tial barrier must be greater than 3400 cal/mole.

An estimate of the potential barrier hindering internal
rotation of the methyl group was made from relative intensity
measurements as described in section 2.5. The potential
barriers determined by this method are listed in Table XXII
and range from 3577 to 3920 cal/mole. The intensity ratios
are not very accurate (0 6%) and can be regarded only as an
estimate. The study of the internal rotation problem in

2-chloropropane is being continued in this laboratory.

98

Table XIX. Hypothetical Unsplit Frequencies (Mc) for

CD3CDC135CH3 in v = 0 and v = 1 Torsional
States.

 

 

 

Transition (0,0) state (1,0) state (0,1) state
212 4 313 19270.60

202 4 303 20103.08

221 0 322 21273.32 21244.7

220 4321 22443.14

322 4 423 28107.19

330 4 431 29200.28

312 4 413 29955.59 29915.78 29919.09
321 4 422 30502.42 30458.86 30474.40
414 4 515 31450.97 31413.26 31407.45
404 4 505 31720.64 31683.16 31673.76
423 4 524 34738.20 34693.61

413 4 514 36516.85 36470.39 36466.88
928 4 927 29004.63 28947.00

1249 4 1248 23496.43 23423.06 23574.63

 

99

 

 

 

 

.N< 060:0: m04 x 4mmmo.m "0005 404004 004040>0000

0000.404 0040.044 0000.044 0000.044 04
4044.044 0000.404 0440.404 0404.404 04
4044.00 0004.04 0040.04 4000.04 04
00.0 4 40.4040 00.0 4 40.0000 00.0 4 44.0000 00.0 4 00.0000 0
00.0 4 00.0000 00.0 4 40.0040 00.0 4 00.0040 00.0 4 00.0040 0
0.0 4 00.0000 0.4 4 00.4000 4.0 4 40.4000 4.0 4 40.0000 0

44u>0004000040000 44.00000004000000 40.40000004000000 40.00000004000000

.>> 04040 400040408
.00040 00440400 40040404 04 0000 0040000 00000400404001N

40 mAN< 5600 0444004 40 0400502 000 A020 040040000 4000440400 .xx 04405

100

Table XXI. Parameters Used in the Calculation of the

Potential Barrier Hindering Internal Rotation
of the Methyl Group in 2-Chloropropane.

 

 

 

CD3CDC1CH3 CD CDClCH3 (CH )2CHCl
(0,1) state (1 8) state (v = f) state

A 6851.55 Mc 6861.67 Mc 8060.24 Mc

B 4148.51 4146.49 4563.43

0 2934.37 2935.11 3202.87

18 73.78345 amu A2 73.67463 amu A2 62.71910 amu A2

1b 121.85845 121.91781 110.77873

IC 172.27923 172.23579 157.83688

Ia 3.161 6.317: 3.161

18 40.33250 0.52402 -0.43124

1b 0.87059 0.78270 0.83176

1C -O.3627O 0.33594 0.34960

r 0.973195 0.940582 0.968472

rI 3.0763 5.9418 3.0613

F 164.3324 ko 84.9375 ko 165.1339 ko

02 0.000203

02 0.000510

YZ 0.000044

 

aDetermined from ground state.

101

Table XXII. Height of Potential Barrier Hindering Internal
Rotation in 2-Chloropropane.

 

 

Relative
Intensity
Species Ratio F (ko) s V (cal/mole)

 

(CH3)2CHC135 (v=1) 0.32 165.1339 110.4 3920 0 500
CD3CDC135CH3 (0,1) 0.17 164.3324 105.2 3709
CD3CDC1350H3 (1,0) 0.28 84.9375 196.3 3577
CD3CDC13SCH3 (0,1) 97.0 34218

 

aLower limit to barrier height determined by no obser—
vable splitting in (0,1) first excited torsional state.

102

A comparison of potential barriers hindering internal
rotation of the methyl group of compounds similar to 2-chloro-
propane is in Table XXIII. The parameters in this series
of related one—top and two—top molecules indicate that the
barrier will increase or remain nearly the same with the
addition of one more methyl group. Therefore, finding a
potential barrier for 2-chloropropane greater than the 2200 cal/

mole reported in reference 38 is not at all unreasonable.

103

Table XXIII. A Comparison of the Height of Potential
Barriers Hindering Internal Rotation in
Related‘Molecules.

