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Studies of molecular complexes.

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Studies of molecular complexes.
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Jao, Tze Chi, 1940-
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English
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xiv, 168 leaves. : ill. ; 28 cm.

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Subjects / Keywords:
Absorption spectra ( jstor )
Carbon ( jstor )
Chlorine ( jstor )
Coordinate systems ( jstor )
Infrared spectrum ( jstor )
Liquids ( jstor )
Molecules ( jstor )
Raman scattering ( jstor )
Solvents ( jstor )
Tetrachlorides ( jstor )
Complex compounds -- Spectra ( lcsh )
Molecules ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 163-167.
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Typescript.
General Note:
Vita.
Statement of Responsibility:
By Tze Chi Jao.

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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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STUDIES OF MOLECULAR COMPLEXES






By






TZE CHI JAO


'" .








A DISSERTATION PRESENTED TO THE GRADUATE
COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY





UNIVERSITY OF FLORIDA
1974








































To my parents

and


my wifce- Carmen
* 9












ACKNOWLEDGEMENTS


Special thanks are for Dr. Willis B. Person for his wise counsel,

constant enthusiasm, and encouragement throughout the entire project.

I should also like to express thanks for their help to Dr. Keith E.

Gubbins, Dr. Yngue Ohrn, Dr. Thomas M. Reed and Dr. John R. Sabin.

I am grateful to the University of Puerto Rico (MayagUiez Campus)

for financial support of my graduate studies at the University of

Florida and also for support from the National Science Foundation

(Research Grant No. GP 17818).

Support of computing expenses by the College of Arts and Sciences

of the University of Florida is gratefully acknowledged.

I should like to express my sincere thanks to Dr. Shigeo Kondo,

Mr. Robert Levine, Mr. James H. Newton, Mr. Gary Peyton and Miss

Barbara Zilles for their friendship and assistance.

Finally, I express my appreciation to Mrs. James H. Newton for

her patience in typing this manuscript.


iii












TABLE OF CONTENTS



ACKNUOWLEDGEMENTS ............................................

LIST OF TABLES ...........................................

LIST OF FIGURES .............................. .............

ABSTRACT ..................................... ...............

CHAPTER

I. INTRODUCTION ................... ............ ..........

II. GENERAL EXPERIMENTAL PROCEDURES ....................

Introduction ........................... ..............

Source of Reagents ....................................

Preparation of Chlorine Solutions ....................

Liquid Cells .........................................

III. ULTRAVIOLET SPECTROSCOPIC STUDIES OF CHLORINE IN
BENZENE SOLUTIONS .....................................

Experimental Procedures ...............................

Analysis of the Ultraviolet Spectroscopic Data from
Chlorine-Benzene Solutions ............................

IV. RAMAN SPECTROSCOPIC STUDIES OF CHLORINE IN BENZENE
SOLUTIONS ...............................................

Introduction ...........................................

Experimental Procedure ................................

Results of the Raman Measurements on Chlorine Solutions

Absolute Raman Intensity of Chlorine in Carbon
Tetrachloride ....................... ........... .....


Page
iii

vii

ix

xii



1

11

11

11

11

17


21

21


29


41

41

41

51


63








Chapter Page

V. INFRARED SPECTROSCOPIC STUDIES OF CHLORINE IN
BENZENE SOLUTIONS ..................................... 69

Experimental Procedure ................................ 69

Analysis of the Experimental Results .................. 88

VI. COLLISION-INDUCED INFRARED INTENSITY OF CHLORINE IN
BENZENE AND IN CARBON TETRACHLORIDE SOLUTIONS ......... 107

Introduction .......................................... 107

General Expression for the Integrated .Collision-
Induced Absorption Intensity ........................... 108

N12 The Number of Collision Pairs .................... 108
+ 12 .
Evaluation of U12 d) ............ ....... 113

Explicit Expression for the Integrated Collision-
Induced Absorption Intensity ......................... 116

Evaluation of [(a /a~ )0 F2 + a2 (3F /31)0 2 ) for
the "Axial" Chlorine-Benzene Pair ................... 116

Actual Calculation of the Infrared Intensity of Chlorine
in Benzene Solution for Collision Pairs in Different
Orientations .................... ................. 120

