Effect of pressure on the conformation of molecules

TitleEffect of pressure on the conformation of molecules (Modernaspects of physical chemistry at high pressure : the 50thcommemorative volume)

Author(s) Whalley, E.

Citation The Review of Physical Chemistry of Japan (1980), 50: 119-131

Issue Date 1980

URL http://hdl.handle.net/2433/47107

Right

Type Departmental Bulletin Paper

Textversion publisher

Kyoto University

The Review of Physical Chemistry of Japan Vol. 50 (1980)

THE L[[SY14:x' Or Pn PSiC.aL Cnemtsrxv ar J.\PA\, VUL. ~O, 19$0

EFFECT OF PRESSURE ON THE CONFORMATION

OF MOLECULES*

By E Whalley

In general, pressure affeca the sizes and shapes of molecules, and the purpose of this paper is to review .chat is known about the effect of pressure on the shapes of small molecules, as described by internal rotation angles. The principal investigations

made so far are on the effect of freezing in[Iuced by pressure changes, the equilibria between conformational isomers in fluids. and the changes in [he structure of molecules

due to changes in imernal rotation angle in both solids and liquids.

1. Introduction

This paper is offered in celebration of [he fiftieth volume of The Review of Physical

Chemistry of Japan, and as a contribution to the Commemoration Volume. 1 send with i[

my congratulations on its previous successes and my best wishes for its continuing success in

the future.

[n general, pressure affects the sizes anJ shapes of molecules. If a molecule is symmetric

enough and issubject to symmetric enough forces. as, for example, a diamond crystal subjected

to hydrostatic pressure, pressure changes only the interatomic distances.. and changes them

uniformly until a catastrophic change to a new structure occurs. [n diamond, the rate of

decrease of al] interatomic distances with increasing pressure is one third the compressibilin•,

or 0.12 A Mbar ` at low pressures. In less symmetric molecules. where the interatomic

angles are not determined by symmetry, or in symmetric molecules that are distorted b}• an

environment of lower symmetry, the interatomicangles are also affected by pressure. The

interatomic angles can be divided into two kinds, namely, bond angles that are determined by

two atoms nest to a third, aitd internal rotation angles, i. e. [he dihedral angle between the

planes ABC and BCD of the non-linear chain of atoms A-B-C-D. The purpose of this

paper is [o review what is known about the effect of pressure on the equilibrium between conformational isomers anti nn the internal rotation angles.

Although it is known by general symmetry arguments that bond angles change with

pressure unless they are de[ennined by symmetry, almost nothing quantitative is known. An

example is the distortion of the ZnCI ion in Cs,ZnCl.,. The ion is on a plane of synunetry,

and is therefore distorted by the crystal forces frmn the tetrahedral symmetry it presumably

has when isolated. [n the isolated ZnCI',- ion one of the stretching vibrations is triply

(Received .~'bvember 7, 1980) • N . ii C. C. No. 19172


110 E. R'halley

degenerate. In the CsiZnCl, crystal, it splits into 3non-degenerate vibra[ions, and the splitting

is a measure of the distortion from tetrahedral. The splitting increases with increasing

pressure" and so the distortion increases. Unfortunately, there are four independen[ CI-Zn-CI

angles and three independent Zn-CI bonds, and the nature of the distortion cannot be

determined even if the change of bond length is neglected.

[t is in general easier to distort internal rotation angles than bond angles because [hey

are weaker. In nddition, some molecules that can change their internal rotation angles have

two or more conformational isomers. The equilibrium between these isomers changes with

pressure, and this changing equilibrium constitutes another aspect of the effect of pressure on internal ro[a[ion angles. The purpose of this paper is to review the curren[ state of

knowledge about small molecules in these areas.

The effect of hydrostatic pressure on molecular conformations is of course part of the

larger subject, the effect of stress on molecular conformations. One of the more spectacular

examples of this subject is the rubberiness of rubber. In rubber, the polymer chains are

irregularly coiled and are pinned to one another at rare cross (inks. When the rubber is

strained, the chains uncoil by changing the rotation abou[ [he bonds to new equilibriuttt

positions. Related effects occur in crystalline polymers. For example, the Young's moduli of highly ordered polyoxymethylene and polypropylene are much smaller than those of highly

ordered polyethylene. In polyoxymethylene and polypropylene, the molecules are coiled, and

the moduli at low strains are determined by the resistance to internal rotation, whereas in

polyethylene the molecules are extended chains, and it is the C-C-C angle bending that

determines the modulus.a' Although these effects are very importam, they will not be

discussed here because this review is restricted to small molecules.