 

fir 1' fi

V—

 

‘Molecule V3(cal/mole) CXC ‘Method Reference
(0H3)20301 3800 112°uz' I8 this thesis
0H303201 3685 ‘ Pb 32
(CH3)3CH 3900 I 67
(CH3)30F 0300 112°nz' I 67
033030 1150 F 68
(033)200 760 116°14' F 26
CH381H3 1700 F 69
. O t

(CH3)281H2 1665 110 59 F 70
cusoa 1070 F 10
(CH3)20 2720 111°37' F 71
CHBSH 1270 F 72
(CH3)ZS 2132 98°52' F 27

 

‘1 fir

aFrom intensity measurements.

bFromfrequency'measurements.

V. THE MICROWAVE SPECTRUM 0F 2-BROMOPROPANE

5.1 Introduction

A study of 2-bromopropane by microwave spectroscopy
should provide important information for the comparison of
the structures of small halogenated hydrocarbons. The struc-
ture of methyl bromide is well-known (73), and that of ethyl
bromide has just been completed (51). These together with
cyclopropyl bromide and tertiary butyl bromide would make
available for possible interpretation a series of monobromo
hydrocarbons similar to the monochloro series.

The only previous work done on 2-bromopropane was by
electron diffraction in 1939 (3#). The following parameters

were reported:

r(CBr) 1.91 i 0.03 A

<ccc = 109.5° 1 3°

<CCBr = 109.50 a 3°
r(CH) = 1.09 A assumed
r(CC) = 1.5h A assumed.

5.2 Preparation of Isotopic Samples

The present investigation was confined to an attempt
to determine the quadrupole coupling constants and the geometry
of the CCBrC skeleton. Consequently only (CH3)20HBr79,
(CH3)ZCHBr81, (CH3)2013HBr, and CI3H3CHBrCH3 were investigated.

104

105

The (CH3)ZCHBr was obtained from the Eastman Kodak Company
and used without further purification. The sample contains
50.52% bromine-79 and 49.h8% bromine-81 in natural abundance.

For the preparation of (CH3)2013HBr, the 19% labeled
isopropyl alcohol remaining from the (CH3)2013HC1 synthesis
was used. A slight excess of pure phosphorus tribromide
was dropped on the labeled alcohol (0.2 cc) in vacuo while
the reaction mixture was stirred in a flask surrounded by
an ice bath. A cold finger was used over the reaction. The
evolved products were trapped as they escaped and were puri-
fied by vacuum line distillations. The infrared spectrum
of the final product showed small impurities in addition to
the 2-bromopropane. The yield was approximately 0.1 cc.

The Cl3H30HBrCH3 species was prepared using the enriched
n—propyl alcohol left from the Cl3HCHClCH3 synthesis. The
n-propyl alcohol (0.2 cc) was distilled into a flask set up
for magnetic stirring. Phosphorus tribromide was slowly
dropped on the alcohol, and the reaction mixture was refluxed
on a trichloroethylene-Dry Ice cold finger. The volatile
products were trapped as they left the reaction mixture and
as the vessel warmed after completion of the reaction. The
n-propyl bromide was separated by vacuum line distillations.
The product was converted to 2-bromopropane by rearrangement
over anhydrous aluminum bromide. The infrared spectrum indi-
cated impurities to be present, but there was insufficient

sample to risk separation by vapor phase chromatography.

106

The mass spectrum of this sample indicated that the sample

was enriched in 013H3CHBrCH3 by 17%. The reaction steps are

3CH3CH2C13H20H + PBr3‘———-+BCH3CH2013H2Br + H3PO3 +(HBr)
13 AlBr3 l3

CH3CH2C H2Br-———-—9 C H3CHBrCH3 + HBr + AlBr3 (polymer).

5.3 Prediction of the Transition Frequencies
By using the experimental parameters from 2-chloro-

propane with the CBr distance and quadrupole coupling constants
determined in ethyl bromide (74), a good estimation of the
transition frequencies for 2-bromopropane were obtained.

The parameters used for the initial computations were

r(CC) = 1.522 A
r(CH) = 1.093 A
r(CBr) = 1.94 A

<<CCC = 113°
<<BrCH = 104.260.

The quadrupole coupling constants used were_><’ =

22
537.5 Mc for the Br79

Br81

species and 22 = Q50.9 Me for the
species.

The preliminary calculations were made by the same
method as those for 2-chloropropane in Chapter IV. A pro-
jection of 2-bromopropane at its ac plane of symmetry is shown

in Fig. 15.

107

maxm a 655v

A.mwmn asp ou amasowucoapoa ma

.zpuoafihm mo woman om one cw mcmaohaothnuN mo cowuownoha < .mH .wwm

 

 

hm

 

m

 

 

108

5.4 Examination of the Rotational Spectra

Based on the first order quadrupole interaction calcu-
lation, most of the transitions selected for study would
appear as two "doublets” showing equal splittings. The Br79
and the Br81 species have transitions of equal intensity separated
by approximately 100 Mc. The transitions were easy to assign,
but the second order quadrupole effects are apparently great
enough to cause an asymmetric splitting of the doublet pairs,
the splitting being larger than predicted in one pair and
being smaller in the other. The first order quadrupole coup-
ling constants are based on transitions where the splittings
in the doublets appeared to be equal.

