STUDIES DFTTTATTS T’TNYLDYDLOPRGPANE. - ~ - - 3
METHYTDTTLTT‘TRDPHGSPHTTTE AND METTTDXTDTFLDOROPHD’TPHTNE ”
AT TADEEEDEAR ROTATTDTTAE SPECTROSCDPY

Thesis TOT The Degree 6T Pit D
MTCTTTGAN STATE UNTVERST‘T‘Y
EDWARD GEORGE CDDDTTTD

T971 '

tyxV‘

I...“

L I B R A Z Y
Michigan-r «tat:

d ”93“,“ 1.7 r

 

This is to certify that the
thesis entitled
Studies of Trans-Vinylcyclopropane,

Methyldifluorophosphine, and Methoxydifluorophosphine
by Molecular Rotational Spectroscopy

presented by

Edward George Codding

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Qhem .I § Hf!

224 «(aim A

Major professor

Date Jgne 10. 19H

0-7639

 

ABSTRACT

STUDIES OF TRANS-VINYLCYCLOPROPANE,METHYLDIFLUOROPHOSPHINE,
AND METHOXYDIFLUOROPHOSPHINE BY MOLECULAR ROTATIONAL SPECTROSCOPY

By

Edward George Codding

A brief historical review of rotational spectroscopy is presented.
The theory of rotational spectra, the coupling of internal rotation to
the overall angular momentum of the molecule, the Stark effect, and
molecular structure determination are discussed. A short description
of the microwave spectrometer, including a description of a new binary
decoder which is useful for placing accurate frequency markers on a
spectral recording, is given.

The molecular rotational spectrum of trans—vinylcyclopropane in the
ground and first three excited torsional states was analyzed. The B and
C rotational constants were determined for all species by analysis of the
spectral frequencies while the A rotational constant was estimated by
analysis of an anomalous Stark effect of the 202-303 transition. The
molecular dipole moments were determined to be pa = 0.486f0.007 D,

”b = 0.0 D, ”c = 0.llOf0.003 D = 0.498f0.007 D. An exhaustive

s 1-1
T
search failed to disclose transitions assignable to another molecular
configuration.

The molecular rotational spectrum of methyldifluorophosphine in

the ground and first excited torsional state was analyzed. The three

rotational con
dipole moments
TC:0.194’:0.0
rotation of th
height was det
which was obta
spectrum and d
assumptions ar
bond length, t

The molec
CH3180”? anc
The three rote
rotational tre
the barrier h“
to be 422 cal,
molecular Con-
cis to the f]
are TTPF) = 1
<(FPF) = 95.3
<(0CH7) = 110

May fT‘Om the

Edward George Codding
rotational constants were determined for both species. The molecular
dipole moments were obtained as: “a = 2.047f0.002 D, “b = 0.0 D,

“c = O.l94f0.03 D, uT = 2.056f0.03 D. The barrier to internal

rotation of the methyl group was found to be 6.l kcal/mole. The barrier
height was determined from the torsional excitation energy, 325 cm'],
which was obtained from relative intensity measurements in the microwave
spectrum and direct observation in the infrared spectrum. If reasonable
assumptions are made about the structure of the methyl group and the PF
bond length, the PC bond length is determined to be l.82 A.

The molecular rotational spectra of the species, CHBOPFZ, 13CHBOPFZ,
CHBIBOPFZ, and CD30PF2 were investigated in the region 26.5-40. GHz.

The three rotational constants were determined for all species. The
rotational transitions are split by tunneling of the methyl group through
the barrier hindering internal rotation. The barrier height was determined
to be 422 cal/mole by analysis of these splittings. The structure of the
molecular configuration having a plane of symmetry with the methyl group
cis to the fluorines has been obtained. The bond lengths and bond angles
are r(PF) = 1.586 A, r(P0) = 1.572 A, r(0C) = l.446 A, r(CH) = 1.09 A,
<(FPF) = 95.3°, <(FPO) = lOl.5°, <(POC) = l23.5°, <(OCH6) = lO7.l°,

<(0CH7) = llO.7°, and <(HCH) = l09.4°. The methyl group is tilted 2.4°

away from the fluorines relative to the 0C bond.

STUDIES OF TRANS-VINYLCYCLOPROPANE,METHYLDIFLUOROPHOSPHINE,
AND METHOXYDIFLUOROPHOSPHINE BY MOLECULAR ROTATIONAL SPECTROSCOPY

By

Edward George Codding

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1971

To my mother and father for their encouragement and faith through

good times and bad, and to Penny for her ever present smile.

ii

ACKNOWLEDGMENTS

I wish to extend my deepest gratitude to Professor Richard H.
Schwendeman for his guidance and encouragement throughout this investigation
and the preparation of this thesis.

Financial support from the National Science Foundation, the Dow
Chemical Company, and the Phillips Petroleum Company is gratefully

acknowledged.

TABLE OF CONTENTS

I. HISTORICAL BACKGROUND ...................... 1
II. THEORY ............................. 4
2.l Introduction ...................... 4
2.2 Rigid Rotor Model .................... 4
2.3 Internal Rotation .................... 7
2.4 Stark Effect ....................... l2
2.5 Molecular Structure ................... 15
III. EXPERIMENTAL .......................... l8
3.l Introduction ...................... 18
3.2 Radiation Sources .................... 20
3.3 Spectral Display .................... 20
3.4 Sample Pressure and Temperature ............. 2l
3.5 Frequency Measurements .................. 21
IV. MOLECULAR ROTATIONAL RESONANCE SPECTRUM OF TRANS-
VINYLCYCLOPROPANE ...................... 23
4.1 Introduction ...................... 23
4.2 Rotational Constants .................. 24
4.3 Dipole Moment ...................... 35
4.4 The Anomalous Stark Effect of the |M| = l
Component of the 202-303 Transition ........... 39
4.5 Discussion of Results .................. 40
V. MOLECULAR ROTATIONAL RESONANCE SPECTRUM OF
METHYLDIFLUOROPHOSPHINE ................... 43
5.1 Introduction ...................... 43
5.2 Rotational Constants .................. 43
5.3 Molecular Structure ................... 47
5.4 Barrier to Internal Rotation .............. 53
5.5 Dipole Moment of Methyldifluorophosphine ........ 57
5.6 The Anomalous Stark Effect of the |M| = 1 Component
of the l01-2 2 Transition ................ 57
5.7 Discussion 02 Results .................. 57

VI. MOLECULAR ROTATIONAL RESONANCE SPECTRUM OF

METHOXYDIFLUOROPHOSPHINE ................... 63
6.1 Introduction ...................... 63
6.2 Preparation of Samples ................. 65
6.3 Rotational Constants ................... 66
6.4 Barrier to Internal Rotation .............. 7l

iv

 

‘llI'IIllTll-lllllll'l Tlll '1 lllIa'lllIN‘llllll‘l-ll I

6.5 Molecular Structure ................... 76

6.6 Discussion of Results .................. 82
LIST OF REFERENCES .......................... 85
APPENDIX ............................... 89

Table

10.
ll.

l2.

l3.

14.

LIST OF TABLES

Notation for the Internal Rotation Problem ...........
Assumed Molecular Parameters for Trans-Vinylcyclopropane . . . .
The Atomic Coordinates and Rotational Constants of Trans-
Vinylcyclopropane in the Principal Axis System Using the
Assumed Parameters of Table 2 .................
Comparison of Observed and Calculated Frequencies for the
Ground and First Three Excited Torsional States of
Trans-Vinylcyclopropane ....................
Rotational Constants and Principal Moments of Inertia for

the Ground and First Three Excited Torsional States of
Trans-Vinylcyclopropane ....................

Comparison of Observed and Calculated Frequencies for a 13C
Species of Trans-Vinylcyclopropane ...............

Rotational Constants and Principal Moments of Inertia for
the 13C Species of Trans-Vinylcyclopropane ...........

The Stark Effect and Dipole Moment of Trans-Vinylcyclopropane. .
Comparison of Dipole Moments of Some Related Hydrocarbons
Assumed Molecular Parameters for Methyldifluorophosphine . . . .

Atomic Coordinates and Rotational Constants of Methyldifluoro-
phosphine in the Principal Axis System .............

Comparison of Observed and Calculated Frequencies for the Ground
and First Excited Torsional State of Methyldifluorophosphine . .

Rotational Constants, Principal and Second Moments of Inertia
for the Ground and First Excited Torsional States of
Methyldifluorophosphine ....................

The PC Bond Length, FPF and FPC Bond Angles as a Function of
the PF Bond Length in Methyldifluorophosphine ..........

vi

Page
9

.25

.26

.30

.32

.36

.36
.37
.38
.45

.45

.49

.50

.54

7---...

 

 

[ll-II lull

 

il'llllll'l
[INN
[I‘ll

AIrlll

15.
16.
17.

18.
19.

20.

21.

22.

23.

24.

25.

26.

27.

Molecular Parameters for Some Difluorophosphine Derivatives. . .

.54
The Stark Effect and Dipole Moment of Methyldifluorophosphine. . .58
Comparison of the Dipole Moments for Some Phosphine and
Difluorophosphine Derivatives .................. 59
Barriers to Internal Rotation About the C-0 Bond ......... 64

Comparison of Observed and Calculated Frequencies and Internal

Rotation Splittings for CHBOPF2 and C13H3OPF2 .......... 68
Comparison of Observed and Calculated Frequencies and Internal
Rotation Splittings for CH3OPF2 and CH 301 .......... 69
A-Level Rotational Constants, Principal and Second Moments of
Inertia for the Normal and Three Isotopic Species of
Methoxydifluorophosphine .................... 70
Internal Rotation Parameters for the Normal and Three Isotopic
Species of Methoxydifluorophosphine .............. 73
Effective Rotational Constants, Principal and Second Moments

of Inertia for the Normal and Three Isotopic Species of
Methoxydifluorophosphine .................... 75
Principal Axis Coordinates for Methoxydifluorophosphine . . . . 79
Calculated Bond Lengths and Bond Angles for Methoxydifluoro-
phosphine ........................... 80
Comparison of Results of Structural Studies on Some

Phosphorous(V) Compounds .................... 83
Binary Representation of the Decimal Numbers Zero to Nine .90

vii

Figure

II.

III.

IV.

VI.

VII.

VIII.

IX.

LIST OF FIGURES

Block diagram of a typical MRR spectrometer ..........

The projection of trans-vinylcyclopropane on to the

molecular symmetry plane ...................

Plots of differences between rotational constants of
trans-vinylcyclopropane in the vth torsional state and

the ground vibrational state as a function of v .......

Projection of methyldifluorophosphine on to the

molecular symmetry plane ...................

PIOtS Of 1/2(A-C) E. K for the a) 61+3-6q2, b) 753-752,
c) 863-862 and d) 973-972 Q-branch transitions of

methyldifluorophosphine ...................

Plots of l/2(A-C) vs, K for a) 753-752, b) 863-862 and
c) 973-972 of the first excited torsional state of

methyldifluorophosphine ...................

Comparison of the observed and calculated Stark effect

for the [M] = 1 component of the 101-202 transition .....

Projection of methoxydifluorophosphine on to the molecular

plane of symmetry ......................

Symbols and truth tables for (a) NAND gates, (b) AND gates

and (c) OR gates ......................

Block diagram of the logic section of the binary decoder . . .

viii

Page

. 19

. 27

. 34

. 46

. 48

. 61

. 81

. 91
. 93

I. HISTORICAL BACKGROUND

Although the first experiments in the microwave region were carried
out as early as 1933 by Cleeton and Williams (l), active experimentation
did not begin until after the development of 1.25 centimeter radar
equipment during World War 11. Much of the early work was devoted to
the development of more sensitive experimental techniques and generally
to theoretical and experimental studies of ammonia which was particularly
suitable because of its very intense spectrum. That high resolution was
attainable in the microwave region was demonstrated by the early work of
Bleaney and Penrose (2,3) and Coles and Good (4) on the inversion
spectrum of ammonia.

Hughes and Wilson (5) suggested that the absorption signal could
be modulated by the application of a periodic electric Stark field to the
sample. The tremendous increase in sensitivity due to this technique has
made Stark modulated spectrometers the most important instruments in
the microwave region.

Theory predicted that the Stark effect shift and splitting for
linear molecules should be proportional to the square of the applied
electric field strength and to the square of the dipole moment. Stark
effect measurements carried out by Dakin, Good,and Coles (6) on carbonyl
sulfide, OCS, confirmed the theory. The theory of the Stark effect was
extended to asymmetric-top molecules by Golden and Wilson (7) and now

dipole moments are routinely determined for many molecules by microwave

2
spectroscopy or molecular rotational resonance (MRR), as it has recently
been called.

The high resolution available with MRR makes it possible to observe
and study the hyperfine structure arising from internal rotations within
the molecule. The theoretical problem of internal rotation was first
considered by Nielsen (8) and Koehler and Dennison (9),and later by
Kilb, Lin, and Wilson (10). Herschbach (ll) has presented an extensive
treatment of the internal rotation problem and has tabulated perturbation
coefficients which are extremely useful in calculating the potential
barrier to internal rotation. In addition,Wilson (12) has reviewed the
subject of internal rotation discussing both the experimental methods
available for obtaining values of the barrier height and the theoretical
interpretations of the data. Analysis of the hyperfine structure resulting
from internal rotation by the MRR technique is currently the most accurate
method for determining low barriers.

The determination of molecular structures is probably the most
important application of the MRR technique. The rotational constants
which are obtained from the assignment of the spectrum are essentially
reciprocal functions of the moments of inertia which are determined by the
physical locations and masses of the atoms within the molecule. Inter-
nuclear distances and bond angles were first determined by varying these
parameters until the computed moments of inertia reproduced the experimental
moments of inertia of several isotopic species. A better method was
suggested by Kraitchman (l3) which provides for fitting the differences
in the moments of inertia of two isotopically different molecules to
determine the atomic coordinates of the substituted atom. This method
requires substitution of all the nonequivalent atoms in the molecule

and is insensitive to atoms which are located near a principal axis or

3
the molecular center of mass. Costain (14) has pointed out that structures
obtained by the use of Kraitchman's relations are more reliable than those
obtained by the direct fitting of the moments of inertia.