For the same reazon, the effects of pressure on the conformation of proteins and polypep-

tides, the radius of gyration of polymer molecules", and [he structure of polymer crystals

will be omitted, and so also will the effect of pressure on order-disorder transitions in lipid

bila}•ers and related materials. Nevertheless, the results reviewed should be relevant to all

these topics.

2. Effect of Pressure on the Equilibrium between Conformers

2-1. Effect of freezirtp art molecular confonnrtlim[a

Many fluids are composed of two or mare conformers in equilibrium. and when they freeze

one of the conformers is usually preferred in the crystal. The effect of freezing by cooling

and by squeezing on the conformer present in the crystal hes been studied by Bresch" and by

Klaeboe and coworkers'-1° in a number oC papers. The results are summarized in Table 1.

In most cases, cooling and squeezing form the same solid, but occasionally form a different

one. Often one of them is metastable, but occasionally nvo stable solids containing differem

conformers occur. Little is known about [he causes of these effects except in general terms.


Effect of Pressure on the Cnn formation of \Solecules I?1

Table 1. Conformations in the solid

conformational isomer

state of molecules haying more than one

MoleculeStatN in solid formed by

Cooling

I,2-dichloroethane

1.2-dibromoethane

1. 1, 2-tricBloroe[hane

L 1, 2, 2-tetracWorocthane

I, 1.2, 2-tetrabrornoe[hane

1,2-dibromopropane

I, 7-dibromopropane

I, 3-diiodoprapnne

methylcyclohexane

chbrop~clohexane

bromocyclohexane

iodocy'Clohexane

cyanocyclohexane

isocyanatocycbhexane

mans-1, 2-dichlorocyclohexane

rraas-1, 2-dibromoq'ebhexane

r ra ns-1.2-chlorobromocyclohezanc

mans-1.2-dime[ hylcycbhexane

cis-I, 3-dimethylcyclohesane

rrmirl, 4-dichlorocyctohexane

rraas-I,4-dihromocy'clohexanc

mans-1, 4diiodocyclohexane

mans-1, 4-brotrachlorocycbhexane

rraas-l , 4-choroiodogclohezane

rraas- I. 4-bromoio docydohexane

trau-1, 4-dimethylcyclohexane

mans

mans

less polar

gauche

usually d

rraas`

RS

88

era at e a[ low

c at low

e ~r

e

ee

as

ee

eea

ee'

tC

ee

ce

ee

squeezing at ~2?`C

ga+rches

high temp. temp.

temp.

rrmrt

rrmrs

either either

mans

usually rrans°

mans`

xg

rr^

e

e°

c'

e°

a

a

ee

as

as

ee or ee+aa

ee

aa^

uu°

as

as

as

as

a~

Ref. for pressure experiment

Brasch" --~ Brasch"

Brasch" Christian er als' Brasch"

Brasch"

Thorbjornsrud er al.B1 Thorbjornsrud er aLr~

Thorbjornsrud er aLr'

Lauer and Peterkinei

Klaeboe+'

Klaeboe9i

Klaeboe"

Horntvedt and Klaeboe161

Horntvedt and Klaeboe101

Klaeboe"'

Klneboe"'

Horntvedt and Klaeboe"'

Lauer and PeterkinE1

Lauer and Peterkin"

Ellestad and Klaeboe"'

Ellestad and Klaeboe"'

Klaeboe"'

Klaeboe"'

Klaeboe"'

Klaeboe"'

Lauer and Peterkinfi'

a=axial, e=equatoria4 g=Soothe, r=trans. The other conformer could also be obtained.

The C-Br bonds are trans. Of Cr,. symmetry.