The measured hyperfine components are listed in Appen-
dix IV. In determining the hypothetical unsplit frequencies,
the approximate first order coupling constants were used to
find l/fi. The average value of the L/k's were taken to find
the Lfitto be used in the rigid rotator expression. The com-
puted hypothetical unsplit frequencies are listed in Table XXIV.

The rotational constants were obtained by fitting the
rigid rotator energy expression by least squares. The least
moment of inertia was not as accurately determined as the
other two moments of inertia since the transitions with any
significant A dependence were of high J, and consequently
the centrifugal distortion effects would cause a deviation
from the rigid rotator expression. Also the l/i's are nor

determined as accurately as possible since the second order

109

.mwcwuuwaam macafihomnc nacho umhwm thm Umumawummm

 

 

 

 

 

 

 

om.owmom oo.onom m:.mmoam mm.mmoam mum :Nm

:o.m~m~m om.mmm~m ms.~mm~m 6m.mmmmm 3mm mam

o:.omamm H:.oN:~m e6.oosmm on.oosmm om.omemm 6H.omomm mam :Hm

mo.aomm~ oo.momm~ Hm.::mom mm.::mmm H:.omnmm mm.mmk6~ 606 wow

mm.mkmmm 6H.mmwmm No.somwm om.nowwm Hm.smomm mm.kmomm 6H6 mam

mm.smmam :H.wmmam 6H.moomm Hm.aaom~ mom so:

6:.mmwam :5.mmma~ 6N.oawam 5m.oawam No.ammam so.ammam ma: Nam

Ho.aooom mm.oooo~ mo.oamow 6m.oawom mm: Nam

km.ommom oo.awmom 3H.momom mm.mo~om mk.o:mom mm.oamom so: mom

mm.ommma No.emmma oo.mkmma as.wsmma oo.momma :o.mommH 3H: mam

om.mmsma om.w~:ma mom mom

mo.msosa mm.msosa man man

Umumasoamo Uo>hmwno @mumHSQHmo Um>hmmno Umumasoamu Um>hmwno cowuwmcmhh
meammmaomxmmov Hmammomxmmov mepmmomxmmov

.wcmaohaoEOLmnN pom onzv mmfiocmdvmpm uwaawco Hmowuwsuoakm .>Hxx manma

110

quadrupole effects have not been taken into account. The
rotational constants, the moments of inertia, and the second
moments for the isotopic species studied are listed in

Table XXV.

5.5 Molecular Structure

The coordinates of the center carbon atom and the bro-
mine atom may be computed using Kraitchman's equations, and
the constants determined from the three isotopic species
studied. The coordinate calculations are based on differences,
and therefore errors due to centrifugal distortion and second
order quadrupole effects will tend to cancel. This is because
the rotational constants are determined by the same method
using for the most part the same transitions. The computed

coordinates are

a 2 s
cmiddle -1.0752 A 0 04029 A
Br 0.8428 0 0.0124 .

The CBr bond distance based on these coordinates is 1.962 A.
The c coordinate for the bromine atom is no doubt too small (46).
A change of 0.03 A in this coordinate will increase the CBr
distance by 0.006 A. If the A rotational constant in the

parent species were in error by one megacycle more than the
A constant in the other two species, the.CBr distance could

be changed by i 0.006 A.

111

 

 

 

Table XXV. Rotational Constants (Mc), Moments of Inertia
(amu A2),8 and Second Moments (amu A2)b for
2-Bromopropane.

(CH3)20HBr79 (0H3)20HBr8l (0H3)2013HBr79

A 8036.64 1 5 8036.32 1 5 8016.99 1 5

B 2917.67 1 0.07 2894.40 1 0.07 2895.74 1 0.07

C 2295.38 1 0.07 2280.92 1 0.07 2283.50 1 0.07

Ia 62.9033 62.9058 63.0575

Ib 173.2653 174.6583 174.5775

IC 220.2385 221.6347 221.3843

Paa 165.3002 166.6936 166.4522

Pbb 54.9383 54.9411 54.9322

PCC 7.9650 7.9647 8.1254

 

aConversion factor: 5.05531

bComputed from equation 2-30.

x 105 Mc—amu A2.