Evaluation of [a' FP2 + a2 F] 2) for Chlorine-
Carbon Tetrachloride Collision Pairs ................. 125

VII. CALCULATIONS OF THE RAMAN INTENSITY ENHANCEMENT.FOR
CHLORINE IN BENZENE AND IN CARBON TETRACHLORIDE
SOLUTIONS ............................................ 130

Introduction ......................................... 130

Theory of the Raman Intensity Enhancement Caused by
Electrostatic Interaction (Bernstein's Collision-
Complex Theory) ....................................... 131

Calculation on the Raman Intensity Enhancement for
Chlorine-Benzene and Chlorine-Carbon Tetrachloride
Pairs in Different Solute-Solvent Orientations ........ 138

Discussion ............................. ....... 146








Chapter


Page


Theory of the Pre-Resonance Raman Effect .............. 148

Application of the Pre-Resonance Raman Effect Theory
to the Interpretation of the Raman Intensity Data
of Chlorine in Benzene Solutions ..................... 152

APPENDIX ............................................... ........ 157'

REFERENCES ................................. .................. 163

BIOGRAPHICAL SKETCH ...................... .................... 168












LIST OF TABLES


Table Page

I. Source and Purity of the Reagents ....................... 12'

II. Extrapolated Values at Time Zero of the Normalized
Absorbance (Ac/CA) for Different Chlorine Solutions ....... 28

III.The Values of Ke280, K, and c280 for Three Different Sets
of Ultraviolet Data from Chlorine-Benzene Solutions
Obtained from the Scott Plot .............................. 35

IV. Values of KE K, and e for Chlorine Solutions from
Scatchard Plots .................................. 39

V. Observed Raman Shifts, Half-Band Widths and Relative
Intensities of Chlorine Solutions in C6HR-CC1 Solvent
6 6 4
Mixtures as a Function of Benzene Concentration ........... 52

VI. Depolarization Ratio of Chlorine in Different Chlorine
Solutions ................................................. 65

VII.Integrated Infrared Molar Absorption Coefficients (A) and
the Parameters of the Lorentzian Functions for the Cl-Cl
Vibration of Chlorine in Benzene Solutions ................ 100

VIII.Parameters Used for the Calculation of the Collision-
Induced Infrared Intensity of Chlorine in Benzene or
Carbon Tetrachloride Solutions ............................ 121

IX. Calculated Collision-Induced Infrared Intensity for
Chlorine-Benzene Pairs in Different Orientations .......... 122

X. Calculated Collision-Induced Infrared Intensity of Chlorine-
Carbon Tetrachloride Pairs in Two Different Orientations .. 127

XI. Coefficients of the 1/R Terms in the Expressions for
S2 2
A(a ) and A(y A) (Eqs. 7-21a and 7-21b) for Several
AB AB
Different Solute-Solvent (AB) Orientations ................ 143

XII.The Calculated Values of A(RAB 2 (YAB )R'
N /N and the Enhancement of Intensity (AP) ............. 145
12 A


vii










A-i. Parameters Used for the Calculations of the Pair-
Correlation Functions of Chlorine-Benzene and
Chlorine-Carbon Tetrachloride Pairs ...................... 160

A-2. The Potential Function ua(R12, wl' '2)/kT for Chlorine-
Benzene Pairs as a Function of Relative Orientation
(at T = 2980K) .......................................... 161

A-3. The Potential Function Ua(R12, W', 2)/kT for Chlorine-
Carbon Tetrachloride Pairs (at T = 298K) ................ 162


viii


Table


Page












LIST OF FIGURES


Figure Page

1. The NMR spectrum of the residue (redissolved in CC1 )
after benzene solutions were evaporated .................. 16

2. Schematic diagram of the infrared liquid cell ............ 20

3. Ultraviolet spectra of chlorine in benzene taken at
different concentrations and at different times .......... 25

4. Plots of the normalized absorbance of chlorine at 280 nm
vs. time for different chlorine solutions (around 0.001 M). 27

5. Ultraviolet spectra of chlorine solutions in a 30% (v/v)
C6H6 and 70% (v/v) CC14 solvent .......................... 31

6. Replotted spectrum of 0.027 M chlorine solution in 30%
(v/v) CH6 and 70% (v/v) CC14 mixture (0.1 mm path-
length) ... .... ................ ......... .............. 32