A sma8 amount of the a conformer remained in the ' Probably Cormed a glass . • At room temperature . Either ee or as cq~stals could be

phous solid formed from the vapor. "Obtained by squeezing the ordinory solid . ' At room temperature . + Probable conclusion.

polycrystalline

obtained by

solids.

amealing at >IO`C an amor-


12? E. R'halley

2-2. F,gnili6riurn 6etroeen emrfurmers in aalydiurt

Until recently, the only method of measuring the difference of volume of conformers has

been by measuring the attenuation of sound waves by the Iluid. The maximum acoustic loss

pm„ Per wavelength due to an interchange between conformers is relate) to the difference

JV of partial volume between the conformers by the equation

i

V arJH

where :f is a constant depending on the concentrations of the conformers at equilibrium and

the standard difference between [hem of the enthalpy JH' and the Gibbs (unction. -and C,

and ar the heat capacity and thermal espansivity of the solution respectively."' It often

happens, however, that

J [• C, P arJH' ~ 1.

and then ,rt,,,, is insensitive to JV. Nevertheless. over thirty volumes of conformational isomerism have been measured by this technique and are summarized by North and Pethrick,"'

but the uncertainties of most of them are high.

The effect of pressure P on the equilibrium constant K of two conformers,

t+ _ OLI app

where a, and ur are the activities of the conformers. is directly related to the difference JV°

of volume between them in the standard states used to define [he activities. The relation is

a In Ti _J V` oo"P Jr ]]T ' where ]t is the gas constant a¢d T the temperature. Usually, the activities are replaced by mole

fractions, so that the standard states are the actual states in the solution, and if the conformers

are in dilute solution, the eyuilibrium constant is often written as the ratio of their concentra-

tions. The effect of pressure on conformational equilibria can, therefore, be used to determine

the difference of volume between the conformers.

Several measurements have been reported recently of [he effect of pressure on the relative

proportions of conformers, and they are summarized in Table ?. Both the infrared and Rantan

spectra have been used to analyze [he mixtures, using either diamond anvils or steel pressure

vessels fitted with windows.

The simplest compound that has been measured is n-heptane.18' and [he concentrations

were measured by the Roman spectra of [he longitudinal compression, or acoustic, vibrations.

The all rrruis conformer, rur, could be distinguished from the single x nuche, rgn, as they have

bands at 3D9 anJ 507 cm-' respectively, and the single garcHe and the double gaucHe, ggrr,

conformers contribute to the band at 312cm'. It was assumed that the normal coordinates

of these vibrations were unaffected by pressure. From the data of Fig. 3 of Schocn er al.1b'


I23Effect u( Pressure nn the Conformation of \lolecules

- - ' Q Q 3 v O ~ S ~ ~ v oi V ~ . G Y G

~ G W V U U U F F G C C C ~ 7 'J 'J 4 CJ [i Q

.`7. -Q C C - - .~ - - ~' .~ rn ti F F F U U U U U

N N ~n v -- N N c c c o - o c c o

1 - - « r r o « « o• « a

I Q CI N

1 1 I I I I I I ~ I~

C .r - 'J '3 .O

~-,~ _ C C F ~ ~ V ` V V V W L I F C ~_ C - G ~ P ~ F ° ~ C V 9 cf ~.. C ~~ G 'C C ._ '^ Q F_ - 2' cC e'Y C -C

L+ U c o

i o'~ u ~ r 9 '~ 9 _V =

r

c H 9 n G GL

o IO

t O V " u

i ~ V i q i - y V V

~ d U _

C V n .V.~ C w

1 j

Q 1 V iC

v • V 6

L ~

~ ? C a

n

~ ~-z =mss

G 1 ~ C ~ 1 V O

i ~ ~ .X !.. •~ 9

i ~ ~ ~ ~ J l C N ~' j R > I ~ y N . J V V C j C_ V C ~ R O_ U C r ~ I N

o I c d . R E' .7 r p ~, . a u

u I

n v d d - - ei d - v' -~ -.i n w w y v v -,. -i 6. >

V

n h h u r n ~ ~ ~ q ri M e t- 0 0 C i ~ i y o 0 0 o O O O C O O C ° Y I

Ci i

F' U~ r r 7 ~ ~ 2

v~ ~n O O O

1 ~ ~ ~ r

a ~ ~ > C > i

~ ,o p f ~ J i > ~ ~ ~ J 7 J 'J L y ~ o N

Y X ~ N C L V V 7 C - L C> J C C . S N i r - U U U U

°- 'x •i h '~ a

n ~ v H u ~ u 7 E a

G . ~ •~ x ` 'v :/ ^ J __ ~ - ~ ~ s C L C C~ T U ° C ° v r u L o -~ ~ n ~: = c o E c L z c a o o

M eo ~ o `o = u ~` ~ ~ c r o

U c c = c ~ ~ ~ v c e ~ 9 u a v 6 m 7 7 r~6 G y~ y

~ _ o L t N N w t `S O c .~. ~ - -= U . v

E 0

a .~

U G v u

v a

v u c u

U V

7 !~

7 I

rl

D

F


l24 $ tl'hallec

the volume change on transforming the rrms to the single gauche is ~-1.8em° mot", and

for transforming it to the mixture of the single and double gauche is ~-1.3 em' mot-'.