Because of vibration-rotation interactions it is difficult to relate
the spectroscopically determined structure to the equilibrium or average
molecular structure (15). However Herschbach and Laurie (16) have suggested
a method for obtaining a good approximation of the average structure from
the effective moments of inertia.

This thesis is concerned with the determination of the dipole
moments, barriers to internal rotation, and structure parameters of the
molecules vinylcyclOpropane, methyldifluorophosphine, and methoxydifluoro-
phosphine. The reasons for selecting these molecules and the results of
the studies are described in Chapters IV, V and VI. Chapters II and III

are concerned with the theory and practice of rotational spectroscopy.

II. THEORY

2.1 Introduction

 

In the calculation of molecular rotational energy levels, as with
most quantum mechanical calculations, one attempts to make approximations
which facilitate the calculations without adversely affecting the accuracy
of the results. The primary assumption made is that the molecule may be
treated as a rigid aggregate of point masses. This approximation may be
justified theoretically, but there is also abundant empirical evidence that
the transition frequencies calculated in this manner reproduce observed

values to within the desired tolerances for all but the lightest molecules.
2.2 Rigid Rotor Model

If x1, y1 and 21 are the effective rigid rotor coordinates of the

ith atom, then the moments of inertia and the products of inertia are

respectively (17),

_ 2 2
Ixx - gmi(y1 + 2i )
N (2'1)
Ixy = -§mixiyi

1

where the sum is over all the atoms of molecules, the mi are the atomic
masses and x, y and z are cyclically' permuted to obtain the remaining
equations. If the origin of the coordinate system is located at the
center of mass of the molecule, defined by,

N

AmiRi = O

1
4

5

th atom, the coordinate system

where R} is the position vector for the i
may be rotated such that the products of inertia vanish and the inertial
tensor becomes diagonal. The resulting diagonal elements are labeled Ia’
Ib and IC in order of increasing magnitude and are called the principal
moments of inertia. The resulting coordinate axes are the principal axes
and are labeled a, b and c to correspond to Ia’ Ib and IC respectively.

The rigid-rotor Hamiltonian may be written as (18),

2 2

a b

2
h )

H (AP

 

+ CPc (2-2)

where A = BTQT—3 B = E;SE;-and C = 8;%I_3 (A132?) and the Pi's are the
principal axis components of the rotational angular momentum.

Solutions of the SchrSUinger Equation, Hp = Eo, cannot be given in
closed form if all three rotational constants are different. However, when
two of the constants are equal, which is the symmetric rotor case,
solutions are readily obtained. The eigenfunctions of the symmetric
rotor case may be used as basis functions for construction of a Hamiltonian
matrix for an asymmetric rotor (AfiBfC). Diagonalization of the Hamiltonian
yields the energies for the asymmetric rotor.

By using the commutation relations for angular momenta in a molecule-

fixed axis system (19),
[Px,Py] = -ifiPz

[Py.PZJ
[P2,Px]

-ifiPx (2-3)

-i‘hPy

the matrix elements of the squares of the angular momenta may be evaluated

2

in a basis set in which P and P2 are diagonal (20,21),

6
<J,K|PZZ|J,K> =‘hK2

2
<J,K|Py2|J,K> = <J,K|Px2|J,K> = fl J(J+1) - K2] (2-4)

<J,K|Py2|J,K+2> = -<J,K|Px2|J,K+2>

2
‘g—{{J(J+1) - K(K+1)}{J(J+l) - (K+1)(K+2)}]1/2

In these expressions J = O, l, 2 . . . etc. and K = O, :_l, :_2 . . .,

:9 represent the quantum numbers for the total angular momentum and the

projection of the total angular momentum on the molecule figure axis

respectively. The combination of J and K uniquely label the energy levels.
For a prolate symmetric top, for which A>B = C, the matrix of the

Hamiltonian of Eq. 2-2 may be shown to be diagonal. The diagonal

values are the prolate symmetric top energy levels which may be written

as (22),

E = h[3J(J+1) + (A-B)K2] (2-5)
For an oblate symmetric top for which A = B>C

E = hTAJTJ+1) + (C—A1K21 (2-6)

For an asymmetric rotor J is still a good quantwn number since the total
angular momentum is a constant of the motion. However, K is not a good
quantum number since there is no longer a molecular axis along which the
projection of J is a constant (23). The energy levels are therefore
labeled by JK_],K] where K_1 represents the absolute value of K obtained
by decreasing B to the prolate top limit and K1 is the absolute value of
K obtained by increasing 8 to the oblate limit. Since it may be shown
that energy levels for a given J do not cross in going from the prolate to
the oblate limit, this provides a unique labeling system. For a given J

the energy matrix is of order (2J+1) with elements only along the diagonal

7
and removed by two above and two below the diagonal (see Eq. 2-4) (22).
The matrix may be factored into four submatrices, two for K even and two
for K odd. The transformation which accomplishes this factoring is known
as the Hang transformation (24) and has the effect of changing from a
basis set of <J,KI to a basis set [<J.KT :_<J,-K|].

The transition selection rules for an asymmetric rotor are AJ = O, jfl
and AK_1 and AK+1 = 0, :1, :2 . . . . Transitions between energy levels
may be classified in several ways. Changes in J of -l, O or 1 take place
during P, Q and R branch transitions, respectively. Further, if AK_1 is
even (0, :2. . .) and AK+1 is odd (:4, :3 . . .), the transition is termed
an aétype transition. Similarly, for a c-type transition AK_1 is odd and

AK+1 is even, whereas both AK-l and AK+1 are odd for a b-type transition.

2
9

where ug is the component of the total dipole moment along the molecule-

fixed 9 axis (9 = a, b or c). The most intense transitions are those for

The intensity of a g-type rotational transition is proportional to n

which the K values change by O or :_1.
2 .3 Internal Rotation

In reality molecules are not rigid rotors and the relative motions of
the atoms may produce observable effects on the total rotational spectrum
of the molecule. Such effects are generally classified as "vibration-
rotation interactions". One such interaction exists in linear polyatomic
molecules where the vibrational bending mode couples with the overall
rotation causing the observed transitions to appear as doublets. This
interaction is called E-type doubling. Another type of interaction
occurs when one part of the molecule rotates about a bond relative to
the rest of the molecule. This type of motion is called torsion or
internal rotation and is observed in methoxydifluorophosphine where the

methyl group may rotate about the O-C bond.

1‘

8

The coupling of the overall and internal rotations produces discernible
effects in the rotational spectrum. These effects are usually small so
that the coupling may be treated as a perturbation. The complexity of
the spectrum resulting from the coupling depends on the height of the
potential barrier hindering the internal rotation and on the moment of
inertia of the rotating group.

A methyl group (-CH3) is by far the most commonly studied example of
a substituent undergoing internal rotation. For this case a convenient
model for construction of the rotational Hamiltonian consists of a rigid
symmetric top (the -CH3 group) attached to a rigid frame which may be
asymmetric. There are four degrees of freedom, three for the overall
rotation and one for the internal rotation. The axis of the internal
rotation must coincide with the symmetry axis of the top; however, the
symmetry axis may have an arbitrary orientation with respect to the frame.
Since the top is symmetric, all the structural parameters of the molecule
are independent of the internal rotation.

The Hamiltonian may be expressed as (10,11),

H = Hr + F(p-P)2 + V(a) (2-7)

where Hr is the rigid rotor Hamiltonian Eq. (2-2) and V(a) is the potential
function hindering the internal rotation. For internal rotation of a

methyl group it has been found that to high approximation
V(a) = 1/2 V3(l-cos 3a) (2-8)

The remaining symbols are defined in Table l. The second term of
Eq. (2-7) may be expanded to yield,

2

sz - 2FpP + FP (2-9)

9

Table l. Notationa for Internal Rotation Problem.

 

 

J,M,K

x, y or 2 refers to principal axis of inertia fixed in the
framework

principal moments of inertia of entire molecule

moment of inertia of internal top about its symmetry axis
direction cosine between t0p axis and the principal axis 9

reduced moment of inertia for internal rotation where:

r = 1 - ZAQZIa/I

g 9

components of the total angular momentum along the principal axes
total angular momentum of the internal top along its symmetry
axis

2P
9 gAgIa/Ig

rotational quantum numbers

the principal torsional quantum number for the harmonic oscillator
limit

an index which gives the symmetry or periodicity of the torsional
eigenfunction. For threefold barrier, o = O for A species and

o = :4 for E species.

 

a taken from reference 11.

10

The term sz is a quadratic function of P and hence may be incorporated

9
directly into Hr' The torsional part,

sz + 1/2 V3(l-cos 30) (2-10)

may be transformed into the Mathieu equation whose solutions are well
characterized and extensively tabulated (25,26). The boundary condition,

which is invariance under a + a :_§1-, yields two solutions; the first

has period gl-in a and transforms as the A species of the C3 group, and

the second has period Zn in a and transforms as the doubly degenerate

E species. Thus, each torsional level consists of two sublevels which

are labelled VA(° = 0) and VE(0 = :1). These levels would normally be

triply degenerate due to the symmetry of the potential function. The

partial lifting of this degeneracy can be considered to be a result of

tunneling through the potential barrier. The rotational levels are

independent of the torsional levels since the latter are not functions

of the quantum numbers J and K. However, the coupling term, -2FpP, transmits

an effect of the torsional motion to the rotational levels. As noted

previously, the coupling terms are generally small and may be treated

by perturbation theory. The coupling term is found to affect the A and

E levels differently; hence, the rotational transitions appear as doublets.
The Hamiltonian of Eq. (2-7) is diagonal in J and a but not in

K or v. The elements off-diagonal in v result from the coupling term

-2FpP. Approximate diagonalization in v may be obtained by applying a

Van Vleck transformation (27,28). The transformed Hamiltonian may be

factored into smaller submatrices Hv , one for each torsional level, as

follows:

_ (n) n
HvO - Hr + FfiWvo P (2-11)

11

The zeroth order terms (n = O in the sum) represent the pure torsional
energy, and do not affect the rotational spectrum. In addition, all
the perturbation coefficients, WVO("), for the A levels (0 = O) vanish
for n odd.

The WVO(n) depend only on the ratio V3/F (when V3 has the form of
Eq. (2-8)) and may in principal be evaluated by nth order perturbation
theory. However Herschbach (11) has shown that since the WVO(")'s are
independent of the molecular symmetry, they may be evaluated in the limit
of zero asymmetry, that is in the case of two coaxial symmetric tops.
Koehler and Dennison (9) have shown that the internal energy levels may

be written as a Fourier cosine series,

W = 1/4 szw c052(e - e ) (2-12)
V0 0
E 2
where the w 's are functions of the torsional level, v, and the barrier

2
height. As the barrier height increases, the wz's vanish rapidly. Further

it can be shown (11) that the perturbation coefficients are related to

Eq. (2-12) by:
n

n a W
whit" = (3,711?) (WT-<1 6 = 0 (2-13)

and thus to the WE coefficients of Eq. (2-12). The utility of this method,
the so-called "bootstrap" method is a result of the fact that the higher
order WVO(")'s may be written as linear combinations of the lower order
wz's. This is because the wz's vanish quickly for moderate barrier heights
(3 1000 cal/mole), so that only a few terms from Eq. (2-12) are required.
If a representation is chosen such that Hr + FWVO(2)P2, the rigid
rotor part of Hvo’ is diagonal, then the odd order terms will appear
off-diagonal. When the separation of the rotational energy levels is

large in comparison with the magnitude of the off-diagonal elements

12
connecting them, the odd order terms may be neglected. However, should
the rotational energy levels not be widely separated, as in the case of
a near symmetric top, it may be necessary to include the odd order terms
(for the E levels only since WVO(") = O for n odd for A levels).
As the barrier becomes lower (g 1000 cal/mole) it may become necessary

to include terms to fourth order in which case Eq. (2-11) becomes:

”yo = Hr + F[on(2)(aPX+BPy+YPZ)2 + wVO(4)(an+BPy+YPz)4]

where a = AxIa/Ix etc. and P has been expanded (see Table I). The
Hamiltonian, Hvo’ now has terms off diagonal in K up to <K|Ki4> (resulting
from the P4 terms). Should the barrier become very low it is necessary

to treat the top as a free-rotor (29).

Koehler and Dennison (9) following Nielsen (15) have presented an
alternative method of treating the internal rotor problem which employs
a transformation from the principal axis system to an internal axis
system in which the symmetry axis of the top is choosen as one of the
coordinate axes. The purpose of this transformation is to decrease the
interaction between the internal and overall rotation. Lin and Swalen
(30) have reviewed the advantages and disadvantages of the various

treatments of the internal rotation problem.
2.4 Stark Effect

When a static homogenous electric field is applied across the molecular
sample an additional term must be included in the rigid rotor Hamiltonian
to account for the interaction between the electric field and the molecular

dipole moment. This term has the form (31,32),

13
where fi'and E'are the molecular dipole moment and electric field vectors,
respectively, and cos 6 is the direction cosine between these two
vectors. Since the magnitude of the interaction depends on both the
dipole moment and the electric field, a convenient means of determining
the dipole moment is available (7).

The presence of an electric field defines a unique direction in
space along which the total angular momentum J is quantized; as M = O,
i}, :2, . . . :0. In the absence of an external field the energy levels
are independent of M and hence M was previously omitted.

If the molecule has an average non-zero dipole moment component in
the direction of the electric field, the interaction is given by the

standard first order perturbation result,

Ej(]) = <¢j(0)lH€le(O)>

and has the form,

5(1) = 715%} (2-14)

It can be shown (7) that such a nonzero dipole component will exist
only in the presence of degenerate energy levels, a condition which is
satisfied for symmetric top molecules due to the degeneracy in K (see
Eqs. 2-5 and 2-6).