7. Scott plots of the complex of chlorine and benzene ....... 34

8. Scatchard plots for the complex of chlorine with benzene;. 38

9. Raman spectrum of the C6H6-CC -CHC13 mixture at a ratio of
6:3:1 .................................................... 44

10. Raman spectrum of 0.12 M chlorine in a C6H -CC1 -CHC1
mixture at a ratio of 8:1:1 .......... .. .............. 47

11. Raman spectrum of 0.5 M chlorine in 6:4 C H -CC1 ........ 48

12. Raman spectrum of the chlorine-free 6:4 C H -CC1
66 4
solution ................................................. 50

13. Plot of the Raman spectral half-band width of chlorine vs.
the concentration of benzene (CD) ........................ 54

14. The relative Raman intensity of chlorine I as a
function of the benzene concentration (M) ................ 57
1 o
15. Plot of l/[I I ]R( vs.-pB /p for chlorine in
benzene solutions ....................................... 60









1 o
16. Plot of p /[(I I R ] vs. (p + C C) for
B R(v) R(v) B A
Eq. 4-4.......... ... ..... ...... ........................ 64

17. Infrared spectra of chlorine (about 0.6 M) in benzene
solutions as a function of the exposure to fluorescent
lights............................ .................. ..... 71

18. Infrared spectra of 0.33 M chlorine in benzene. The path-
length of the cells for all studies is 3 mm............... 76

19. Infrared spectrum of chlorine in 60% (v/v) benzene and
50% (v/v) carbon tetrachloride. The pathlength is 3 mm
for all spectra....................... ............. 78

20. Infrared spectrum of chlorine solution in 20% (v/v)
benzene and 80% (v/v) carbon tetrachloride. Pathlength
is 3 mm .................... .............. .......... 80

21. Spectrum of chlorine in carbon tetrachloride. Path-
length is 3 mm for all spectra............................. 82

22. Infrared spectra of chlorine in carbon tetrachloride. The
pathlength is 3 mm for all measurements................... 85

23. Infrared spectrum of chlorine in carbon tetrachloride solu-
tion with the 6 mm pathlength liquid cell................. 87

24. Replotted infrared spectra of chlorine in benzene solutions;
the concentration of chlorine in each solution is 0.5 M
and the pathlength is 3 mm................................ 90

25. Lorentzian curve (F) fitted to the observed absorption
spectrum of chlorine in benzene (I)....................... 93

26. Lorentzian curve (F) fitted to the observed absorption
band (I) of chlorine in 60% (v/v) benzene and 40% (v/v)
carbon tetrachloride.................................... 95

27. Lorentzian curve (F) fitted to the observed absorption
band (I) of chlorine in carbon tetrachloride.............. 97

28. Scott plot of the infrared data for the complex of
chlorine with benzene (neglecting the intensity of "free"
chlorine in the presence of carbon tetrachloride)......... 103

29. Scott plot of chlorine complex with benzene, using a
recalculated intensity of chlorine, as given by Eq. 5-9,
and described in the text................................. 105


Page


Figure








Figure Page

30. Coordinate system used in defining the orientation of
linear molecules............................................ 110

31. Coordinate system used in defining the orientation of
chlorine and carbon tetrachloride......................... 126

32. Coordinate system and symbols used for deriving the
electrostatic potential due to a dipole.................. 132"

33. The relative orientation between cartesian coordinates
(x, y, z) and the polar coordinate unit vectors
(eR e ) .......... ...... ............ 133
iRm 0e lo o o e e~ O e O OO~ o o O e I











Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy



STUDIES OF MOLECULAR COMPLEXES


By


Tze Chi Jao


March, 1974



Chairman: Willis B. Person
Major Department: Chemistry


Molecular complexes of chlorine in benzene solutions were studied

by ultraviolet, Raman and infrared spectroscopic techniques. Ultra-

violet spectroscopic studies verify the order of magnitude of the

previously reported equilibrium constant for the assumed benzene-
-1
chlorine 1:1 complex. Its value, K = 0.025 + 0.015 liter mole1,

agrees quite well with values obtained from Raman and infrared spectro-

scopic data.