The effect of pressure on the equilibrium between mans and gauche 1, 2-dichloroe[hane

and 1. 2-dibromoe[hane, which are almost the archetypes of conformational isomerism, was

measured by Taniguchi er al.'1° using a steel pressure vessel with glass windows. The

concentrations were determined by means of the anisotropic Roman spectrum of the carbon-

halogen stretching vibrations, as they appear to be sufficiently uncoupled from the other bands

to be used for this purpose. The ratio of the integrated intensities of the two gm+che bands

to that of the rrm+s symmetric bands was taken as the ratio of the concentrations. The

logarithm of the ratio was linear in the pressure and gave vol mne changes at the mans-to-

gauche transformation of 1, ?-Jichloroethane in 20q~ and 30 o t'/v solution in n-hexane of -3 . 8 and -3.5 em' mot'' respectively. For 1. 2-dibromoethane in 104; v/v solution in

2-methyl6utane and acetonitrile, the volume change was -4. i and -'!.0 em' mot-' respec-

tively.

The remaining compounds in Table ? were studied by Christian er al-1°'"' by infrared

spectroscopy using a diamond anvil cell. There are more problems in using infrared than

in using Roman spectroscopy, particularly the bending of the anvil faces, which would cause a

non-uniform sample thickness. However, at the small pressure ranges used, this may not be

important.

At least three effects contribute to these volume changes, namely, the overlap of the

methyl groups, the change of local packing of the sot cent and solute, and the change of the

long-range electrostatic interaction with the solvent.

Only the first two effects contribute significantly to the equilibria in n-heptane. The

distance between the methyl groups in [he gauche conformer is -~3.1 A, which is much

shorter than the distance 4.0 A which is a typical methyl-methyl distance in cq•stals.301 The

overlap volume is. therefore, of the magnitude of a few cm' mot-'.

The intermolecular packing effect has been discussed theoretically for n-butane by Prau cr

at."' using as a model rigid methyl and methylene groups in a molecule whose otily degree of

freedom was the internal rotation angle. .For n-butane dissolved in carbon tetrachloride and

in n-bmane the volume change for the mans-to-gaucl+e transformation was calculated as-4.7

and -., -'Z cm' mot-' respectively. On the basis of Schoen er al. 's101 results on n-heptane.

and taking account of the contraction due to the overlap of the methyl groups. these values

may be somewhat high, but are of the right magnitude. A semiquantitative discussion of the

same effect. was given by Schoen er aL161

As [he two gauche-l, ?-dihaloethanes are polar molecules, having dipole moments of about

3 D, and [he mans conformers have no dipole moment, the volume difference between them is

determined partly by electrostatic effects, as well as by the internal and intermolecular steric

effects that dominate the volume change in n-heptane. Electrostatic effects can often be

represented crudely by a model in which the molecule is represented as a spherical distribution


Effect of Pressure nn the Conformation of Molecules 125

of charge that is characterized by dipole and quadrupole moments, and the solvem is repre-

sented by a continuous dielectric having aloes-frequency permittivity =. The difference JG

between the conformers of the change of Gibbs function on transferring the molecule from

vacuum to the dielectric is readily calculated."' The electrostatic contribution to the volume

difference between the conformers can be obtained by differentiating it with respect to

pressure."'

The electrostatic dipole and quadrupole momens of 1. 2-dichloroethane and 1. 2-dibromo-

ethane were calculated assuming that they could be representeJ by carbon-halogen point dipoles

directed along the bonds and situated at their centers. The calculated electrostatic volume

differences are -3.3em' mot-' for 1, ?-dichloroethane in n-hexane solution and -1.5 and

-1 .9cm' mot-' for 1, 2-dibromoethane in 2-methyl butane and acetonitrile solution respectively.