112

The CBr distance in 2-bromopropane is 0.012 A longer
than in ethyl bromide (51) which in turn is 0.011 A longer
than in methyl bromide (73). The CBr internuclear line
makes an angle of 12°14' with the a inertial axis.

The calculated rotational constants for (CH3)ZCHBr79
were only 60 Mc higher than those determined experimentally.
This is approximately the difference one finds between the
experimental rotational constants and those determined from
substitution coordinates. This would indicate that the
initially assumed parameters are very nearly the correct
ones.

Work is continuing in this laboratory to determine
the rotational constants for Cl3H3CHBr790H3 so that a more
complete structural analysis can be made. The spectra for
this species is complicated by the probable presence of
n-propyl bromide and perhaps from new second order effects
brought about by the loss of the symmetry in the molecule.
An analysis of these second order effects which is very

lengthy is not yet complete.

5.6 Quadrupole Analysis

 

The first order quadrupole coupling tensor was obtained
from transitions that appear as doublets of equal splitting
such as the 514 ~ 615 and 322 ~ 423. The first order coup—
ling constants for bromine-79 and bromine-81 in the principal

inertial axis system are listed in Table XXVI.

113

Table XXVI. Quadrupole Coupling Constants in 2-Bromopropane.

 

 

 

79 81
(CH3)20HBr (CH3)20HBr
qum 477.9 1 3 Mc 400.4 1 3 Mc
qumn —47.8 1 6 Mc -40.7 i 6 Me
n -0.100 1 0.01 -0.102 1 0.01
><ea 477.9 1 3 Mc 400.4 1 3 Mc
:Xibb -262.9 1 4 -220.5 1 4
:X:CC -215.1 1 4 -179,8 1 4

 

 

In CBr Bond Axis System

 

 

 

 

 

 

81
(CH3)2CHBr79 (CH3)2CHBr
la 2b 3a 4b
.7K22 512.113 Mc 525.718 Mc 429.013 Mc 441.018 Mc
nbondc 0.02710.006 0 0.02810.006 0
ezd 12°14' 14°15'110 12°14' 14°20'110-
I 19% 17% 18% 16%

 

8Assuming that the z axis of the quadrupole tensor and
the CBr internuclear line coincide.

bAssuming cylindrical charge distribution.

Cnbond = (XXX "YW>./XZZ°

dez is the angle between the a and the z axes.

114

The quadrupole coupling constants are computed in a
molecular axis system by assuming a cylindrical charge dis-
tribution about the CBr bond, or that the z principal axis
of the quadrupole tensor and the CBr internuclear line coin-
cide. The results from these calculations are listed at the
bottom of Table XXVI. If the off-diagonal element ac can
be determined from the second order calculations, it will be
possible to diagonalize the quadrupole tensor which will
allow a check as to which of the foregoing assumptions is
the more valid.

The ionicity may be computed from equation (4-15) where
quat for Br79 is -769.8 Mo, and quat for Bral is -643.1 Mo
(16). The ionic character of the CBr bond is less than that
of the 001 bond in 2-chloropropane. This is the expected
trend based on the electronegativities of the halogens.

A comparison of quadrupole coupling constants and bond
lengths for a series of bromides is given in Table XXVII.
The trend in coupling constants and bond lengths is similar
to that for the chlorine analogues. It would be interesting
to have an accurate parameter for the CBr distance and coup-
ling constant for tertiary butyl bromide. One might be able
to give a reasonable estimate for the bond length and coup-
ling constant by an analogy between the listed series in

Table XXVII and the similar chlorine series.

115

Table XXVII. A Comparison of Quadrupole Coupling
Constants of 2-Bromopropane with Those of

Similar Compounds.

 

 

 

CH3Br79 1.939c 577.3d 577.3

CH3CH2Br79e 1.950 547.1 541.0
f

(CH3)20HBr79 1.962 525.7 512.1

 

aAssuming cylindrical charge distribution.

bAssuming that the z axis of the quadrupole tensor
and the CBr internuclear line coincide.

cReference 73.
dReference 75.
eReference 51.

fThis thesis.

VI. SUMMARY

The microwave spectra for a number of isotopic species
of 2-chloropropane and 2-bromopropane have been examined and
their rotational transitions assigned. From an analysis of
the hyperfine splittings due to the chlorine and bromine
nuclear quadrupole moments the first order quadrupole coup-
ling constants were obtained.