If the molecule does not possess an average nonzero component, the
electric field may induce one and produce a second order stark effect.
The second order interaction, which is normally much smaller than the
first order effect, may be calculated from the standard second order

perturbation results:

 

< 0 0 >< 0 o ,
[(2) = 2 wj( )|HE|¢$ ) AiI )lHele( ) (2 15)
w (5340) - 51(0)) . ‘

14

The <wi(0)|HE|pj(0)> are the dipole matrix elements, multiplied by the
electric field, in the asymmetric rotor representation which diagonalized
the energy matrix. The transformations required to bring the asymmetric
rotor dipole matrix elements into this form are available from the
solution of the energy level problem. The required direction cosine
matrix elements have been given in a convenient form by Schwendeman (33).

Since HE is pr0portional to u and e, E(2) will be pr0portional to
their squares. Substitution of the appr0priate dipole matrix elements
into Eq.(2-15) and summation gives the result that E(2) may be written as

a sum of two terms (7),

EJ(2) = 2(AgJ + M23gJ )n9252 (2-16)
K-1TK+1 9 K-1’K+1

K-l ”(+1

where g = a, b or c. The second order Stark effect will exist for
asymmetric rotors (the K degeneracy has been lifted) unless accidental
near-degeneracies exist between energy levels.

A molecular rotational resonance spectrometer employing stark
modulation was first described by Hughes and Wilson (5). The basic
principle involves modulation of the absorption signal by application of
a periodic electric field across the sample.

The Stark effect is also very useful in assigning transitions. From
Eq. (2-16) it can be seen that the perturbation energy is a function of M2,
in addition to u and 6. Therefore, application of a sufficiently large
Stark field will split a particular energy level into J+l components. When
the Stark field is parallel to the microwave radiation electric field,
the selection rule for M is AM = O. The intensity of the components is

given by Jzupper - M2 (except for M = 0 when it is l/2 Jzupper) for an

15
R-branch transition and by M2 for a Q-branch transition. Thus an R-branch
transition (J + J+l) will exhibit J+l components, while a Q-branch
transition (J + J) will exhibit only J components. Therefore, the value
of Jlower for a transition may be determined by counting the number of
Stark components, and the characteristic intensities of the components identify

the transition as Q or R-branch.
2.5 Molecular Structure

As shown previously.Section 2.1, the rotational energy levels and
hence the transition energies are completely determined by the three
rotational constants A, B and C, which are inversely pr0portional to the
corresponding principal moments of inertia. Since the moments of inertia
are sums of products of atomic masses and molecular coordinates; changing
the mass at one of the atomic positions by means of isotopic substitution
moves the center of mass and changes the moments of inertia of the molecule.
If the assumption is made that isotopic substitution does not alter the
molecular structure, it is then possible to relate the differences in the
principal moments of inertia of the isotopically substituted and normal
molecules to the coordinates of the substituted atom relative to the center
of mass of the normal molecule.

Kraitchman (13) has shown that in the case of an asymmetric molecule
the relationships are easily developed from the principal second moments

of inertia which are defined as:

(2-17)

16
with the remaining terms obtained by cyclic permutation of x, y and 2.

In the substituted molecule these moments become:

1 _ 2
Pxx PX + “x

(2-18)

nyI = ny etC

where u = MAm/(M+Am), M is the mass of the normal molecule, and Am is
the change in mass due to substitution. These new second moments are now

the elements of an inertial tensor:

 

Px + ux2 uxy uxz
Py + L,x2 uyZ (2-19)
2
PZ + uz

 

It is known that definite relationships exist between the coefficients

of a cubic equation and its roots. For example, if Px', P ' and P2' are

y
the roots of a cubic equation in P', then:

l3_ |2+ '- =
P (PX +Py +Pz )P (PxPy+PyPZ+PZPX)P PX Py P2 0

If the secular equation of Eq. (2-19) is expanded and the corresponding
coefficients are equated to those in the above expression, three equations

in x2, y2 and 22 may be obtained. Solution of these equations yields,

|x| =r123myu1y) Mtg-1,) - (lg-1,11

(11—1)-(1'-1)+(1'-1)
XU + x x milfi Z Z 1 (2-20)

 

I l I /2
(IX -1x) + (Ix -Iy) - (I2 -1) 1

Z
XE] + NIX-127 J}

 

17
where Eq. (2-17) have been used to put the expression into the form
involving the principal moments of inertia. Expressions for y and z are
obtained by cyclic permutation of the subscripts. Thus, in principal,
to obtain a complete molecular structure one needs only to make an isotopic
substitution at each atomic position and employ Eq. (2-20) to determine
the atomic coordinates relative to the center of mass of the original
molecule.

In some cases it may be impractical or impossible (synthesis very
difficult or no stable isotope available) to substitute isotopically at
each position. In such cases the nine independent moment equations, i.e.,
the three principal moments of inertia, three products of inertia, and the
three center of mass equations, may be used to calculate the coordinates
for three atoms (14). Thus for a general asymmetric rotor of N atoms only
N-3 atoms must be isotOpically substituted. If the molecule has some
symmetry, such as a plane of symmetry, fewer substitutions will be required
since the symmetrically related atoms form a redundant set. This is the
case for methoxydifluorophosphine where only three substitutions are

required to determine the positions of eight atoms.

III. EXPERIMENTAL

3.1 Introduction

Molecular Rotational Resonance Spectroscopy shares many of the
general characteristics usually associated with other forms of spectroscopy.
A klystron or backward wave oscillator (BWO) serves as a source of
microwave radiation which passes through an absorption cell, usually
constructed of brass X-band waveguide, containing the sample. The
signal is monitored by a crystal diode detector and amplified by a tuned
preamplifier-phase sensitive detector combination. The resulting amplified
signal is then displayed either by an oscilloscope trace or strip chart
recorder. A simplified block diagram of a typical MRR spectrometer is
shown in Figure I.

The MRR spectrometers on which this work was done are typical
Hughes-Wilson (5) stark modulated Spectrometers of 33 1/3, 90 and 100 kHz(])
modulation frequencies. The 33 1/3 kHz instrument is a Hewlett-Packard
model 8460 A R-band spectrometer (26,500 to 40,000 MHz) while the others
are of conventional design. The characteristics and operation of these
spectrometers have been presented elsewhere (34-37), therefore only a
brief description of the major components which differ from typical

spectrometers and experimental conditions will be discussed here.

 

(1) 1 Hz = 1 sec-l; 1 kHz = lO3Hz; 1 MHz = 1o5Hz; 1 GHz = 109Hz

18

19

.cmumsoguomam mm: pageaxu a mo Eagmmwc xqum .F «gnaw;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

cm>vmumm
ovumm
nmumgnepmu ,
concoumx . . ,m x .
pause mwx< > maoomoFFAUmo P < apaaam
awgam *1 _ Emmm Peso x Lmzom ozm
- asmmgm cmpm_Fas< m>m3
cap ~I¥ cop :7 xqu Nzx memacm Nzx gouacmcw
Lo om cop co om . cop Lo om .coppucau
3 .1. 1 8
= _ = L m
co F. FE

 

 

 

Ppmu mFQEmm teem x

qumxgo L we

amaczou cmppqpppzz xucmzamc

swame u_:oguom_m zucoawmsw m
saaum> NI: m zococuwz

1 *

 

 

 

 

.

il In... a

 

 

20

3.2 Radiation Sources

While klystrons have been the microwave sources of choice in the
past, recent advances in Backward Wave Oscillators (BWO's) coupled with a
decreasing initial investment have made them extremely attractive.
Klystrons require simultaneous adjustment of the reflector voltage
and resonant cavity size to maintain optimum operating conditions while
tuning the oscillation frequency. It is this feature which makes recording
a spectrum with a klystron tedious. However, the frequency of a BWO is
dependent only on the voltage applied to the helix of the tube. Thus,
varying the helix voltage provides a very convenient means of sweeping
the frequency. At Michigan State University the BWO frequency is varied
by adding a small amplitude, low frequency sawtooth or triangular wave to
a constant helix voltage. A Wavetek model 112578 function generator
supplies the variable voltage and at its maximum output of 30 volts provides

150 to 750 MHz sweep widths, depending on the frequency of the BWO.

3.3 Spectral Display

 

Spectra may be displayed either on a strip chart recording or an
oscilloscope. The latter is usually used in these laboratories. However,
recording the Spectra is more desirable when greater sensitivity or higher
resolution are required. The Hewlett-Packard spectrometer is designed for
recording tracing only.

All the frequency and Stark effect measurements for vinylcyclopropane
and methyldifluoro-phosphine were made using oscilloscope display with the
exception of the 13C (in natural abundance) measurements in vinylcyclo-
propane and the intensity measurements in methyldifluorophosphine. All
the measurements on methyldifluorophosphine were made with the Hewlett-

Packard spectrometer and recorder diSplay.

T N I ll 11 ill. '1 I: III Ill!
lll-ll'llll'cll’..ll|ll N

 

fil‘...’ .. (.u

 

 

lilii‘l

21

3.4 Sample Pressure and Temperature

Sample pressures are normally monitored using a RCA 1946 thermocouple
tube. This method does not provide absolute pressure measurements but does
provide a means for approximately reproducing the sample pressure from
experiment to experiment. A Baratron type 77 vacuum gauge equipped with
a 1 mm Hg pressure head is available for absolute pressure measurements
when required.

Measurements with the Baratron gauge indicate that the studies on
vinylcyclopropane were done in the 15-25 micron range, methyldifluorOphosphine
in the 8-15 micron range and methoxydifluorOphosphine in 40-80 micron range.

Sample temperatures are normally maintained at -78°C by packing
dry ice around the sample cell. Should the sample vapor pressure be too
low at this temperature a refrigeration unit is available which is capable
of maintaining temperatures from room temperature to -15°C.

All Spectral measurements in this study were made at -78°C unless

otherwise noted.

3.5 Frequency Measurements

 

Rotational transition frequency measurements were made in a
conventional manner (34) with an absolute accuracy of :,05 MHz. The
local oscillator to which the experimental frequencies are referenced is
a 1 MHz quartz crystal controlled oscillator.(1) This oscillator is
periodically compared to one of the carrier frequencies of the National

Bureau of Standards Radio Station WWV.

 

(1) Manson Laboratories RD-l40A.

22

Although strip chart recording is a common means of displaying a
spectrum, placing accurate frequency markers on the recording has been a
persistent problem. In this laboratory a Hewlett-Packard electronic
counter, model 5245L, equipped with a Hewlett-Packard transfer oscillator,
model 5257A, is available. This combination provides direct and continuous
frequency measurements from 8,000 to 18,000 MHz. The counter is equipped
with an output which provides a binary representation of each digit of the
displayed frequency measurement. A binary decoder was designed by the
author and constructed in the Chemistry Department Electronics Shop.
The decoder monitors the binary frequency representation and provides a
voltage pulse to drive an events marker on the recorder each time the
binary representation meets certain preset conditions, e.g., at preset
frequency intervals. By this means frequency markers are available in
intervals varying 2 kHz to 1 GHz. For most recording purposes intervals
of l, 2, 5 and 10 MHz are sufficient. A complete description of the
decoder is given in Appendix I.

The Hewlett—Packard spectrometer automatically provides frequency markers

on the spectral recordings at a selected interval from 1 kHz to 10 MHz.

 

.
an ‘1

 

 

 

IV. MOLECULAR ROTATIONAL RESONANCE SPECTRUM OF TRANS-
VINYLCYCLOPROPANE

4.1 Introduction

 

In the past several years rotational resonance studies of several
cyclopropyl derivatives have been undertaken in these laboratories.
Results of studies of cyclopropanecarboxaldehyde and cyclopropanecarboxylic
acid fluoride were recently reported by Volltrauer and Schwendeman (38,39).
The torsional potential constants were evaluated for both molecules and
discussed in terms of being the net result of electronic effects of the
orbitals of the axial atoms and steric effects of the nonbonded atoms.
Another study, by Lee (40) on methyl cycloprOpylketone, has just been
completed. Unfortunately, in this case only the cis configuration (oxygen
cis to the ring) could be assigned and therefore the torsional potential
function could not be completely evaluated. A study of vinylcyclopropane
was undertaken because it appeared that this compound would be an
excellent example from which to obtain additional information concerning
the theoretical interpretation of torsional potential constants in
cyclopropyl compounds.

[Uttke and de Meijere (41) have reported results of NMR studies which
indicate that vinylcyclopropane exists in two configurations: a cis

form (6 = 0°, the vinyl group cis to the ring) and a trans form (a = 180°).
X
Variable temperature studies of the equilibrium coefficient, K = 75¥Efl§-,
ClS
indicate that the trans form should be energetically favored by

23

24
1.1 :_O.2 kcal/mole. In a more recent electron diffraction study EUTtke
and de Meijere (42) report that at 20°C vinylcyclopropane consists of
trans and gauche (e = 60-70°) comformers in a 3:1 ratio with the trans
form being more stable by 1.1 :_O.2 kcal/mole.

The spectrum of vinylcyclopropane is rather sparse, and transitions
in molecules in the ground and first three excited torsional states of the
trans configuration were definitely assigned. However, an exhaustive
search failed to disclose any transitions assignable to the cis or any
other configuration. The dipole moment of the trans configuration was
determined.

The sample of vinylcyclopropane was obtained from Chemical Samples

Company, Columbus, Ohio, and was used without further purification.

4.2 The Rotational Constants

 

The first approximation to the principal moments of inertia and the
corresponding rotational constants were calculated assuming the molecular
parameters given in Table 2. The calculations were facilitated by the
computer program STRUCT which had been written by Dr. R. H. Schwendeman.
This program locates the molecular center of mass and then diagonalizes the
resulting inertial tensor. The diagonalization transforms the initial
axis system into the principal axis system. In addition, STRUCT calculates
the atomic coordinates in the principal axis system. The results of this
calculation for trans-vinylcyclopropane are given in Table 3 and the
projection of the molecule on the molecular symmetry plane, the a-c
inertial plane, is shown in Figure II. Since the b axis is perpendicular
to the molecular plane of symmetry, the b component of the dipole moment,
“b’ will be zero; therefore, only a and c-type transitions should be

deserved. The calculated rotational constants also indicate that this

25

Table 2. Assumed Molecular Parameters for Trans-Vinylcyclopropane.