These values, when -1.3 and -'-SCm' mot-' are added for halogen overlap in [he gauche

conformers, agree reasonably- well with the measured values listed in Table ?, but fail to

represent the difference betveen t, 2-dibromoethane in 2-methylbu[ane and aceloni[rile.

The existence of an electrostatic effect on the volume change seems to be demonstrated by

the differences between n-heptane and the dihaloethanes, but the effects of the internal overlap

and intermolecular packing are not experimentally differentiated.

3. Effect of Pressure on Internal Rotation Angles

If an internal rotation angle is determined by symmetry, as in ethane, small changes of

pressure will not affect it. However, if the cis conformation of ethane has the smaller volume.

it will be preferred- and at a high enough pressure, a transformation will occur from the

staggered to the cis conformation. No example of this kind of conformational change is yet

known.

If an internal rotation angle is not determined by symmetry, it w•iIl depend on the pressure.

Two molecules are now known whose change of internal rotation angle with pressure has

been measured. They are I, ?-dichloroethane and trithiane.

There are no general ways of measuring the effect of pressure on internal rotation angles.

and each case must be treated as a separate problem. Nmr spectroscopy may be useful if

there are no conformers intercom•erting faster than the nmr time scale, but no measurements

have been reported. Two methods have been used so far, both using Raman spectroscopy.

In one (trithiane) the intensity of a vibration could be expanded in an empirical power

series in the deviation from the eclipsed conformation, where it has zero intensity. If the

first term is taken. [here is only one parameter, which can be eliminated by comparing

intensities at high and low pressure. In the other (I. ?-dichloroethane) a simplified model

of the tvo coupled oscillators was treated, which yielded the relative intensities of two bands

as a function of the internal rotation angle. Each will be treated in turn.

Trithiane is a puckered six-membered ring compound (CH,S)„


126 E, Whatte}'

,CH.~ CII_ ~S / Som. CH,~S/

Its conformation is not determined by symmetry. and so it should depend on the pressure, as

well as nn the solvent. phase, and other aspects of its environment. It is not immediately

obvious whether pressure will tend to flatten or to pucker the molecule further. The first

evidence that the molecule might flatten order pressure was reported by Braseh er al.aa' and

Hamann er al.II1 Several bands itt the infrared spectrum of the solid. and also in the spectrum

of triosane, were greatly reduced in intensity relative to the rest of the spectrum at pressures

estimated to be of the magnitude of 50 kbar. The authors speculated [hat the changes in the

spectrum might be due to a flattening of the molecule. It turns out. hota~ever, that the observed

effects and the assumedaa~a" vibrational assignments arc not consistent with flattening, but the

assignment could be changed in a plausible way to make it so for trithiane.as' but triosane

appears not to flatten significantly.au

The puckered tri[hiane ring has symmetry C„ and the vibrations belong to species A, and

£, which are active in both the infrared and Raman. and .9,, which is inactive in both. The

flattened ring has symmetq~ Dam,. The A, vibrations that become symmetric to the horizontal

plane in [he flat molecule lose infrared activity. as du also the E vibrations that become

antisymmetric to the horizontal plane. The A, vibrations that become antisymmetric to the

horizontal plane lose their Raman activity-. Although the changes in the infrared spectrum?"

after some reassignment.as' agreed with flattening, they were purely qualitative and cannot

be further analyzed.

The only readily measurable Raman bard that loses its intensity in the planar molecule is

i.o

r N 2 W

r z

,~ 0,5 F a J W

o~

0

e

8e

0

0 a

a

a

B 0

0 a

0 5 IO IS 20

v~kbar

Fig. 1. The relative intensity of the J09 cm-' ring-flattening vibration of trithiane

and its neighbors zts a function of pressure.=~' The scale of the ordinate

is arbitrary.


liffect. of Pressure nn [he Cnni urmation ni \lnlecules I2'

the ring-flattening or internal rotational vibration at 309 cm-`. Its Raman intensity"' relative

to its neighboring bands, is plotted on an arbitran• scale in Fig. I. Fay 18 kbar it has

decreased to about a quarter of its value at zero pressure.