The ground state rotational constants for a sufficient
number of isotopic species of Zvchloropropane were obtained
enabling a complete determination of the molecular structure
by the substitution method. The important bond distances
and bond angles were determined to be r(CC) = 1.522 A,
r(CCl) = 1.798 A, <CCC = 112°42', <0001 = 109°24'. An
estimate of the vibration effects on the atom coordinates
as determined by Kraitchman's equations was made by assuming
small reductions in the bond lengths upon isotopic substi-
tution. It was clearly illustrated that the zero-point
changes in the vibrational energy upon isotopic substitu-
tion can have a significant effect on the bond distances
and bond angles computed by the substitution method. A
study of CH3CHClCH3 and CD3CD010H3 in the first excited tor-
sional state allowed an estimation of the height of the
potential barrier hindering internal rotation of the methyl
group.

116

117

Using the rotational constants obtained from the three
species of 2-bromopropane analyzed, the CBr bond distance
was determined by the substitution method. The computed
bond length is r(CBr) = 1.962 A.

The quadrupole coupling constants obtained for both
2-chloropropane and 2-bromopropane fill important places in
the methyl to tertiary butyl halide series. In both series
a regular increase in bond length and ionic character and
a corresponding decrease in the quadrupole coupling constant
is observed. This trend is discussed in terms of the induc-
tive effects of methyl group addition. The two assumptions
for transforming the quadrupole coupling tensor from the
principal inertial axis system to the carbon-halogen axis
system are considered in terms of which is the "best" one
to use when making comparisons. It is argued that when com-
paring coupling constants between symmetric and asymmetric
top molecules, the constants obtained by employing a cylin-
drical symmetric charge distribution should be taken as the

"best” of the two values.

118

 

 

 

6N.AN66H 46.66665 y\a 1 y\a
w HA.:H66H y\6 1 y\6
66.66664 64.6H66H «\6 1 m\6
56.6366H H~.HH66H 06.6Nm6H y\6 1 n\a
65.66664 6N.6656H 66.6666H ~\6 1 m\6
66.6H66H 86.66664 :m.m~m6a «\A 1 “\6
no.6omsa 61.6NN6H «\H 1 yxa

66.6666a 6:.6H68H :m.a¢mma m\6 1 m\6
as.omoma asywmwsa .3N.6H~6H “\6 1 «\6
11.6uoms 66.6668H s~.:amma “\6 1 ~\H
om.6soma om.oamsa :6.H6N6H n\6 1 m\6
16.6866H «6.66654 o~.om~ma m\k 1 6\6
Nos 1 sea

86.66~5H “\H 1 n\a

3.660.: 666.63.: «\m 1 «\6
No.Nsosa .m:.oaa¢a m\6 1 «\6
66.6668a o~.~oN:H «\6 1 “\H
66.66635 66.6666H :m.ama¢a «\6 1 n\6
~6.mkosa as.aomma 64.1648H “\k 1 n\6
«as 1 Has

 

Honouxmmov.mmo Homomm o Hommaomfimmov

N m N n so one
mm mm ma mm Homo A mow mmHUmU A mov Haw he

mm

 

 

mama0haohoaco1m mo mowomam owaouowH Mom AOZV wucmcoqaoc mawmhwahm Umhnmmmz

H XHQmem<

119

 

 

 

 

 

N6.Hmmsm «\m 1 N\H

66.6HH8N 6H:.ommsm No.6658N 66.6666N s6.666:~ N\6 1 N\6
ms.sossm 6:4.momsm 56.66::N 6o.mwwm~ 66.8«63N N\A 1 N\6
HO.H~H3N 61.6NN3N 66.6683N 66.8666N 11.6865N m\6 1 ~\A
66.6666N 66.6666N N\6 1 N\H
AH.6Homm 66.nowmm 65.6666N N\6 1 N\6
NH.soomm 16.66N6N 66.:6ANN om.:~mm~ N\A 1 «\6
66.6Homm noo.mkmmm 660.166NN 66.6666N N\m 1 «\n
mo.osmam 666.6skam 66.omomm w om.oma- «\6 1 «\H
66.046HN 666.6:AHN ~:.Hwomm 66.~HAHN 66.56HNN N\6 1 «\6
61.646HN :o.amsam 16.666NN 66.664NN N\A 1 N\6
ma.:ama~ mo.omsa~ 66.:womm 6N.6HAHNV 16.:6HNN «\m 1 m\k
mom 1 Nos

«\6 1 Q6

55.6:kom 16.666HN 66.616om 86.noaam mm“ 1 mmm

N 6 1 N a

HA.m:som 66.66osm NA.N66ON 36.6oaam «\m 1 N\s

646 1 was

mmaooomxmmov mmommaomommmao mmaom6HoNA6mov smaomomxmmov mmaomomemmov 8630666605

 

 

UmscwucoonnH NHDmem<

120

 

 

 

 

 