 

 

r(CH) = 1.08 A < (0105010) = 125°
r(CC) = 1.52 A < (H12C10H13) = 117°
r(C5H]0) = 1.34 A < (H6C2H7) = 116°
r(C]H5) = 1.50 A < (H11C5C10) = 121°

 

26

Table 3. The Atomic Coordinatesaand Rotational Constants of Trans-
Vinylcyclopropane in the Principal Axis System Using the Assumed

Parameters of Table 2.

 

 

 

Atom a b c
C] -0.244 0.000 -0.442
C2 -l.453 0.760 0.078
C3 -l.453 -0.760 0.078
05 0.989 0.000 0.412
C10 2.215 . 0.000 -0.128
H4 -0.078 0.000 -l.519
H6 -l.352 1.260 1.041
H7 -2.083 1.260 -O.656
H8 -l.352 -l.260 1.041
H9 -2.083 -1.260 -O.656
H1] 0.844 0.000 1.482
H12 3.103 0.000 0.486
H13 2.360 0.000 -l.l98

A = 14936. MHz

B = 3043. MHz

C = 2926. MHz

 

a Coordinates are in Angstroms.

 

 

1 ’ {i
a I!

[till-if}

 

27

 

C
H11
C5 /H‘2
0
C10
H
13
1A A

 

 

 

Figure 11. The projection of trans-vinylcyclopropane onto the molecular

symmetry plane.

28
conformation is a near prolate symmetric t0p (8 approximately equals C
and both are much smaller than A). Thus, the a-type transitions should
appear in closely spaced groups approximately separated by (B + C).

The preliminary rotational constants were used to calculate rotational
energy levels and transition frequencies. These calculations were
performed by the computer program EIGVALS which was written by Hand and
Schwendeman (43).

With only rotational constants, quadrupole coupling constants and
dipole moments as input data the EIGVALS program calculates the rotational
energy eigenvalues, quadrupole coupling energies, transition frequencies,
line strengths and Stark effect coefficients for a rigid asymmetric rotor.

The Hamiltonian matrix elements are generated from the appropriate
Wang symmetric rotor basis functions (depending upon whether the molecule
is a near oblate or prolate top). The energy matrix is then diagonalized
by a continued fraction method to yield the rotational energy level
eigenvalues which in conjunction with the appropriate selection rules
result in the transition frequencies. The matrices of the coefficients
of the diagonalizing transformation (T matrices) are also generated and
stored.

The line strength for each transition is calculated by transforming
the appropriate direction cosine matrix elements (33,44) to the proper
asymmetric rotor representation using the previously determined
T matrices. The resulting line strengths are then used to calculate
transition intensities which are very useful in assigning the Spectrum.

The Stark effect coefficients are calculated by second—order
perturbation theory from the line strengths and energy levels. The

coefficients are further multiplied by the appr0priate squared dipole

29
moment components and by a factor which insures that the resulting
coefficients have units of Hz (volt/cm)'2. These coefficients are then
used to predict the Stark effect for any transition, which is extremely
useful for spectral assignments.

A search of the spectral regions predicted by EIGVALS disclosed
groups of transitions which were approximately separated by B + C as
expected for a-type transitions. Since each group involved transitions
whose J quantum numbers had increased by one - i.e., the first group
would be J = 1-2, the second J = 2-3, etc. - the gross assignment of the
spectrum was straightforward. Individual transitions within a group were
assigned to the pr0per rotational quantum numbers by making use of the
relative position of each transition in the group, the relative intensities
of each and the Stark effects.

Although the preliminary calculations indicated that the spectrum
should consist of a and c-type transitions for the trans configuration,
only a-type transitions were observed. The observed and calculated
frequencies of the assigned transitions are compared in Table 4. Because
trans-vinylcyclOprOprane is a near prolate symmetric t0p the frequencies
of the a-type R-branch transitions which were assigned are only slightly
dependent on the A rotational constant. This makes an accurate determination
of A from these frequencies impossible. However, the observation and
subsequent analysis of a peculiar Stark effect for the |M| = 1 component
of the 202-303 transition made a somewhat more accurate determination of
the A rotational constant possible. The analysis of this Stark effect
will be discussed below.

The low J transitions, J = l + 2 and J = 2 + 3, were used in a least
squares analysis to determine the rotational constants and moments of

inertia which are given in Table 5. The final rotational constants are

3O

A~¢.mvoo.mm_om Amw.mvmm.n—Fom

A~_.mvmo.nmoom

Anm.mvmm.mmmm~

momrcow

 

Amm.mvao.~_oem _me-omm

Am~.mv_m.m_oem NNA-FNM

Aeo.~vom.oeoem Amm.ov_o.o_oem mNA-N~m

Aem.mvom.memem m_e-~_m

AFN.OVSm.OAmmm Amo.mvmm.moam~ S_A-m_m
AmN.PvSm.mmOSN Aeo.~voo.mooem Ao¢-mom

Aoo.avam.ammap mam-N_N

Ame.evma.eoomp mom-~om

Amm.mv_e.mmpmfi Amm.mvem.mm_mp __N-o__

Apm.mvoe.mome_ ASA.mVAA.mmm__ ~_N-___

Aom.mvmm.mmom_ A_e.evee.eoom_ Nom-_o,

m u> N u > F u > o u > cowgwmcmcp

 

 

.mcmaocqopuzu_»c*>umcmch mo magnum chowmcoh

umpwuxu moczh “mew; vac uczocw on» com ammwucmzcwga mumpm_:upmu ecu uo>cmmno mo comwcmasou .e wpnmp

1

3

.~12 menu mam mmwucmacwee umezmmmz.~:z :A a

.mwmmgucmema cw mam mmwucmzcmee umgmpau_mu mo mpwmwu omega ummA a

 

AmA.Ava.mNNOm
Ame.AVAm.monm

AwA.~va.NAmmN

ANA.ovee.om_om
AAm.AvNA.Aonm
Amo.NVAN.NAAom
AAm.mVSm.mmAmN

Fm.m mo.mmoom

v
mo.mVSA.AAoom
V
o¢.evmm.¢mAmN

A
A
ANM.A mm.Ammom
A

Ame. m N_.mmoom

Amm. m AA.momom

V
A3 .smN.AAoom
v
ANA. myom.moumm

mmm--¢
Amm-mme
GFmIMFV
mpmuepv

 

:o_uwm:mgh

 

Anm=:_pcouv A AAQAA

32

 

 

 

Table 5. Rotational Constantsa and Principal Moments of Inertiab for
the Ground and First Three Excited Torsional States of
Trans-Vinylcyclopropane,

v = 0 v = 1 v = 2 v = 3

A 15050.

8 3061.41 3071.43 3081.38 3091.22

C 2941.34 2944.02 2946.70 2949.27

Ia 33.57980

Ib 165.07932 164.54092 164.00973 163.48734

I 171.81818 171.66157 171.50585 171.35618

 

a In MHz. Uncertainties are as follows: A, :15 MHz; 8, :0.05 MHz;
C, :0.05 MHz.
b In u AZ. Assumed conversion factor of 505376.(u -A2)(MHz).

33
quite close to those predicted by STRUCT (see Table 3) which supports
the premise that the assigned transitions are due to the trans-configuration
of vinylcyclopropane.

A search for vibrationally excited states revealed that each
transition is followed at higher frequency by a series of approximately
equally spaced, progressively weaker transitions which exhibit Stark
effects which are identical with the main transition. The intensities
of these transitions decrease by a factor of approximately 2.5 between
successive excited states which indicates a vibrational excitation
energy of approximately 125 cm']. Presumably the only vibration present
in vinylcyclOprOpane having this low an excitation energy is the out-of-
plane torsion of the vinyl group about the carbon-carbon bond. A
comparable value of 100 cm'1 has been obtained by Volltrauer (45) for
cyclopropanecarboxaldehyde. Although as many as five excited states were
observed, frequencies were measured for only the first three states because
of the rapid decrease in intensity. The assigned transitions along with
the observed frequencies are given in Table 4, and the derived rotational
constants and principal moments of inertia are given in Table 5. The
linear plot of the rotational constants y§:v, as shown in Figure III,
provides evidence that the potential function hindering the torsional
motion is essentially harmonic.

An extensive search for transitions which could be assigned to the
cis or to some gauche configuration proved unsuccessful. All unassigned
transitions in the spectrum are at least a factor of ten lower in
intensity than transitions assigned to the trans configuration. There
are three possible explanations for this result. First, the molecular
population of any other configuration may be very small; second, the
dipole moment of any other configuration may be very small, and third,

some combination of these.

 

Figure III.

34

I
q-
q

Plots of differences between rotational constants of trans-
vinylcycloprOpane in the vth torsional state and the ground
vibrational state as a function of v. The vertical scale

is marked in units of 5 MHz.

35

The search for a second configuration did disclose transitions
which were assigned to a naturally occurring molecular species having
130 substituted at one of the ring positions C2 or C3. Since these
positions are equivalent, the intensity of the transitions was twice
that of transitions resulting from other 13C species. The assigned
transitions and their measured frequencies are given in Table 6 and the
derived rotational constants are given in Table 7. No attempt was made
to assign transitions belonging to other 13C species since they were
predicted to occur in regions having a high density of normal species

transitions.

4.3 Dipole Moment

 

The molecular dipole moment may be calculated from Eq. (2-16)
provided that the displacements, Av, of the Stark components from the
zero-field transition can be measured as a function of the applied
electric field e. The coefficients AJ and BJ were calculated by EIGVALS
as mentioned previously.

Values of Av :3, K were determined for the M = 0 components of the three
J = l + 2 transitions and the M = 0 component of the 202-303 transition.
The slopes, 30/852, were used with Eq. (2-16) to calculate the three
components of the dipole moment by a least squares analysis. As
expected, the out of plane component, “b’ was zero within experimental

error. The p and DC components were then recalculated with “h set

a
equal to zero with the result that their values were not significantly
changed from the previous calculation. The resulting values of pa, “c
and “T(“T2 = uaz + ucz) are given in Table 8 along with a comparison of
the experimental and calculated values of the slope. Table 9 shows a

comparison of reported dipole moments for some related hydrocarbons.

36
Table 6. Comparison of Observed and Calculateda Frequenciesb for a

13C Species of Trans-VinylcyclOprOpane.

 

 

 

Transition Frequency

303.404 23666.5(6.58)
312.413 23927.0(6.89)
404.505 29575.7(5.83)
414.515 29275.9(5.74)
413-514 29906.8(6.73)
423.524 29593.1(3.36)

 

a Last three digits of calculated frequencies are in parenthesis.

b In MHz. Measured frequencies are :0.15 MHz.

Table 7. Rotational Constantsa and Principal Moments of Inertiab for the

13C species of Trans-Vinylcyclopropane.

 

 

A 15050.

8 3022.66

C 2896.45

Ia 33.57980
Ib 167.19555
Ic 174.48141

 

a In MHz. Uncertainties are as follows: A, :15 MHz; 8, :,1 MHz;
C, :,l MHz.
b In U°A2. Assumed conversion factor of 505376.(U'A2)(MH2)

37

Table 8. The Stark Effect and Dipole Moment of Trans-Vinylcyclopropane.

 

 

 

Transition lMl EXEP’b 2252
38 obs 35 calc

111-212 0 5.64 5.82
101-202 0 -10.21 -10.13
‘10'211 0 2.34 2.25
202-303 0 2.17 2.14

A, = 0.486:0.007 0

,b = 0.0 0

DC = 0.110:0.003 0

0T = 0.498:0.007 0

 

a Hz/(volt/cm)2 assuming ”ocs = 0.7152 0.

b Uncertainty in observed slopes is :_l.0%.

38

Table 9. Comparison of Dipole Moments of some Related Hydrocarbons.

 

 

 

Compound uTa Ref.
Propylene 0.364 ’ 46
Isobutene 0.503 47
Methyl-allene 0.401 48
ISOprene 0.25 49
trans-Vinylcyclopropane 0.498 this work

 

a The total dipole moment in Debyes.

 

39
Since the intensities of MRR transitions are directly proportional
to the square of the dipole moment components the ratio of uaziucz of
19.5 offers an explanation for the failure to observe c-type transitions.
This ratio indicates the c-type transitions would only be 5% as intense
as the a-type transitions. As mentioned previously, the strongest

unassigned transitions are at least a factor of ten weaker than the

a-type transitions.

4.4 The Anomalous Stark Effect of the |M| = 1 Component of the 202-303

 

Transition

 

As was discussed in Chapter II, the Stark effect in an asymmetric
rotor normally possesses a quadratic dependence on the electric field e
and may be treated by second order perturbation theory. However, when
one or more of the energy differences in the denominator of Eq. (2-15)
becomes small, the necessary conditions for a second order perturbation
treatment are no longer met and a direct calculation is required. This
situation commonly exists for near symmetric t0ps because the energy
difference between asymmetry doublets is small.(]) In the present case
a third energy level, the 202 level, is near both the 110 and 1]] levels
and for |M| = l a perturbation connection exists between the 202 and the
110, 1]] levels. Although there is no direct connection between the 202
and 1]] levels,(2) the 202 level is perturbed by its proximity to the
110 and 1]] levels. If the dipole moment components in Table 8, which

were obtained using M components exhibiting normal quadratic Stark

 

1. For a near symmetric prolate top the asymmetry doublets consist of
the pairs of energy levels having near maximum and equal values for
K_1 and having values of K+] differing by l, i.e., the pair of
energy levels 110 and 1]].

2. This is a b-type connection and since pb is zero it is not allowed.

40
effects, and the rotational constants which were obtained from fitting
the spectra are assumed, the second-order perturbation theory calculation
in EIGVALS predicts that at 1 kV electrical potential the [MI = 1
component of the 202-303 transition should be displaced to higher
frequency by 0.5 MHz. The actual displacement is approximately 6 MHz.
Furthermore, a plot of Av pg, e2 for this component shows an upward
curvature; i.e., av/ae2 increases with increasing 8.