Careful experimental measurements were made of the absolute Raman

and infrared intensities of the CI-C1 stretching vibration of chlorine

in solutions of benzene in carbon tetrachloride. Specially designed

infrared long path liquid cells, inert to chlorine, were constructed

and used to obtain the absorption spectra of chlorine in the mixtures

of benzene and carbon tetrachloride. The resulting infrared studies

xii







were more accurate than previous work, and the collision-induced infrared

absorption spectrum of C12 in CC14 could also be observed.

The v 'venumber of the Raman band of C12 shifts uniformly from
-1 -1
530 cm benzene solution to 543 cm in carbon tetrachloride solu-

tion, alti.>ugh the half band width clearly broadens at a 1:1 ratio of

benzene to carbon tetrachloride. The infrared absorption by chlorine

shifts slightly from 527 cm-1 in pure benzene to 532 cm1 in 2.26 M

benzene in CC14; with a big jump to 545 cm- for chlorine in pure

carbon tetrachloride. This difference between the Raman and infrared

spectra for chlorine in benzene solutions suggests that the infrared

absorption is from only the completed chlorine, while the Raman band

is a composite of two unresolved bands, one for the completed chlorine

and the other from free chlorine. The absolute infrared intensity and

the relative Raman intensity for the C1-C1 vibration of chlorine both

increase approximately by a factor of five from those for the Cl2

solution in carbon tetrachloride to the solution in benzene.

In order to interpret these observed Raman and infrared spectra,

theoretical calculations were made of the effect on the Raman and

infrared intensities from direct electrostatic interactions. The basic

theory of collision-induced infrared absorption intensity by Van

Kranendonk and Fahrenfort and of the Raman intensity enhancement by

Bernstein was applied, using statistical mechanics of liquid structures

with angularly dependent pair-correlation functions of chlorine in

benzene solutions. The isotropic and anisotropic effects were taken

into consideration for the calculations of both Raman and infrared

intensities. The calculated intensities were then compared with the


xiii








experimentally measured values.

The electrostatic effect predicts a maximum Raman intensity

enhancement of 100% for chlorine from gas phase to solution in CC14,

and 134% for solution in benzene, compared with an observed enhancement

of more than 400, from solution in carbon tetrachloride to solution in

benzene. The contribution of the electrostatic 'effect to the infrared

intensity of chlorine in benzene was predicted to be, at most, 50% of

the total measured intensity of 333 cm mmole-I. The vibronic charge-

transfer effect may be responsible for the intensification of infra-

red absorption while a pre-resonance Raman effect involving the charge-

transfer absorption band may explain the enhancement of the Raman band.


xiv













CHAPTER I


INTRODUCTION


Complexes of halogens with benzene have been studied quite

intensively in the last two decades by both experimental and theoretical

methods (1-34). The general subject of molecular complexes has been

reviewed by several authors (35-40). The experimental studies include

those by ultraviolet, visible, Raman and infrared spectroscopic techni-

ques, while the theoretical studies are concerned with the mechanism

of the interaction and the theory of the associated experimental

phenomena, and particularly the relative importance of the electro-

static and charge-transfer effects. The complexes of iodine with

aromatic donors have been studied quite thoroughly by these methods.

Less attention has been paid to the complexes of bromine and chlorine

with benzene or other aromatic donors, because the latter are more

reactive.

In the first careful study by Andrews and Keefer (6) the complex

of chlorine with benzene was found to exhibit an additional strong ul-

traviolet adsorption band near 278 nm, which is absent in the spectrum

of each individual constituent solution. From their ultraviolet data,

they found by the Benesi-Hildebrand method (2) that the equilibrium

constant of the complex is about 0.033 liter mole- with a maximum

-1 -1
absorptivity e for the complex at 280nm of 9090 liter mole cm .
max
The equilibrium constant for the complex of iodine with benzene

1








was found (2) to be about 0.17 liter mole- with E of about 15000
max
-1 -1
liter mole -cm so that the complex of chlorine with benzene is

weaker than that for iodine with benzene, in agreement with the expect-

ed Lewis acid strengths of chlorine and iodine.