6N.666N6 66.66N66 N\6 1 N\6

66.666N6 66.66N66 N\6 1 N\6

66.666N6 6N.66N66 N 6 1 N\6

66.666N6 66.66N66 N 66 1 N\6

NNJ T HNM

66.6666N 6 66.6666N N\6 1 N\6

66.6666N 66.6666N 66.6666N N\6 1 N\6

66.6666N 66.6666N 66.6666N 66.6666N N 6 1 N\6

66.6666N 66.6666N 66.6666N 66.6666N N 66 1 N\6

66.66666 66.66666 66.66666 66.66666 N\6 1 N\6

66.66666 66.66666 66.66666 N\6 1 N\6

N6.66666 66.66666 6N.66666 66.66666 N 6 1 N\6

66.66666 66.66666 66.66666 66.66666 N 66 1 N\6

6N6 1 NN6

66.6666N N\6 1 N\6

66.6666N N\6 1 N\6

66.N666N N\6 1 N\6

66.6666N N6.6666N 66.6666N6. 66.N666N Nm6 1 Nm6

N 6 1 N 6

66.6666N 6N.6666N N6.6666N 66.6666N N\6 1 N\6
N 6 6 6 N N 6 N 6

666666 A 666 66666666 6666 66666666 66:66 66666 6 666 666666 A 666 6666666666

 

 

Umdcwucoo11H XHQmem<

121

ww.©nmmm

Nm.omeN
mm.dwmmm
mm.mwmmm
mm.HmMNN

ow.mmomm

m:.oaoma

666.66666

w:.awom~

wo.mo¢~a
mo.mo:NH

m:.nm::m

66.6666N
66.6666N
N6.6666N
666.6666N

Nn.womma
oa.oomna
om.momma
NH.momMH

oo.amama
mm.NNH¢H

mm.HmNmN

00.nammm
m©.NNwMN
H©.Hmwmw
:©.wHwMN

N\6 1 N 6
N\66 1 N 66
y\66 1 N\66
N\66 1 N\66

 

m N\6 1 N 6
N\66 1 N 66

“\6 1 N 6
wN\66 1 N 66

666 1 666

 

Uo>aomohcs

 

N\6 1 N\6
N\6 1 N 6
N\66 1 N 66
N\66 1 N\66

6N6 1 666

 

 

N 6 6 6 N 6 N 6
666666 6 666 66666666 6666 66666666 A :66 666666 6 666

WMHUENAMHAUV COHHHWCGHH

 

 

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122

.6066» wcwuhoomh 6 606m UwMSmmmzn

.cowuwmcmhu wawhompochw

 

 

 

6\6 1 6\6
66.66N66 w.N\6 1 666

N\6 1 N 6
6N.66N66 «N\66 1 N 66
66.6N66 N\6 1 N\6
66.6N66 N\6 1 N\6
66.6N66 N\6 1 N\6
66.6666N N\6 1 N\6
66.6N66N “\6 1 N 6

66.6N66N N\66 1 N 66
66.6666N N\66 1 N66

 

 

666666N66m66 66666666666666 6666:666N66m66 666666N66666 6666m6N66666 6666666666

 

 

vaCHHEOO11H NHQmem<

123

 

 

 

 

N\6 1 N\6

N\6 1 N\6

N\6 1 N\6

N\6 1 N\6

66.66666 N6.NN666 66.66666 N6.66666 N\6 1 N\6
666.66666 66.66666 66.66666 66.66666 N\6 1 N\6
66N 1 666

N\6 1 N\6

.N6.66N66 666 1 N\6
66.66666 N6.N6666 66.66666 N\6 1 N\6
N6.66666 66.66666 66.66666 66.66666 N\6 1 N\6
66.66N66 N6.66666 66.66666 6N.66666 N\6 1 N\6
66.66N66 N6.66666 6N.66666 66.N6666 N\6 1 N\6
N6N 1 666

N\6 1 N\6

N\6 1 6\6

6\6 1 N\6

N\6 1 m\6

66.66666 66.66666 N\6 1 N\6
66.66666 6N.66666 N\6 1 N\6
N6N 1 666

66166666666N66666 6>66mo6666m66N66 6666666666666Nm6 6866666666666N66 6666666666

 

 

mammo6QOQOH£O1N mo wmwomam owaouomH pom Aozv mucmcomEoo mcwmpwazm poppmmwz

HH NHQmem<

124

 

 

 

 

 