Since the dipole moment components are accurately known, the origin
of the discrepancy in the |M| = 1 component of the 202-303 transition
must lie in the value of the A rotational constant. Calculation of the
Stark shift of this transition by direct diagonalization of the entire
energy matrix for a variety of values of A gave good agreement with
experiment for a range of values of A between two distinct values. The
upper bound occurs as A is increased to approximately 15066.MHz where the
energy of the 202 level becomes less than that of the 1]] level.(]) This
causes a change in sign of the Stark contribution from the 202-111
connection which results in a change in Sign of the calculated displacement.
The lower bound results when A is decreased to approximately l4946.MHz
where the energy of the 202 level becomes greater than that of the 110
level. This results in a sign change of this connection and an abrupt
increase of more than two orders of magnitude in the calculated lepe.

The region of best agreement occurs at A = 15050.:_ 15. MHz.
4.5 Discussion of Results

There are three important results of this study. First, the

configuration with the vinyl group trans to the ring is confirmed to

 

1. The energy of the 1 and l 1 levels, given by A + C and A + B
respectively, depenAostrongly on A. By contrast the energy of the
202 level is essentially independent of A.

41
be the major species present. The evidence supporting this is as follows:
the ub component of the dipole moment is zero within experimental error,
and the experimental rotation constants are in excellent agreement with
those calculated assuming a trans configuration. This result is not
surprising in view of the fact that there is a close approach of hydrogen
atoms in either the gauche or the cis configuration. Also, in the cis
configuration CH bonds would eclipse one another across the C1C5 bond.
However, previous results on cyclopropylcarboxaldehyde, cyclopropane
carboxylic acid fluoride, cyclopropyl methyl ketone, and cyclopropane
carboxylic acid chloride show that eclipsed CH bonds across a bond to
the cyclopropyl ring are by no means unusual. This geometry has been
rationalized previously as being due to the apparent ability of the
cyclopropane ring to conjugate with attached n-bond systems.

The second result concerns information about the nature of the
torsional potential about the CC bond joining the vinyl group to the
ring. Unfortunately it was not possible to assign transitions to a
second species. Thus, the conclusion of Lfittke and de Meijere that
the second species is a gauche conformer whose population is one-third
that of the trans species at 20°C (AG = 1.1 kcal/mole) could not be
confirmed.

Also, the kind of analysis performed by Volltrauer and Schwendeman
could not be carried out. The apparent absence of spectra due to a
second species may be rationalized on one or more of the following
grounds: (1) the population may be less than the 12% at -78°C
predicted by the LDttke-de Meijere value of AG, i.e., the Lfittke-de Meijere
AG may be too small; (2) the dipole moment of the second species may be
considerably smaller than that of the trans species thereby making the
intensity ratio considerably smaller'than the population ratio; or (3)

there may be a severe vibration-rotation interaction in the second

42
species which could make it very difficult to assign the transitions.
However, even without a second species the fact that transitions in
five excited states of the torsional motion have been observed and that
the frequencies of the transitions vary linearly with the vibrational quantum
number restricts the shape of the potential function and also implies that
the barrier to conversion to a second Species must be of the order of
3 kcal/mole or higher.

The third result of this study is the value of the dipole moment
shown in Table 8. Comparison of this value with those of other
hydrocarbons (Table 9) shows that the dipole moment of trans-vinylcyclo-
propane is unusually high. The well-known comparison of a cyclopropane
ring to a vinyl group would suggest that there would be considerable
cancellation of dipole moment contributions in this molecule and that

the dipole moment would be unusually small rather than so large.

V. MOLECULAR ROTATIONAL RESONANCE SPECTRUM 0F METHYLDIFLUOROPHOSPHINE

5.1 Introduction

 

A study of methyldifluorophosphine was undertaken as a result of
the recent interest expressed in difluorophosphine derivatives in these
laboratories and elsewhere (50-54). Determination of the barrier to
internal rotation would provide an interesting comparison to the
reported values for methylphosphine (55), methylamine (56), methyldifluoro-
amine (57), and methyldifluoroarsine (58) of 1959, 1980, 4170 and 1325
cal/mole, respectively. The barrier for methyldifluoroamine has been
discussed by Pierce, gt_gl, (57) in terms of the CXF or CXH angle. The
marked decrease in the barrier for methyldifluoroarsine is almost
certainly due to steric interactions since structural calculations
using the reported molecular parameters indicate the H-F distance is
less than the sum of the Van der Waals radii.

Any forthcoming structural information could be compared to the
reported P-C bond lengths for methylphosphine (55) and cyanodifluoro-
phOSphine (52) and the FPF and CPF angles to those reported in (50-54).

The sample of methyldifluorophosphine was obtained from Dr. K. Cohn
and was used without further purification. The rotational spectrum was

observed at both room and Dry Ice temperatures.
5.2 Rotational Constants

The preliminary principal moments of inertia and rotational

constants were calculated from the assumed molecular parameters given
43

44
in Table 10. The resulting atomic coordinates in the principal axis
system and rotational constants are given in Table 11. The projection
of the molecule onto the molecular plane of symmetry (the a-c inertial
plane) is shown in Figure IV. Since the b axis is perpendicular to the
plane of symmetry, the b component of the dipole moment, ob, should
be zero; therefore only a and c-type transitions should be observed.
The preliminary rotational constants indicate that methyldifluorophosphine
is a near oblate symmetric top (A approximately equals 8 and both are
larger than C). The rotational constants were used with the computer
program EIGVALS to calculate approximate rotational energy levels and
transition frequencies, as previously described.

An initial search in the predicted spectral regions discloSed the
000-101 and 111-212 transitions which were identified by their characteristic
Stark effect. Since the frequencies of these transitions are given by
the expressions (B + C) and (B + 3C), reSpectively, the B and C rotational
constants could be determined. Observation of the 110-211 transition,
whose frequency is given by (38 + C), confirmed this partial assignment.
The assignment was completed by the observation of the 101-202 and 101-220
transitions which depend strongly on the value of the A rotational
constant. The assignment was confirmed by the observation of two R-branch,
a-type J = 2 - 3 transitions and several Q-branch a-type transitions.

The Q-branch transition frequencies are given by (59) as,
v = 1/2(A-C)AE(K)

where E(K) is a dimensionless parameter called the reduced energy and
AE(K) is the difference between the values of E(K) for the upper and
lower energy states. The reduced energy E(K) is a function of the

asymmetry parameter K defined by K = (28-A-C)/(A-C) and has been

45

Table 10. Assumed Molecular Parameters for MethyldifluorOphoSphine.

 

 

r(PF) 1.57 A <(FPF) 97°
r(PC) 1.84 <(FPC) 101°
rTCH) 1.093 <(PCH) 109°

 

Table 11. Atomic Coordinates and Rotational Constants of Methyl-

difluorophOSphine in the Principal Axis System.a

 

 

 

Atom a b c
P 0.025 A 0.000 A -0.523 A
F] 0.653 1.176 0.307
F2 0.653 -l.l76 0.307
c -1.636 0 000 0.269
H1 -1.525 0.000 1.356
H2 -2 189 0.891 -0.037
H3 -2.189 -0.891 -0.037

A = 7333. MHz

8 = 6730.

c = 4415.

 

a The molecular parameters in Table 10 were assumed.

46

 

 

 

 

 

C
”5
c 523 _
"T
1 \ 4,( a
H8,7 7
. 1A J ' P

Figure IV. Projection of methyldifluorophosphine onto the molecular
symmetry plane. The orientation of the dipole moment vector,

HT, is also shown.

47
extensively tabulated (60). Plots of V/AE(K) :3, K for the various
Q-branch transitions should all intersect at a common point, thereby
defining the correct values of l/2(A-C) and K. This method is very
useful in cases where either A or C is not well determined and Q-branch
transitions are observed. Plots for several members of the Q-branch
series JJ_2’3 + JJ_2’2 are shown in Figure V. The graphical value for
l/2(A-C) of 1395.5 MHz is in excellent agreement with the value of
1395.40 MHz obtained by least-squares fitting of the frequencies.

The assigned transitions and their observed frequencies are given
in Table 12. The rotational constants were determined by a least
squares analysis of the first seven transitions listed in Table 12 and
are given in Table 13.

A search for vibrationally excited states revealed that each R-branch
transition is accompanied at lower frequencies, and each Q-branch
transition is accompanied at higher frequencies, by a much weaker
transition which exhibits a Stark effect identical to that of the main
transition, as expected for vibrationally excited states. These transitions
were assigned to the first excited torsional state, v = l, of the
methyl group about the P-C bond. The assigned transitions and their
observed frequencies are given in Table 12 and the rotational constants
derived from the five R-branch transitions are given in Table 13.

Plots of v/AE(K) yg, K for the three Q-branch transitions are shown in
Figure VI and the graphical value of 1413.8 MHz for v/AE(K) agrees well
with the fitted value of 1413.87 MHz.

5.3 Molecular Structure

 

Since no isotopic species were studied for methyldifluorOphOSphine,

it is impossible to obtain the molecular structure unless assumptions

48

1420 .C
1410 «-
1400 -r

v/AE(K) T- 1395.5

 

 

1390 '1'” a
b1
c
1380 «-
d
1370 '-
.7562
: 4. T I e .
.752 .754 .756 .758 .760
K
Figure V. Plots of V/AE(K) gs, K for the a) 643-642, b) 753-752,

c) 863-852 and d) 973-972 Q-branch transitions of
methyldifluorophosphine.

49

b

Table 12. Comparison of Observed and Calculateda Frequencies for the Ground

and First Excited Torsional State of Methyldifluorophosphine.

 

 

 

Transition v = 0 v = 1
000-10] lll79.90(9.79)

101-202 20216.04(5.97) 20154.51(4.44)
101-220 30765.04(4.81)

111-212 l9908.95(8.87) l9839.7l(9.73)
‘10'211 24810.36(0.29) 24797.l7(7.l6)
212-313 28788.33(8.29) 28674.26(4.27)
211-312 34396.54(6.68) 34355.29(5.28)
221-322 33539.24(9.37)

202-22] 8405.39(5.40)

313-312 12960.52(0.53)

303-322 13125.39(5.50)

422-44] 10092.18(2.74)

413-432 l3223.01(3.60)

423-422 12733.52(3.92)

533-532 12317.97(8.70)

532-55] 11575.81(6.86)

634-633 18085.57(7.65)

643-642 ll680.69(l.74)

753- 52 10822.73(4.03) 10906.70(8.66)
863-862 9772.44(3.88) 9826.54(8.95)
973-972 8574.28(5.70) 8597.59(600.28)

 

a Last three digits of calculated frequencies are in parenthesis.

b In MHz. Measured frequencies are :0.05 MHz.

50

Table 13. Rotational Constantsa, Principal and Second Moments of

Inertiab for the Ground and First Excited Torsional State

of Methyldifluorophosphine.

 

 

 

v = 0 v = 1
A 7155.34 7167.99
8 6815.25 6818.96
0 4364.54 4340.25
Ia 70.6292 70.5045
Ib 74.1537 74.1133
Ic 115.7913 116.4392
Paa 59.6579 60.0240
Pbb 56.1334 56.4152
Pcc 14.4958 14.0893

 

a In MHz. Uncertainties are as follows:

C, :,05 MHz.

A, :,05 MHz; 8, :,05

b In U°A2. Assumed conversion factor of 505376-(u-A2)(MH2).

MHz;

1440

1430

1420

v/AE(K)

1410

1400

Figure VI.

51

 

 

~0-
F' 1413.8
0
b»
A. C‘
.7531
. . i l t t
.748 .750 .752 .754 .756
K
Plots of v/AE(K) yg, K for a) 753-752, b) 863'362 and

c) 973-972 of the first excited torsional state of
methyldifluorOphosphine.

52

are made concerning some of the molecular parameters. There is ample
evidence available to support the assumption that the geometry of a
methyl group is relatively insensitive to its environment and that
reasonable parameters for its geometry could be taken as; r(CH), 1.093 A
and <(PCH), 109.7°. If the PF bond length is also assumed, the remaining
molecular parameters, r(PC), <(FPF) and <(FPC), may be determined by

p

a fit of the rotational parameters Ma’ M Paa’ Pbb, and Pcc of

C’ ac’

the parent Species (Nb is the 9th center of mass condition defined as
M9 = gmigi = 0). However it was found, as shown in Table 14, that
the calculated PC bond length is quite sensitive to the assumed PF
bond length while the FPF and FPC angles are relatively insensitive.
Variation of the methyl geometry produces negligible change in the
calculated parameters.

Results of some recent structural studies on difluorOphosphine
derivatives are shown in Table 15. These results indicate that for
substituents which have chemical properties and electronegativities
similar to those of a methyl group a PF bond length of 1.580 to 1.586 A
is expected. Within this interval the calculated PC bond length is
approximately 1.82 A which lies between the reported values of 1.810 A
and 1.863 A for cyanodifluorophosphine and methylphosphine (55),

respectively.

5.4 The Barrier to Internal Rotation

 

As previously discussed in Section 2.3, if the potential barrier
hindering the internal rotation of the methyl group is low enough, the
rotational transitions may be split into doublets consisting of

transitions among A and E levels. This splitting is a result of the

53

 

 

 

Table l4. The PC Bond Lengtha, FPF and FPC Bond Anglesb as a Function
of the PF Bond Length in MethyldifluorOphosphine.

r(PF) r(PC) <(FPF) <(FPC)
1.574 1.842 99.1 97.3
1.576 1.838 98.9 97.4
1.578 1.834 98.8 97.5
1.580 1.829 98.6 97.6
1.582 1.825 98.4 97.8
1.584 1.820 98.3 97.9
1.586 1.816 98.1 97.9
1.588 1.812 97.9 98.1

Assuming: r(CH) = 1.093 3

(HCH) = 109.2°

 

a

In Angstroms.

 

 

 

b In degrees.

Table l5. Molecular Parameters for Some DifluorOphosphine Derivatives.
Molecule r(PF) <(FPF) <(FPX) REf-

PFZOCH3 l.586 K 95.3° 101.5° this work
PFZNHZ 1.585 K 94.7° 101.7° 50

PFZH l.582 K 99.0° 95.3° 54

PFZCl 1.571 K 97.3° 99.2° 51

PFZCN 1.557 K 99.1° 97.2° 52

 

54
coupling of the internal and overall angular momenta. The magnitude of
the splitting may be used to evaluate the barrier height.