In an attempt to explain the results of these ultraviolet spectro-

scopic studies (1, 2) of iodine with benzene, Mulliken (11) introduced

the "charge-transfer" resonance structure theory. This theory described

the ground state electronic wavefunction N of a donor-acceptor

complex approximately by a combination of two resonance structure

functions V and ~Y:


N (D'A) = aTV(D,A) + bt~(D+ A) .(1-1)
N 1
(no-bond) (dative)

Here a and-b are the coefficients of the no-bond and dative structures,

respectively. In the ground state of a weak complex, a is expected

to be approximately 1.0 and b expected to be less than about 0.1.. The

stability of the complex depends on the extent of the mixing between

the wavefunctions of the no-bond and dative structures.

If the ground state structure of a complex is given by VN' then

according to the "charge-transfer" theory, there is an excited state

which is called a charge-transfer state, given by
V

V = b 0Y(D,A) + a T1(D+ A) (1-2)

A
The coefficients b and a are determined by the quantum theory require-

ment that the excited state wavefunction be orthogonal to the ground

state function:

J T~ d = 0.
NV








The electronic absorption frequency of the new band formed in the

complex corresponds to the energy difference between the ground state

(N) and this charge-transfer excited state (V) of the complex. The

charge-transfer theory also explains the characteristically high in-

tensity of the electronic absorption band of the complex (for

further discussion see Ref. 37).

The first infrared study of the complex of chlorine with benzene

was made by Collin and D'Or (13). A new weak and relatively broad

absorption band was observed near 526 cm-1 for solutions of chlorine

dissolved in benzene. The Raman shift for chlorine (35 C12) in carbon

tetrachloride was known (22) to be at 548 cm-1. More quantitative

studies of the infrared spectrum of chlorine in benzene were carried

out by Person and associates (18, 21).

An attempt was made by Friedrich and Person (26) to interpret the

changes in vibrational frequency and intensity of the halogen-halogen

stretching vibration when the halogen molecule, an ao acceptor (37),

complexes with benzene, a br donor (37) (or with other electron donor

molecules) in terms of charge transfer theory (11). They postulated

that a relationship existed between the vibrational frequency shift

(Av) and b the coefficient of the dative wavefunction:


FIN = (b2 + abS1) = Ak/k0 = 2Av/v0 (1-3)

2
Here FN is the weight of the dative structure in TN (FN = b + 2abS01)
IN N lN 01"
S is the overlap integral between T and P k is the force constant
01 0 1
and v0 is the vibrational wavenumber of the isolated molecule, while

Ak and Av are the changes (k0 k or v0 v, respectively) in the

complex.








In the following, we shall summarize some of the material from

Ref. 41 relating to the theories of charge-transfer and of electro-

static effects for the interpretation of the changes in infrared

intensity of halogens forming complexes with benzene. The experi-

mental absolute infrared intensity (A.) of the ith normal vibrational
1
mode of any molecule can be related to the dipole moment derivative

(Dp/E1) by (41)

2 2 2
A. = Nig./3c (Op/2.) = K(ap/3a.) (1-4)
i i i 1

Here N is the Avogadro's number, g. is the degeneracy of the ith

normal vibration at wavenumber v., (Dp/*.) is the magnitude of the
1 1
dipole moment derivative for the ith normal vibration with respect

to normal coordinate (5 ). The integrated molar absorption coeffi-
i
cient Ai is defined experimentally by:


'A = (l/nt)'fn(I /I)dv (1-5)
1 0
-I
Here n is the concentration of the absorbing molecules in liter mole

a is the pathlength in cm, I and I are the transmitted and incident

intensities of monochromatic light at wavenumber v .

Based on charge-transfer theory (11), Friedrich and Person (26)

argued that the dipole moment derivative for the C1-Cl stretching

vibration in the complex is given by


ap/a = '91 /3 + (2b).(3b/8 ) Ef | (1-6)
1 N i i 1 0

Here p/8a represents the magnitude of change in the C1-Cl dipole
N i
moment of the uncomplexed Cl molecule when the Cl-Cl coordinate (E.)
2 i
-n -l +
changes; Iu 11 0 is the difference between the dipole moment in the
dioemmn 0nh







dative state p~ and that in the no-bond state i0, and is approximately

equal to .VN' the electronic transition moment for the charge-transfer

absorption band. The second term (ab/~C.) is the change in the coeffi-

cient b as the C1-C1 bond length changes (C ) and gives the vibronic

charge-transfer effect.