666 1 N\6

66.6666N 6N.6666N N66 1 N\6

6.6666N 6N.6N66N 66.6666N 66.6666N N\6 1 N66
66.6666N 6N.6N66N 66.6666N 66.6666N N\6 1 N\6
6N6 1 6NN

N\6..N\6

66.666NN 66.666NN N\6 1 N\6

66.66N6N 66.666NN 66.666NN N\6 1 N\6
6N.6666N 66.666NN 66.N66NN N\6 1 N\6
NN6 1 6NN

6N.666NN N\6 1 N\6
66.666NN N\6 1 N\6
66.666NN 66.6666N 66.66N6N 66.6666N N\6 1 N\6
6N.N66NN N6.N666N 6N.66N6N 66.6666N N\6 1 N\6
666 1 N6N

N\6 1 N\6

66.6666N N6.6666N 66.66N6N 66.6666N mNm6 1 Nm6
N 6 1 N 6

6N.6666N 66.6666N 66.66N6N 66.6666N MN\6 1 N\6
666 1 N6N

66u>66666m6N66m66 6666666666666Nm6 6666666666666Nm6 6866666666666N66 6666666666

 

 

Umncfluco011HH xHszmm<

125

 

 

 

 

 

66.666N6 66.66666 66.66N66 N\6 1 N\6

66.666N6 6N.66666 66.66N66 N\6 1 N\6

66.N66N6 66.66666 66.66N66 N 6 1 N\6

66.666N6 .66.N6666 66.N6N66 N 66 1 N\6

NN6 1 6N6

N\6 1 N\6

66.66NN6 66.66666 66.6N6N6 N\6 1 N\6

66.N6NN6 66.66666 66.6N6N6 N 6 1 N\6

66.66NN6 6N.66666 66.6N6N6 N 66 1 666

666 1 N66

66.66666 66.6666N 66.N6666 N\6 1 N66

66.66666 66.6666N 66.66N66 N\6 1 N\6

66.66666 66.N666N 66.66N66 N 6 1 N\6

6N.66666 66.6666N N6.66N66 N 66 1 N66

6N6 1 NN6

N\6 1 N\6

N\6 1 N\6

66.6666N 6.6666N 6.6666N N\6 1 N\6
66.6666N 66.6666N 66.6666N N6.6N66N NW6 1 Nm6
N 6 1 N 6

66.6666N 66.6666N 6N.6666N 66.6N66N. MN\6 1 N\6
N66 1 66N

66u>6666666N66m66 6>66m66666m66Nm6 6666666666666N66 6866666666666N66 6666666666

 

 

poacwuco011HH xHszmm<

126

.cowuwwcmuu wcwummhmuch

 

md.wmmma
:w.HNNmH
0:.dmmma

0a.:NH3m

om.m:adm m:.mmadm

pw>aomohcp

 

N\6 1 N 6
N\66 1 N 66
N\66 1 N\66
N\66 1 N\66

 

N\6 1 N 6
6\66 1 N 66

“\6 1 N 6
N6.66666 mN 661N 66

 

6m.mawmm vm>6owmhcs

 

 

66u>66666m6N66666

6>66mo6666666Nm6 6666666666666Nmo

AbvmmUmMHUgn—Nmo GOHprCGPB

 

 

Umficwuc0011HH NHszmm<

127

APPENDIX III

Measured Hyperfine Transitions (Mc) for CDBCDC13SCH3 in vv'
Torsional States

 

 

 

 

 

 

 

 

 

Transition (0,0) State (1,0) State (0,1) State
212 * 313

7/2 6 9/2 19272.04

1/2 6 3/2}

5/2 6 7/2 19268.63

3/2 _. 5/2

202 ” 303

7/2 6 9/2 20103.43 21249.1
5/2 6 7/2 20104.44 21234.2
3/2 6 5/2 20100.48 21244.8
1/2 6 3/2 20099.36-

221 “ 322

7/2 6 9/2 21277.68

5/2 6 7/2 21262.54

3/2 6 5 2 21273.29

1/2 6 3/2 21288.25

220 7 321

7/2 6 9/2 22447.84

5/2 6 7/2 22431.77

3/2 6 5/2 22442.70

1/2 6 3/2 22458.82

322 * “23

9/2 6 11 2 28109.32

7/2 6 9 2 28103.42

5/2 6 7/2 28105.64

3/2 6 5/2 28111.29

330 7 “31

9/2 6 11 2 29204.91

7/2 6 9 2 29190.62

5/2 6 7 2 29197.75

3/2 6 5/2 29212.49

APPENDIX III-~Continued

128

 

 

 

 

 

 

 

 

 