Careful examination of the spectrum for methyldifluorophosphine
failed to disclose any splittings in either the ground or first excited
torsional states. Assuming that any splitting greater than 0.5 MHz
could be resolved, theoretical calculations were performed on the first
excited state in an attempt to establish a lower bound to the barrier.
Results of these calculations indicate that the barrier to internal
rotation in methyldifluorophosphine must be at least 3600 i 200 cal/mole.

The height of the potential barrier may also be determined from
the torsional excitation energy. If the excitation energy is large, the
potential function hindering the torsion will be essentially harmonic
and a, the torsional angle, will be small. With these assumptions the

expression for a threefold barrier may be written as;

- 2 2 2
V3 " 811 C VT Ir/g

where VT is the torsional excitation energy in cm'1 and Ir is the reduced

moment of interia of the internal rotor about its symmetry axis. Ir is

defined as (ll),
2

Ir = Ia[1-Ia;§g§J g = a, b, c

where Ag is the direction cosine between the 9th principal axis and

th

the symmetry axis of the internal rotor and I is the g principal

9
moment of inertia.

The value of u may be estimated from relative intensity data as;

T

= KT£n(Iv /I )

vT = 1 v = o

where the 1's are the relative intensities of the same rotational transitions

55

in the ground and first excited torsional states. The intensities were
measured at room temperature using the Hewlett-Packard model 8460 A
R-band spectrometer. Unfortunately, it proved impossible to locate any
ground state - first excited state pairs which were completely free from
interference due to overlapping transitions or Stark lobes from adjacent
transitions. However, the results of twenty-one measurements on the

-3 transitions (the most satisfactory pair) gives an average value

2
11 12 r
of 318 :_30 cm" for the excitation energy. To confirm this value an

1

'. . _"I- ("9

infrared spectrum was taken in the region 250-400 cm' ; the corresponding
absorption was observed at 325 :_15 cm']. Since this value must be 1

more reliable than the relative intensity value, it was used with the

771‘

 

above equation to calculate a value for the barrier height of 6.1 :_0.3 s
kcal/mole. The indicated uncertainty is greater than that resulting
from VT due to the uncertainty in Ir from the assumed structure.

Pierce, gt_al, (57) have discussed the large increase in the
barrier of CH3NF2 (4170 cal/mole) compared to CH3NH2 (1980 cal/mole)
in terms of the CNX angle. They point out that the CNF angle in CH3NF2
is some 7.4° smaller than the CNH angle in CH3NH2. Additional evidence is
supplied by the comparison of CH3SH (1270 cal/mole) with CH30H
(1070 cal/mole) where the CSH angle is 6.5° smaller than the COH angle.
Indeed, it does seem intuitively reasonable to expect the barrier to
increase as this angle decreases. However, comparisons of CH30H to
CH30Cl (3060 cal/mole), where the COC1 angle is 7° larger than the COH
angle, and CH PF to CH PHZ’ where the CPX angles are essentially equal,

3 2 3
serve to point out that such simple approaches are not entirely reliable.

56

5.5 Dipole Moment

Displacements of the Stark components as a function of the electric
field were determined for the M = 0 components of the J = 0 + l and the
three J = 1 + 2 transitions. The resulting slopes, ii?) were used with
Eq. (2-16) to calculate the three dipole moment components. As expected,
the b component, “b’ was zero within experimental error. With “b set.equa1 to
zero the a and c components were then recalculated. The observed and FM”
calculated slopes along with the resulting dipole moment components :
and total dipole moment are given in Table 16. The total dipole

moment was found to make an angle of 5.5 :_0.1° with the a-axis. Although L

 

the sign of this angle and the dipole moment itself are not determined
by the data, the orientation is most likely that shown in Figure IV.
A comparison of the reported dipole moments for some difluorophosphine

derivatives is given in Table 17.

5.6 The Anomalous Stark Effect of the |M| = 1 Component of the 101-202

 

Transition

 

As previously discussed, when one or more of the energy differences
in the denominator of Eq. (2-15) becomes small, the necessary conditions
for a second order perturbation treatment are no longer met and a
direct calculation is required.

In the present case the 202 and 212 levels are nearly degenerate
with the 212 being higher in energy by only 33 MHz. For |M| = 1 a
direct c-type connection exists between these levels resulting in a
strong perturbation of the Stark energies.

It should be noted that the |M| = 1 component of the 111-212

transition also exhibits an anomalous Stark effect; however, it is

57

Table 16. The Stark Effect and Dipole Moment of Methyldifluorophosphine.

 

 

 

. . a,b 2 a
Tran51t10n av/aez)obs av/ae )calc
000-101 M = 0 233.78 233.83
101-202 M = 0 60.88 ‘ 60.80
111-212 M = 0 -73.38 -73.26
110-211 M = 0 48.05 48.13

“a = 2.047f0.002 D
ub = 0.0 D
we = 0.194:0.03 0

HT = 2.055:o.03 D

.' C": . 5‘!“ -4- ‘ v'fi 3'51

 

 

a Hz/(volt/cm)2 assuming “0C5 = 0.7152 0.

b Uncertainty in observed slopes is :0.5%.

58

Table 17. Comparison of the Dipole Momentsa for Some Ph05phine and

Difluorophosphine Derivatives.

 

 

 

Compound “T Ref.
Methylphosphine 1.100 55
Difluorophosphine 1.32 54
CyanodifluorOphosphine 2.393 52
Aminodifluorophosphine 3.029 50
ChlorodifluorOphosphine 0.89 51
Methyldifluorophosphine 2.056 This study

 

a In Debyes.

 

59
somewhat less spectacular than that of the 101-202 transition illustrated
here.
The observed Stark effect is as follows: as the applied voltage
is increased the Stark component is displaced to lower frequency until
it reaches a maximum displacement of approximately -4.8 MHz at 375
volts. As the voltage is increased further, the component reverses

direction and begins to move back toward the zero-field line reaching

its original position at approximately 560 volts. Further increase of
the applied voltage displaces the component to higher frequency in a
nearly normal manner.

With the rotational constants from Table 13 and the dipole moment

 

1“"

components from Table 14 a direct calculation was performed by means of
the procedure outlined in Section 4.4. The observed and calculated
Stark effects are shown in Figure VII. The agreement is excellent, which

confirms the calculated values of the dipole moment components.
5.7 Discussion of Results

There are three important results of this study, the PC bond length,
the barrier to internal rotation of the methyl group, and the dipole
moment.

To determine the PC bond length from only three moments of inertia
it was necessary to make several assumptions. The values assumed for
the CH bond distance, PCH bond angle, and tilt of the methyl group all
had relatively slight effects on the remaining parameters. One more
assumption was necessary and the PF bond distance was selected. Recent
determination of PF bond distances in PFZX molecules demonstrates a
dependence of the PF distance on the electronegativity of the group X

(Table 15). Values for this distance near the value in PFZH were

60

N
l
1

m l 203 390 430 500 590
' Mth'# T

APPLIED VOLTAGE

 

I
N
J

r

1
w
J
t

 

 

Figure VII. Comparison of the observed (circles) and calculated (solid
line) Stark effect for the |M| = 1 component of the 101-202

transition.

_..-. 5,

 

 

 

 

61
selected and the remaining parameters were determined as described above
(Table 14). The best value of the PC bond distance appears to be near
1.82 A which is 0.04 A shorter than the value reported for CH3PH2. This
is a significant difference in an important bond length and should be
verified by studies of the 13C species in the molecules.
The barrier to internal rotation, 6.1 kcal/mole, determined here

from the torsional splittings is larger than the barrier in CH3NF2

“-
5.

(4.17 kcal/mole) and considerably larger than in CH3AsF2 (1.325 kcal/mole).
As mentioned above, the barrier height in CH3NF2 has been discussed by
Pierce gt_gl, (57) in terms of the CNF angle. A similar reasoning does

not seem valid here since the bond angles in CH3PF2 and CH3PH2 are

 

apparently quite similar. L?
The dipole moment in CH3PF2 (2.056 D) is considerably larger than

that in PFZH (1.32 0). Since the primary electronic effects of CH3

and H are usually considered to be comparable, this is further evidence

of some unusual electronic effect in CH3PF2.

VI. MOLECULAR ROTATIONAL RESONANCE SPECTRUM 0F METHOXYDIFLUOROPHOSPHINE

6.1 Introduction

 

The study of methoxydifluorophOSphine was undertaken as a result
of the recent interest in difluorophosphine derivatives as mentioned
above.

Methoxydifluorophosphine appeared to be an excellent example for
further investigation of the effects of (p-d)n bonding resulting from the
delocalization of the oxygen p-orbital lone pairs into the vacant
d-orbitals on phosphorus. Bonding of this type has been recently
postulated to account for the planarity of the -NH2 group in NHZPFZ.

To determine the structure of the molecule the MRR spectra of the parent
compound and three isotOpically labeled species were investigated. In
addition, it was expected that the structural data would provide
additional information regarding the relationship of the PFZ geometry to
the electronegativity of the substituent and also determine the molecular
configuration.

Because of the moderate barrier height characteristically associated
with internal rotation about a C-0 bond, as shown in Table 18, the
rotational transitions should be split into doublets due to coupling
with this motion. Analysis of the splittings would yield the height

of the potential barrier to internal rotation.

62

 

63

Table 18. Barriers to Internal Rotation of Methyl Groups About the

 

 

 

C-0 Bonds.

Compound Formula V3(cal/mole) Ref.
Methanol CH30H 1070. 62
Methyl formate CH3C00H 1190. 63
Methyl nitrate - CH30N02 2321. 64
Dimethyl ether (CH3)20 2720. 65

Ethylmethyl ether CZHSOCH3 2530. 66

 

64

6.2 Preparation of Samples

The normal and isotOpic species of methoxydifluorOphOSphine were

prepared in collaboration with Dr. C. E. Jones(1) by the following reactions:

CH30H + m3 + 0130202 + (CH30)2PC1 + HCl+ + m3

U011

standing CH30PC12

SbCl5
CH30PC12 + SbF3 -———+-CH30PF2

The experimental details are as follows:0.5 g (0.016 moles) of
methanol is added dropwise with stirring to 2.33 g (0.017 moles) of
phosphorus trichloride in a small round bottom flask. The reaction is
slightly exothermic and hydrogen chloride gas is evolved. A mixture of
products, consisting of methoxydichlorOphosphine and dimethoxychloro-
phosphine is initially formed; however, upon standing dimethoxychloro-
ph05phine further reacts with the excess phosphorus trichloride to give
a near quantitative yield of methoxydichlorOphosphine. This conversion
is conveniently monitored by periodically examining the proton NMR
spectrum which consists of two overlaping doublets. One doublet, due
to methoxydichlorophosphine, is centered at a chemical shift of 3.8 ppm
with a coupling constant, JP-H’ of 10 Hz. The other doublet, due to
dimethoxychlorophosphine, is centered at 3.7 ppm with a coupling constant
of 13 Hz. The reaction mixture is allowed to stand until the integrated
proton NMR spectrum indicated that the reaction was approximately
95% complete, which usually took 12-16 hours.

The methoxydichlorOphosphine sample is fluorinated by slowly

dropping it onto solid, finely ground antimony trifluoride which has been

 

1. Present address: University of Leeds, Leeds, England.

(5" ——

 

65

wetted by approximately 5% by weight of antimony pentachloride which
acts as a catalyst. The gaseous products are collected in a trap at
-78°C. The products are partially separated by trap-to-trap distillation
with traps at -78°C, -112°C and -196°C. The fraction collected at
~112°C is retained. Final purification is accomplished by low-temperature
co-distillation using helium as the carrier gas.

The isotopic species were prepared in the same manner starting with

50% 13CH30H, 40% CD30H. and 40% CH3‘30H.
6.2 Rotational Constants

Since the barrier to internal rotation of a methyl group about a

 

C-O bond is typically of moderate height (Table 18), the rotational
transitions were predicted to appear as doublets due to the internal
rotation splitting (see Section 2.3). If the barrier is not too low,
the A-level transitions should still closely approximate the rigid-rotor
model and, barring any accidental degeneracies, exhibit the normal
second order Stark effect. However, the E-levels may not fit the rigid-
rotor approximation since the internal rotation introduces terms
containing odd powers of the angular momenta. Furthermore, since the
E-levels are doubly degenerate (o = jj) the E-level transitions may
exhibit a first-order Stark effect and thus be readily discernible

from the A-levels.

After selecting representative molecular parameters from similar
compounds, the computer programs STRUCT and EIGVALS were used to
calculate the preliminary rotational constants, rotational energy levels
and transition frequencies. A plane of symmetry was assumed with the
carbon atom cis to the fluorine atoms, as shown in Figure VIII. The

calculations predicted that the molecule should be a near prolate top

66

with the b axis perpendicular to the molecular plane, and therefore
that a and c-type transitions should be observed.

Initial examination of the spectral regions predicted for the
J = 4-5 and J = 5-6 a-type transitions of the normal species and
analysis of the Stark effects of the prominent transitions in these
regions confirmed the presence of'A and E level doublets split by
internal rotation. The A-level, a-type J = 4+5 and J = 5+6 transitions
were assigned by their characteristic Stark effects and their positions
relative to one another. Only the two lowest energy J = 5+6 transitions
were observed; the remaining transitions occur at frequencies which are
higher than those presently attainable in these laboratories. Since
methoxydifluorophosphine is approximately a near prolate top the a-type
transitions are not strongly dependent upon the A rotational constant.
Therefore an effort was made to selectively assign those transitions with
the greatest dependence upon the A rotational constant rather than to
assign and measure the frequencies of all the available transitions.
The observed and calculated frequencies of the assigned transitions
for the A-levels of the normal species are given in Table 19. The
rotational constants, principal and second moments of inertia derived
from these frequencies are given in Table 21.