This result can be analyzed as follows. Symmetry requires that the Raman intensity be

even in .r, where .r is the distance behveen the carbon and sulphur planes, and to be zero at

the Flat conformation. for which a-=0. It also requires it to be zero in the (unrealizable)

fully puckered conformation, in aehich all the carbon atoms are superimposed, and so are the

sulphur atoms. For this conformation, -r=a, the C-S bond length. The simplest formula

Cor the Raman intensity 7(.c) as a function of [he equilibrium imerplanar distance .v that

meets these conditions is

The intensity as. a function of pressure is. then,

where P is the piessure..r the equilibrium value of a- at pressure P. and .ro the a-alue of .r

at P=O. From the structure of the trilh is ne crystal ae.zn a=1 glg ,~ fur all bonds and xo is

0.652 A. To he formally accurate. the C-S bond lepgth ought to be treated as a function of

pressure. To the accuracy ul' the theory. however, it can be taken as constant. From these values. [he intensities of Fig. I, and Eq. (1), the value of .r/.r, as a function of pressure can

be obtained. It is plotted in Fig. ?. Within experimental error it is linear in [he pressure

and iF an extrapolation is valid, trithiane would become planar at X38 kbar.

L0

x/xo

0-5

a0

a

ae

8

a

Cg O

O

O/

0 =18.4 khI}ar x/xa= o.s

0 5 10 15 20

p /k bar

Fig. ?. The equilibrium value of x/.ra of trithiane as a function oC pressure.-s'

I28

GO

50 w J l7 Z a 40 z 0 F c

it ~

20 r

z

to

0

Fig.

The internal

angles are not r

their cosines is i

cis conformatio

and so the rate

With the same

pressure, and t6

The first ste

change with pre

angle. A mode

significantly cou

bonds change in

be shown that r

in-phase carbon

where v_ and v+

The Review of Physical Chemistry of Japan Vol.

E. RTalley

`~

.

.`

50 (1980)

5 q IS 20 25 30 35 dp p/kbar

3. The internal rotation angle B of trithiane as a function of pressure.=51

rotation angle at zero pressure is about 66°."•S°' The S-C-S and C-S-C

elated to one another by symmetry, but by assuming that [he difference of

ndependent of the pressure. the internal rotation angle 0, measured from the

n, changes with x/.r° at the rate

of change of D with pressure is"'

dp

assumption, the internal rotation angle can be calculated as a function of

e results are shown in Fig. 3.

p in determining how the internal ro[ation angles of the 1. ?-dihaloethanes

sure is to determine how the Roman intensities change with internal rotation

I is assumed in which the two carbon-halogen stretching motions are not

pled to the other vibrations. and the polarizabilities of the carbon-halogen

a cylindrically symmetric manner when the bond is stretched. Then it can

atio of the integrated anisotropic Roman intensities of the out-of-phase and -halogen stretching vibrations is'°'

R_(aniso) _?_ A (~ )

are the frequencies of the asymmetric and symmetric vibrations respectively,

A=3(sin'n cos' ~ 0-sin'ncos` ~ 0),


Effect of Pressure on the Conformation of Molecules l29

3

2

A

11-A

2.6r M

2.4

R-

R+

22

2.0

o ao

fig. 4. The quantity

so 8

Alli-~)

izo

of Eq.

iso

fZ~.rv

Mf

. 30 x 20

% X

dichloroethane in n-hezane

e

z

~Y

l

0 I 2 3 4 5

p / kbor Fig. 5. The ratio of the anisotropic Aaman intensities of the the as>'mmetric

and symmetric carbon-chlorine stretching vibrations oC gauche-l.2- dichbroethane.291

a the C-C-halogen angle, and B the internal rotation angle from the cis conformation. The

factor A/(I-A), which is plotted in Fig. 4, is, therefore. a unique function of the internal

rotation angle, and so the angle can be determined from the measured relative intensities and

frequencies.

The experimental measurements of the ratio of the anisotropic Ratnan intensities of the

carbon-halogen stretching vibrations of 1, 3-dichloroethane dissolved in n-hexane are shown

as a function of pressure in Fig. 5. They are somewhat scattered, but are consistent with a

slope of -0.12 kbar-', which corresponds to a change of internal rotation angle of about -2° kbar '. "this is of the same magnitude as . the rate of change of the internal rotation

angle in trithinne. Its value implies that if the slope were independent of pressure , the cis