Transition (0,0) State (1,0) State (0,1) State
312 7 413
9/2 6 11 2 29956.19 29916.37 29919.70
772 6 9/2}. 29955.39 29915.58 29918.87
3 2 6 5 2
5/2 6 7/2 29954.35 29914.56 29917.86
321 7 “22
9/2 6 11 2 30504.84 , 30461.21 30476.89
7/2 6 9 2 30498.43 30454.92 30470.42
5/2 6 7/2 30500.41 30456.87 30472.36
3/2 6 5/2 30506.74 30463.21 30478.70
“14 * 515
11 2 6113322} 31451.20 31413.47 31407.05
9 2 6
7/2 6 22} 31450.39 31412.69
5/2 6 7/2
“04 ” 505
11 2-613/2} 31720.83 31683.40 31673.98
9 2 6 11 2
7 /2 6 9 21} 31720.10 31682.59 31673.21
5/2 6 7/2
“23 7 524
11 2 6 13/2} 34739.27 34694.78
5 2 6 7 2
9/2 6 11 2}, 34736.75 34692.07
7/2 6 9 2

t 514

2 6 13 322} 36517.04 36470.64 36467.11

12 6 11

7/2 6 92 36516.32 36469.80 36466.32

5/2 6 7/2}

129

APPENDIX III--Continued

 

 

 

 

 

 

 

 

Transition (0,0) State (1,0) State (0,1) State
808 7fi827
17/2 6 17/2 31830.22
15/2 6 15/2
19/2 6 19/2 31828.68
13/2 6 13/2
928 7 927
unresolved 29004.63 28947.36
12 6 12
310 39
unresolved 35985.64 35911.31
1028 "’ 1029
unresolved 34107.55
1249 7 1248
27/2 6 27/2] 23497.42 23424.02 23575.49
21/2 _. 21/2
25/2 6 25/2 23495.13 23423.06 23573.33
23/2 6 23/2

 

130

APPENDIX IV

Measured Hyperfine Components (Me) for Isotopic Species of
2-Bromopropane

 

 

 

 

 

 

 

 

Transition (CH3)2CHBr79 (0H3)20H8r81 (CH3)2013HBr79
212 6 313

7/2 6 9/2 14661.26

1/2 - 3/2

5/2 6 7/2 14690.24

3/2 6 5/2

202 7 303

7/2 6 9/2 15423.41

5/2 6 7/2 15421.42

3/2 6 5/2 15451.13

1/2 6 3/2 15453.61

313 7 “14

9/2 6 112 2 19502.12 19372.88 19390.33
7/2 6 19513.96 19382.95 19402.07
5/2 6 19519.21 19387.29 19407.32
3/2 6 5/2 19508.34 19578.22 19395.82
303 7 “04

9/2 6 11 2 20338.02 20203.06 20218.45
7/2 6 9 2 20335.52 20201.09 20216.03
5/2 6 7/2 20349.70 20212.96 20230.21
3/2 6 5/2 20352.03 20214.75

322 7 “23

9/2 6 11 2 20793.08 20646.46

7/2 6 9 2 20840.74 20686.28

5/2 6 7/2 20823.76 20672.24

3/2 6 5/2 20632.44

312 7

9/2 6 1122 21974.30 21810.76 21822.63
7/2 6 21985.23 21819.87 21833.66
5/2 6 21992.49 21825.92 21840.99
3/2 6 5/2 21980.78 21816.14 21828.99

131

APPENDIX IV--Continued

 

 

 

 

 

 

 

 

 

Transition (CH3)20HBr79 (0H3)20H8r8l (0H3)2013H8r79
“04 7 505
11 2 6 13 2 25097.49 24936.69
9 2 6 11 2 25095.57 24935.04
7/2 6 9 2 25103.64 24941.91
5/2 6 7/2 25106.44 24944.17
515 7 616
13/2 6 15/2 29054.57 28865.38 28892.57
11 2 6 13 2 29057.24 28867.62 28895.21
9 2 6 11 2 29061.24 28870.85 28898.26
7/2 6 9 2 29058.35 38868.46 28896.40
505 7 606
13/2 6 15/2 29729.13 29543.68 29568.21
11 2 6 13 2 29726.98 29541.95 29566.12
9 2 6 11 2 29732.56 29546.56 29571.77
7/2 6 9 2 29734.45 29548.24 29573.60
514 7 615
13/2 615/2 32633.64 32398.66 32417.85
11 2 6 13 2 32635.70 32400.37 32419.96
9 2 6 11 2 32640.29 32404.19 32424.62
7/2 6 9 2 32638.17 32402.44 32422.37
523 7 624
132 2 6 15/2). 32675.17 32328.85 32353.40
7 6 9 /2
1122 6 13 2:} 32590.13 32317.23
9 2 6 11 2
524 7 625
13 2 6 15/2} 31046.23 30826.28
7 2 6 9 /2

31033.13 30815.29

11 2 7 13 2;}
9 2 7 11 2

 

10.

11.

12.
13.
14.

15.

16.

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