Initial values of the rotational constants for the isotopic
species were obtained by adding the difference between the STRUCT and
experimental rotational constants of the normal species to those calculated
by STRUCT for the isotopic species. These rotational constants were then
used with EIGVALS to calculate the approximate rotational energy levels
and transition frequencies. In this manner it was possible to predict
the experimental transition frequencies to within :15 MHz, thus making

assignment of the spectra quite straightforward. An effort was again

 

67

F-

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A_o.mvm~.mmmam 4mm-mmm

Ama.av~m.a_mmm m~e.¢~m

Amm.mvoo.~_e Apu.mvmo.mmoam Amo.mvom.¢~¢ Aoo.mvpe.o~mwm ooe-mom

Apm.mv_¢.mm~- Aom.ave~.me-m Awo.mvom.~m~- A_o.mvmm.emuam o_o-m_m

A-.mvsp.m_amm Ao~.~vmm.~mm+n m~m--+

, Am~.mvoe.~mp¢m Nam-Pme

Am~.avmo.om Amm.pvm¢._~wmm “mm.¢ve¢.+__ Amw.mv¢m.u-+m ¢~m-mpe

Amm.ov~m.owmmm e~m-m~¢

Amo.mvmo.oo¢ Aam.mvme.mmm.m Amm.evmo.m~¢ Amm.~v¢m.~em~m mom-eo¢

«mo.mvmm.mom- Acm.mvmo.mom_m Am~.ovm~.o.m- Aom.uvo_.ma-m m.m-¢_+

Aem.mvsm.m-- m.¢-~Fm

5.38583 Sign

Aea.mvmo.~¢ao~ Aeo.~vmm.~am- -¢-P~m

Am1<v>< nucosamcm Amu<v>< aucmauagu cowuwmcnch
Neaomzump

 

.«aaomxump can «use

«:8

so» mmcpuu_pam covuuuom .mcgmu:~ ucmnvowucmaaogm «noun—aupou van uw>gomno mo compgoasoo .m_ opamh

68

x
s
r.‘r.“.~§lll. 3%... .04..1n .. {.13. I n

P:

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.~:z :H n

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toe mmcwuu__qm cowpouoa chcmucH can nmowucmacmgd mumpmpaupmu new um>cmmao mo com_emneou .om apnoh

69

 

 

 

 

Table 21. A Level Rotational Constantsa, Principal and Second

Moments of Inertiab for the Normal and Three Isotopic

Species of Methoxydifluorophosphine.

CH30PF2 3CH30PF2 CH3180PF2 0030952
AA 5991.04 5973.28 5935.14 5718.40
BA 3641.81 3542.67 3566.40 3252.63
CA 3127.85 3058.98 3086.88 2894.59
Ia 84.35529 84.6062 85.1480 88.3771
Ib 138.77038 142.6538 141.7050 155.3745
Ic 161.77038 165.2107 163.7173 177.6618
Paa 107.99387 111.6292 110.1363 122.3296
Pbb 53.57878 53.5815 53.5811 55.3322
PCC 30.77651 31.0246 31.5687 33.0449
a In MHz. Uncertainties are as follows: A, 10.1 MHz; 3, 10.05 MHz;

C, :0.05 MHz.

b In u°A2. Assumed conversion factor of 505376.(u-A2)(MH2).

 

70
made to selectively assign and measure the frequencies of those
transitions having the greatest dependence on the A rotational constant.
The assigned transitions and observed frequencies for the isotopic
species are given in Tables 19 and 20, while the calculated values of
the rotational constants, principal and second moments of inertia are

given in Table 21.

6.4 Barrier to Internal Rotation 5+-

The low potential barrier hindering the internal rotation of the
methyl group resulted in large splittings between the A and E levels.

To account for these splittings terms to fourth order were included in

 

the calculation of the HVO matrix of Eq. (2-11),

4

= + (n) 11
Hv0 Hr Fnilwvo P

The matrix elements which are required for Hv0 have been given by
Herschbach (11). The resulting energy matrix, which factors into
blocks of order 2J + l for each J, was diagonalized; the eigenvalues
are the desired energy levels. The calculations were carried out using
a computer program, INROT, which was written for use on the Control
Data 6500 computer.

As mentioned previously, the transitions among E-levels exhibit
a first order Stark effect and thus are readily discernable from the
A-level transitions. A preliminary internal rotation calculation was
made using a barrier height of 1. kcal/mole to predict the frequencies
of the E transitions. Once this information was available the E
transitions were readily assigned. The assigned E level transitions
and the observed internal rotation splittings (VA-0E) for the normal and

three isotopic species are given in Tables 19 and 20.

I! l.I . ‘ lull

 

 

 

 

.L'ub‘1!
' I

71

The internal rotation parameters, the three-fold barrier height
(V3), the moment of inertia of the internal rotor about its symmetry
axis (Ia), and the angle between the symmetry axis of the internal
rotor and the a principal axis (6), were calculated by a least squares
fit of the A-E splittings. The molecule was assumed to have a plane of
symmetry such that the direction cosine, Ab, between the symmetry axis
of the internal rotor and the out-of-plane b axis was zero. It was

further assumed that the A-E splittings would vary linearly with the

---‘_qn-

various parameters qi as,

3A0.
6AVJ° = f(—‘laqi)5qi

 

The derivativesaAvj/aqi where evaluated numerically by changing the -5

I
j 5. If the

resulting values of the qi's fell outside the increments used to

qi's in small increments and noting the effect on the Av

evaluate the derivatives, the increments were readjusted and the entire
process repeated. Although the AVj's are also functions of the rotational
constants the derivatives with respect to the rotational constants

were found to be very small and therefore these terms were not included
in the least squares fit. The parameters were fit without constraints
to yield the best agreement to the observed splittings of the normal
species. Since 13C or 180 isot0pic substitution should not affect
either V3 or 10, these parameters were held constant and only 6 was

fit for these isot0pic species. Deuterium substitution on the methyl
rotor not only nearly doubles Ia due to the increase in mass but also
results in an effective shrinkage of the methyl rotor due to "zero
point" vibrational effects (66). Therefore it was necessary to include
all three parameters in the least squares fit for the CD3OPF2. The

results of these calculations for V3, 10 and 6 are given in Table 22.

 

 

 

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nu ompko. omemo. mmmem. momma. 5‘

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«.3 no..H mm.o «.3 No.o.u mp.m 5H

opos\_au .m.u .moe m_os\P~u .m.H .Nue m>
Neaomou Nuaompmzu mono 18m, Naaomzo

 

.mcenamogaogoapmwuzxogpmz mo mmvomqm ergonomfi mass» was Fmsgoz on» toe

mgmumEmgmg cowpmuom Pmcgmucm .NN m—nmp

73

The values of the barrier height calculated in this manner are near
the lower limit for which the perturbation treatment of Section 2.3 is
applicable. To test the validity of this treatment for the present
study a calculation was done using a low-barrier approximation in which
free-rotor wavefunctions formed the basis set for the torsion of
the methyl group (29,67). The results of this calculation agree with
those of the perturbation calculation to within the uncertainties of the
perturbation results. As a result, the perturbation treatment was used
in all subsequent calculations.

The A-level rotational constants in Table 21 contain a contribution

from internal rotation. They were obtained by a least squares fit to

 

a rigid-rotator Hamiltonian. To remove the internal rotation contribution
and calculate rotational constants, A0, B0, and Co, which are free of

the effects of this motion, the following procedure was employed:

the frequencies of the A transitions were computed using the INROT
program with approximate rotational constants, QINROT (Q = A, B, or C).
The computed frequencies were then fit by means of program EIGVALS to
obtain effective rotational constants, QEFF- The first approximation

to the rotational constants 00 was then obtained by the following

relation

Qo = QA + (QINROT'QEFF)'

The procedure was repeated until QEFF = 0A, and 00 = QINROT- The
adjustment of the rotational constants produced no significant changes
in the calculated A, E splittings. The resulting effective unsplit
rotational constants, and the principal and second moments of inertia

are given in Table 23.

74

 

 

 

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a

75

The uncertainty in V3 depends primarily on the uncertainty in
Ia and only slightly on the uncertainty 6. Uncertainties of 10.1 u-X
in Ia and 1j° in 6 result in uncertainties of 1J5 cal/mole and 12 cal/mole,
respectively, in V3. The absolute error in the experimental values of
the Splittings are much smaller than the uncertainties in the calculated
Splittings and thus make a negligible contribution to the uncertainty
in V3. The larger uncertainties for the parameters of the CD30PF2
species are a result of the fact that the A, E Splittings are much
smaller in this molecule than in the other species while the absolute

uncertainties in the Splittings are comparable.

6.5 Molecular Structure

 

As discussed in Section 2.5, to obtain a complete Kraitchman
substitution structure it is necessary to isotopically substitute at
each atomic position. Such a complete substitution is impossible for
methoxydifluorophOSphine since phoSphorous and fluorine each have only
one stable isotope. However, if it is assumed that methoxydifluoro-
phosphine possesses a plane of symmetry which bisects the FPF angle
and one HCH angle, the four isot0pic species studied here are sufficient
to determine a complete structure provided that one piece of information
about the H atom locations is assumed.

As previously discussed, the isotopic species CH3OPF2, 13CH30PF2,
CH3180PF2, and CD3OPF2 were studied and the resulting effective rotational
parameters are given in Table 23. However, since the C03 species involves
simultaneous substitution at two nonequivalent hydrogen positions the
resulting information is not directly applicable to the structure
determination. Nevertheless it may be used to aid in determining the

geometry of the methyl group.

76
The assumption of a molecular plane of symmetry may be justified
by comparison of the Pbb values, the out-of-plane second moments of
inertia, given in Table 23. Pbb is defined as §mi512 (see Section 2.5)
and if the b principal axis is perpendicular to the plane of symmetry

any isotopic substitution in the plane should leave P unchanged (bi = O).

bb
The fact that the observed Pbb values for the normal, 13C, and 180
species are essentially equal provides conclusive evidence for a
molecular plane of symmetry.

The principal axis coordinates of the oxygen and carbon atoms were

determined using the Kraitchman substitution equations and second

moments of inertia for the 18O and 13C species, respectively. For these

 

calculations the Kraitchman equations are more conveniently expressed as,

bb 'Pbb cc

lal = [%(Paa'-Paa)(1+r—)(1+::c—+———fwn

Equations for |b| and |c| may be obtained by cyclic permutation of the
subscripts. Since there is a molecular plane of symmetry which results
in a near equality of the Pbb values, the factor including the difference in
Pbb values was set equal to one.

The remaining molecular parameters, i.e., the geometry of the CH3
and PF2 groups, were determined by a least squares fit to Ma, MC, Pac:
Paa’ Pbb: and Pcc of the normal species. Since the methyl geometry
can not be determined directly from the CD3 information, a series of
calculations were done for various CH bond lengths and OCH angles to
determine the methyl geometry which best predicted the observed moments
of inertia of the CD3 species. The only constraint placed on the methyl
geometry was that it be symmetric, i.e., that the HCH angles be equal.
The best agreement was found at a CH bond length of 1.090 1 0.003 A and

77
an OCH angle of 109.5 1 O.2°. As expected, the PF2 geometry was quite
insensitive to small variations in the methyl geometry.

Using the principal axis coordinates of the oxygen and carbon
atoms the angle between the 0C bond and the a axis was calculated to
be 53.11 1_0.05°. This result may be compared to the value of e, the
angle between the symmetry axis of the methyl rotor and the a axis,
determined from the internal rotation analysis (see Table 22) of
50.68 1_.l°. The inequality of these two angles indicates that the
methyl group is "tilted" such that its symmetry axis no longer lies
along the OC bond but is 2.43° away from the OC bond. "Tilted" methyl
groups are commonly observed in internal rotation studies (55-57). As in
all previous studies where the methyl group is attached to an atom
having unshared electron pairs, the methyl "tilt" in this study is
toward the unshared electron pairs on the oxygen. Without being
specific about the forces involved, the "tilt" can be rationalized as
resulting in a lowering of "bond-bond repulsions" at the expense of an
increase in "bond-unshared pair repulsions".

The structure fitting calculations were repeated with the methyl
group "tilted" 2.43° away from the fluorine atoms with no significant
changes in any of the molecular parameters except the OCH angles. The
atomic coordinates resulting from the structure calculations are given
in Table 24. The corresponding bond lengths and angles are given in
Table 25 and the projection of the molecule onto the molecular plane of
symmetry is shown in Figure VIII.

Although not strictly chemically correct, it may be instructive
to compare the results of this study with the results of x-ray crystallo-
graphic studies on some phosphorus (V) compounds containing methoxy

groups (Table 26). Cruickshank (71). from a comparison of ph05ph0rus (V)

 

78

Table 24. Principal Axis Coordinatesa’b for Methoxydifluorophosphine.

 

 

Atom a b c
P] 0.526 1_.005 0.000 -0.549 1 .003
0.529 1 .004 0.000 -0.548 1 .002
F2 0.787 1 .004 1.172 1 .002 0.489 1 .002
0.784 1 .003 1.171 1 .002 0.489 1 .002
F3 0.787 1 .004 -l.l72 1 .002 0.489 1_.002
0.784 1 .003 -l.l7l 1_.002 0.489 1 .002
04 -l.040 1_.002 0.000 -0.641 1_.002
-l.040 1_.002 0.000 -0.641 1 .002
C5 -l.909 1 .002 0.000 0.516 1 .002
-l.909 1 .002 0.000 0.516 1_.002
H6 -2.949 1 .002 0.000 0.190 1 .002
-2.934 1 .002 0.000 0.146 1 .002
H7 -l.7l6 1 .002 0.889 1 .002 1.115 1 .002
-l.742 1 .002 0.889 1_.002 1.123 1 .002
H8 -l.7l6 1_.002 -0.889 1_.002 1.115 1 .002
-l.742 1 .002 -0.889 1_.002 1.123 1 .002

 

 

a Coordinates for tilted methyl are given in second line.

b In Angstroms.

 

79

Table 25. Calculated Bond Lengthsa and Bond Anglesb for Methoxydifluoro-

phosphine.

 

 

Symmetric Methyl Group,

 

 

r(PF) .587 1 .005 <(FPF) 95.2 1 .4
r(PO) 569 1.005 <(FPO) 101.7 1.3
r(OC) .446 1 .006 <(POC) 123.5 1_.4
r(CH) .090 1_.003 <(0CH) 109.5 1_.2
<(HCH) 109.4 1.2
"Tilted” Methyl Group
r(PF) .586 1.005 <(FPF) 95.3 1 .
r(PO) .572 1.005 <(FPO) 101.5 1.3
r(OC) .446 1 .006 <(POC) 123.5 1_.4
r(CH) .090 1_.003 <(0CH6) 107.1 1
<(0CH7) 110.7 1.2
<(HCH) 109.4 1.2

 

a In Angstroms.

b In degrees.