130 E. Nhallev

conformation would become the stable one at --15 kbar. The transition state between the

nvo gauche conformers would have become a stable state.301

In liquids. each molecule is, of course, being continually bombarded by its neighbors and

so undergoing continuous distortion. Under Certain circumstances, the mean square value of

this distortion and the effect of pressure can be. measured by the Raman spectrum. The

underlying theory of the method is obtained b}' specializing Eq. (2) to small deviations ¢

from the mans conformation 8=,. It then becomes

R_Canisa)__ 3 --sinaa fSr. R+(anisc) 4 ;+

Of course, any distortion that removes the center of symmetry will make the asymmetric

stretch of the rran.r conformer Raman active. However, the internal rotation coordinate is much

the weakest coordinate. and might be expected to be the most distorted. Then the Raman activiq•

induced by the distortion may be attributed in a Cirst approximation to the distortion of the

internal rotation angle. [f this isso, the vtean value of the intensity ratio averaged over a time

that is long compared to the time of the significant fluctuations of the internal rotation angle

gives the mean square value of the angle.

The asymmetric band of u-uns-1, 2-dibromoethano,"' which is the only substance for

which measurements have been made so far, is overlapped by the symmetric band of the

gauche conformer, and so its enact intensit}• is uncertain. It is about 0.02 and 0.04 respec-

tively in 2-~methylbutane and acetoriitrile,"' which correspond to root mean square deviations

from the trans conformation of -y10 and -~l5' respectively. The resolution of the two

bands is sufficiently uncertain that the effect of pressure on the distortion cannot at present

be obtained accurately. but the method will be applied in more favorable cases.

References

1) P. T. T. Wong, J. Chem. Phyr., 88, 2347 (1977). 2) W. B. Black, "International Review of Science", Physical Chemistry. series ?, Vol. 8, Macromolecular

Science, ed. G E. H. Bawn, Buttenvonhs (1975), p. 33. 3) G. C. Hammel, G. \'. Schulz, and M. D. Lechnep Europ. Polym. J., 15, 209 (1979).

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The Review of Physical Chemistry of Japan Vol.

Efect of Pressure on the Conformation of Volecules t3l

P. E Schoen, R. G. Priest. J. P. Sheridan, and .1. M. Schnur. J. Cheer. Phys., 71, 317 (1979). Y. Taniguchi, 3i. Takaya, P. T. T. Wong, and F.. Wh¢Iley, Effect of pressure on molecular con-formations. 11. Traits-gauche equilibrium of I. 2-dichloroethane and I. ?-dibromoethane. To be published. S. U. Christian, 1. Grun Jnes. and P. Klaeboe. !. Cheer. Phys., fi5, 496 (1976). S. D. Christian, 1. Grandees, and P. Klaeboe, J. Amer. Chem. Soc.. 97, 3864 (1975). L. Pauling, "The Nature of the Chemical Bon)", Cornell Universiq~ Press, New Yurk (1960). 3rd edi[ioa, p. 261. C. R. Pr¢tt, C. 5. Hsu. and D. Chandler, J. CGenr. Pips.. 68. 4202 (1978). C. S. Hsu. G R. Pran. and D. Chandleq ibid., 88, 4213 (1978). See. for esample, R. J. Abraham and E. Bretscl[neider., "internal Rota[ion in Molecules", ed. W. ]. Orville-Thomas. N'ile}'. London (1974). p. 481. 1. W. Branch, A. J. hielvegeq E. R. Lippincon, and S. U. Hamenq .fpplied Specr., 21, 184 (1970)-5. D. Hamann. M. Linton, and C. W. F. T. Pistorius, Nigh Temp-High Pressures, 5. 575 (1973). G. J. Lewis and H. Whalley, J. C'henr. Ph}•s., 69. 1119 (1978). h1. Nakahara, P. T. T. Wong, G. 1. Lcwis, anJ E. Whalley, Can. J. Cheer., G7, 2869 (1979). 1. E. Fleeting and li. L}mton, ibid., 45. 353 (1967). G. \'alle. V. Busetti. M. Mammi, and G. Cara-rvolo, .icra Crpsr.. B25. 143? (1969). H. Tak¢ya, Y. Taniguchi. P. T. L Wong, anJ B. Whalley. Effect of pressure on nwlecular con-formations. III. Internal rotation angle in gaurlrr ],2-dichloroethane and 1.2-dibromoethane. To be published. W'. J. le Noble. A. R. Miller. and S. D. Hamann, !. Org. Cheer., 42, 338 (1977).

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Effect of pressure on the conformation of molecules