 

80

 

0
1A

 

l
I

Figure VIII. Projection of methoxydifluorophosphine in the molecular

plane of symmetry.

 

81

derivatives, has estimated the P0 single and double bond lengths to be
1.71 and 1.38 A, respectively. The shortening of the P0 bonds given in
Table 26, which should be single bonds, has been postulated as due to an
increase in the P0 bond order. In this respect, it would seem reasonable
to conclude that the P0 bond in this study, whose bond length agrees well
those of Table 26, has also been shortened due to some form of multiple
bonding.

The reported CO bond length in dimethyl ether (64) (1.417 A) may be
compared to that in methyl nitrate (63) (1.43 A). The high barrier
(9.1 kcal/mole) to the internal rotation of the nitrate group in methyl
nitrate has suggested a partial double bond between the oxygen attached to
the carbon and the nitrogen atom. Presumably such double bond character
would result in a lengthening of the adjacent CO bond. Comparison of the
CO bond length in this study, 1.446 A, to that of methyl nitrate and those
shown in Table 26 indicates that the CO bond length CH30PF2 is longer than
expected for a simple single bond, presumable a result of multiple bonding

in the P0 bond.
6.6 Discussion of Results

The most stable conformer of methoxydifluorophosphine apparently has

a plane of symmetry with the methyl group cis to the fluorine atoms. This
was not predicted since in this configuration there is an opportunity for
steric hindrance between the hydrogens and the fluorine atoms. Indeed,
two pieces of evidence from the final results suggest that some steric
effects are operating. First, the barrier to internal rotation of the
methyl group is low, even for a CH30X molecule (Table 18). If it is
assumed that the equilibrium configuration of the methyl group occurs

with the 0P bond staggering the CH bonds, at equilibrium the two hydrogens

 

HEP

 

 

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83

are near their point of closest approach to the fluorine atoms. A steric
interaction in this configuration would tend to raise the minimum of the
potential function, which would in turn reduce the barrier height. The
second evidence for steric interaction is the result that the hydrogens

of the methyl group appear to be tilted off the CO axis. The tilt is in
the direction which moves the hydrogens away from the fluorines. For the
proposed structure the minimum HF distance is 2.62 A (the sum of

van der Waals' radii is 2.55 A). Without the tilt the minimum HF distance
would be 2.59 A.

The COP angle (123.5°) suggests the sp2 hybrid orbitals are used by
the oxygen atom to form the 0C and DP bonds. The oxygen lone pairs could
then be described by a p orbital perpendicular to the plane of symmetry
and another sp2 hybrid. The p orbital would have the correct symmetry
for (p+d)n bonding with a phosphorus d orbital. As mentioned above,
there is evidence that the P0 bond is shorter than a hypothetical pure
single bond. In this description, however, the sp2 oxygen lone pair and
the phosphorous lone pair should repel one another and lengthen the P0 bond.

As discussed in the chapter on methyldifluorophosphine, results of
recent studies of PFZX derivatives suggest a dependence of the PF bond
length on the electronegativity of the group X. Since the PF distance in
CH3OPF2 is very nearly equal to that reported for PFZNH2 (Table 15), this
suggests that the effective electronegativity of the -NH2 and-OCH3 groups

are the same. In view of the similar inductive effects of these two

substituents this result is not surprising.

 

LIST OF REFERENCES

'II.

 

10.

11.
12.
13.
14.
15.
16.
17.

18.

19.

20.

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D. K. Coles and W. E. Good, Phys. Rev., 19, 979 (1946).

R. H. Hughes and E. B. Wilson, Jr., Phys. Rev., 11, 562 (1947).

T. W. Dakin , W. E. Good and D. K. Coles, Phys. Rev.,_ZQ, 560 (1946).

S. Golden and E. B. Wilson, Jr., J. Chem. Phys., 1g, 669 (1948).
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R. W. Kilb, C. C. Lin, and E. B. Wilson, Jr., J. Chem. Phys., 2Q,
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D. R. Herschbach, J. Chem. Phys., 21, 91 (1959).

I'fi
W

. Wilson, Jr., Adv. Chem. Phys., 2, 367 (1959).

J. Kraitchman, Am. J. Phys., 21, 17 (1953).

C. C. Costain, J. Chem. Phys., 29, 864 (1958).

H. H. Nielsen, Revs. of Mod. Phys., 22, 90 (1951).

D. R. Herschbach and V. W. Laurie, J. Chem. Phys., 22, 1668 (1962).

H. Goldstein, Classical Mechanics, Addison- Wesley Publishing
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H. C. Allen, Jr. and P. C. Cross, Molecular Vib—Rotors, John Wiley
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H. Erying, J. Walter and G. E. Kimble, Quantum Chemistry, John
Wiley and Sons, Inc., New York, 1944, p. 39.

 

Reference 18, p. 10.
84

 

 

ill" .I.I

85

List of References (Continued)

21.

22.
23.
24.
25.

26.

27.
28.

29.
30.
31.
32.

33.
34.

35.

35.
37.
38.
39.
4o.
41.

42.

J. Wollrab, Rotational Spectra and Molecular Structure, Academic
Press, New York,71967, p. 12.

 

G. W. King, R. M. Hainer and P. C. Cross, J. Chem. Phys., 11, 27 (1943).
Reference 21, p. 19.
S. C. Wang, Phys. Rev., 21, 243 (1929).

Tables Relatingito Mathieu Functions, Columbia University Press,

 

New York (1951)}

R. W. Kilb, Tables of Degenerate Mathieu Functions, Harvard University
Press, Cambridge, MassaCfiDsetts (1956).

 

B. L. Crawford, Jr., J. Chem. Phys., 2, 273 (1940).

D. R. Herschbach, Tables for the Internal Rotation Problem, Harvard
University Press, Cambridge, Massachusetts (1957).

 

 

C. 01in and J. D. Swalen, Rev. Mod. Phys., 21, 84 (1959). :_2
C. C. Lin and J. D. Swalen, Rev. Mod. Phys., 21, 841 (1959).
Reference 21, p. 244.

C. H. Townes and A. L. Schawlow, Microwave Spectroscopy, McGraw
Hill Book Company, New York, 1955, p. 248.

 

R. H. Schwendeman, J. Mol. Spectry., Z, 280 (1961).

H. N. Volltrauer, Ph.D. Thesis, Michigan State University, 1970,
Section 4.

R. S. Rogowski, Ph.D. Thesis, Michigan State University, 1968,
Section 3.

Reference 21, Chapter 9.

Reference 32, Chapters 14-17.

H. N. Volltrauer and R. H. Schwendeman, J. Chem. Phys., éfl, 260 (1971).
H. N. Volltrauer and R. H. Schwendeman, J. Chem. Phys., §1, 268 (1971).
P. L. Lee, Ph.D. Thesis, Michigan State University, 1971.

W. LOttke and A. de Meijere, Angew. Chem. Internal. Edit., 5,
512 (1966).

A. de Meijere and W. Lfittke, Tetrahedron 2g, 2047 (1969).

86

List of References (Continued)

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45.
46.
47.
48.
49.
50.

51.
52.
53.
54.
55.
56.
57.
58.
59.
60.

61.
62.
63.
64.
65.

J. H. Hand, Ph.D. Thesis, Michigan State University, 1965.

M. W. P. Strandberg, Microwave Spectrosc0py, John Wiley and
Sons, Inc., New York, 1954, p. 4.

 

Reference 34, Chapter V.

D.
V.

D
D
A.
to
A

P.

R.
W.
. R.
. R.

H.
be published.

. H.
L.

Lide, Jr. and D. E. Mann, J. Chem. Phys., 21, 868 (1957).
Laurie, J. Chem. Phys., 99, 1516 (1961).
Lide, Jr. and D. E. Mann, Ibid., 864 (1957).

. . - Wt?!

Lide, Jr. and M. Jen, J. Chem. Phys., 99, 252 (1964).
Brittain, J. E. Smith, P. L. Lee, K. Cohn and R. H. Schwendeman,

Brittain, J. E. Smith and R. H. Schwendeman, to be published.

 

Lee, Ph.D. Thesis, Michigan State University, 1971, Section 6.

This Thesis, Section 6.

R.

T
K.
L

L.

Kuczkowski, J. Am. Chem. Soc., 99, 1705 (1968).

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. Pierce, R. G. Hayes and J. F. Beecher, J. Chem. Phys., 99, 4353 (1967).

L. J. Nugent and C. D. Cornwall, J. Chem. Phys., 91, 523 (1962).

Reference 21, p. 30.

Rotational Energy Levels of Asymmetric Top Molecules, Tables of

 

Reduced Energies, Grumman Research Department, Grumman Aircraft

 

Engineering Corporation, Bethpage, New York.

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Herschbach, Bibliography for Hindered Internal Rotation and

 

Microwave Spectroscopy, Lawrence Radiation Laboratory, Berkeley,
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Reference 35, Section 6.

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P. G.
Acta.

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V. Malmstadt and C. G. Enke, Digital Electronics for Scientists,
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Benjamin, Inc., New York, 1969, Chapter 4.

 

APPENDIX

 

APPENDIX I

A binary decoder was designed to provide a convenient and accurate
method of placing frequency markers directly on a spectral recording.
To accomplish this it was necessary to distinguish between the various
binary representations of one digit of the microwave frequency as supplied
by a Hewlett-Packard 5245 L counter fitted with a Hewlett-Packard 5257 A
transfer oscillator. The binary representations of the decimal numbers
zero to nine are given in Table 27. A combination of integrated circuit
solid state devices called NAND gates, AND gates and OR gates was used
to differentiate between the various representations. The symbols and

truth tables for these devices are given in Figure IX, (72). The states

 

0 and 1 may be conveniently represented electronically by voltages of L
0 and +5 volts respectively; this representation may be extended to the
binary representation given in Table 27. When all the inputs of a NAND
gate are in state 1 (at +5 volts) the output will be in state 0 (at 0
volts). This is the unique situation, since the output will be in state 1
for all other input combinations. For an AND gate the unique output
is state 1 and occurs when all inputs are in state 1. For an OR gate
the unique output is state 0 and occurs when all inputs are in state 0.
An example of a combination of gates which may be used to differentiate

between zero and the other representations of Table 27 is shown below:

Air-{E1
Des...

 

 

B¢>—1]}

ohm—xj/Lxl:

 

 

9.179

 

88

89

Table 27. Binary Representation of the Decimal Numbers Zero to Nine.

 

 

 

20 21 22 23
o o 0 o o
1 1 o o o
2 o 1 o o
3 1 1 o o
4 o o 1 o
5 1 o 1 o
5 o 1 1 o
7 1 1 1 o
8 o o o 1

ND
_4
O
C)
_.1

 

90

 

 

 

 

A B Out A B Out A B Out
0 0 1 0 0 0 0 0 0 '—
1 0 l 1 0 0 1 0 1
O l l O 1 0 0 l l
l 1 0 l l l l l 1
(a) (b) (C)

Figure IX. Symbols and truth tables for (a) NAND gates, (b) AND gates
and (c) OR gates.

91

The circuitry represented by "I" is designed to insure that the
incoming signal has the proper voltage (0 volts for state 0 and +5 volts
for state 1) and to invert the input state (0 + 1 and l + 0). The X
inputs to the AND gates are held in state 1. Thus, if all the binary
inputs are zero, they are inverted to ones by the I circuits and mixed
with ones from the X's. From Figure IXb it is seen that the outputs of
the AND gates will be all ones. Any other decimal input will have at
least one binary input non—zero, and hence at least one AND gate output
equal to zero. If all the AND gate outputs are one, the NAND gate output
will be zero (Figure IXa). If any one (or more) of the AND gate outputs
is zero, the NAND gate output will be one. In this manner the decimal
digit zero may be distinguished from the other decimal digits. The output
state 0 (0 volts) may be manipulated in any convenient manner to activate
the events marker pen and place a frequency marker on the recording.

Since frequency markers were desired in intervals of 2, 5 or 10
units (the magnitude of the intervals depends upon which digit is being
monitored), the decoder consists of three sections, one for each interval.
The logic diagram of the decoder is given in Figure X, where the three
sections of the decoder are identified according to the resulting marker
intervals.

Switching from one logic section to another, i.e. from one marker
interval to another, is accomplished by means of the X, Y and 2 inputs to
the AND gates. When these inputs are in state 0 the output must be state
0 and the section is "turned off". In the previous example X was in
state 1 while Y and 2 were in state 0.

The inputs A, B, C and 0 may be mechanically switched to monitor any
one of the four right-most digits of the counter's display. For normal
counting rates the decimal point of the displayed frequency is two digits

from the right; thus, digits representing 10 kHz to 10 MHz may be monitored.

 

92

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.x 2:3...

 

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93

The PC input in Figure X is a print command from the counter which
indicates when the counting cycle has been completed and the measured
frequency is ready to be monitored. While the counter is "counting"

PC is in state 1. When the cycle is complete, PC switches to state 0
which is inverted to state 1 and locks the output of C3 to either state
0 0r 1 depending upon whether the other input is 0 or 1, respectively.
In the previous example the unique output was 0 which would pass the OR
gate as 0 and be inverted by C2 to state 1. If PC is in state 0 both
inputs to C3 will be in state 1 resulting in an output state 0 which is
inverted by C4 to state 1 which represents the unique output state of

the decoder.

 

Closing S2 introduces the "auto" section into the circuit. This _2_
section may be mechanically switched to monitor any one of the second
through fifth digits from the right of the counter. In normal operation
52 is switched to the digit just to the left of the one being monitored
by inputs A, B, C and D. The purpose of this section is to provide
continuous markers whenever the digit being monitored is zero, regardless
of the situation existing at inputs A, B, C and D. For example, if
markers are being placed on the recording in 5 MHz intervals then every
twentieth marker, i.e., every 100 MHz, will be broader then the others.
This function is very useful in correlating the markers with the correct

frequencies.