The derivative (3p/9E.) is related to the derivatives with
1
respect to the internal coordinates (R.) by:
J
+ +
p/aci = Z L.ji(p/3R) (1-7)


Or conversely,
-1 +
p/R. = E L Op/S ) (1-8)
3 i ij i

Here L.. is the jith coefficient from the normal coordinate transforma-
1 -
-I
tion, while L is the corresponding element from the inverse transfor-
ji
nation. In analogy with Eq. 1-6 we have


8p/aR.= ap/3R + (2b)(9b/lR) ~i 0 (1-9)


Assuming a8 /3RR is not different from the dipole moment derivative

of the free molecule, it has been shown (41) from Eq. 1-9 that the

vibronic contribution (M ) to the infrared intensity change, for the
d
special case Rj = R the stretching coordinate of the X-Y bond of a

completed halogen molecule, can be obtained from the following equation:

Md = (ap/R) ( N/R ) (2FNFIN)(aEv/3R1)/A -1

(1-10)

Here FN is the weight of the no-bond structure in TN (F N a + abS )
ON N ON 01
and is related to FIN by FON + FIN = 1; A is the difference between the

energies of the dative and no-bond structures and Ev is the vertical
A







V
electron affinity of the acceptor, and appears because b depends on E ,
v
so that Db/DR is related to 3E /PR The comparison between the
1 A i
calculated M and the observed values is shown in Table 1.8 of Ref.
d
41. The agreement is qualitatively good, but the calculated values

in some cases are larger than experimental by a factor of 2 to 5.

The defect of the model of Friedrich and Person arises from two

sources: one is the oversimplified assumption that 3y /aR can be
N 1
0
approximated by 3p O/R the dipole moment derivative of the free
1
molecule, the other is because aE V/R (and, to a lesser extent, the
A 1
other parameters such as FN ) cannot be obtained a priori.
IN -
In an alternative treatment, Hanna and associates (30, 31) attempt-

ed to interpret the change in the infrared intensity of halogens in

benzene as a purely electrostatic effect. They estimated an induced

dipole for chlorine in a complex arising from the interaction of the

field along the six-fold z-axis from the benzene molecule with the

polarizable halogen molecule:


i = (1/2) a (E + E). (1-11)


Here a is the polarizability of the halogen parallel to its axis (in

the z direction); E is the field from the benzene at the nearest

halogen atom (X), and E is the field at the halogen atom (Y) further

away from the benzene. Taking the derivative of Eq. 1-11 with respect

to the internal coordinate R of the halogen,


(O /R ) = (1/2)(a '/R )(E + E )
i 1 1 2

+ (1/2) a'[(DE 1/R ) + (3E /aR )] (1-12)
1 1 2 1








The calculated infrared intensity for the halogen completed with benzene

from Eq. 1-12 is compared with the observed values (31). Again the

agreement is good (within a factor of 2).

The values from the model of Hanna and associates (30, 31) appear

to be the right order of magnitude, but the parameters needed for this

calculation are not easy to determine. For example, the polarizability

derivative (aa /aR ) of chlorine was estimated from the semi-empirical
1
Lippincott model (42); the experimental studies reported here (Chap. IV)

found that this estimate is too large. There is also some considerable

uncertainty in the parameters chosen for E and E since estimation of
1 2
the correct values requires quite good molecular wavefunctions of the

benzene molecule.

The subject of electrostatic "collision-induced" infrared

absorption is an old one, having been studied by Van Kranendonk (43),

Fahrenfort (44) and others (45). In the original formulation of

collision-induced infrared absorption given by Van Kranendonk (43)

and Fahrenfort (44), homonuclear diatomic molecules or nonpolar linear

molecules under high pressure are predicted to have induced infrared

absorption due to (a) an atomic distortion effect and (b) a quadrupole

distortion effect. The former arises from mutual repulsion of electron

clouds at small intermolecular separation, while the latter comes from

the interaction between one polarizable molecule and the electric

field generated by the quadrupole moment of the other molecule. Hanna

and associates (30, 31) have considered the second effect in the

benzene-halogen case. In line with the correct collision-induced in-

frared absorption theory (43, 44), the estimated induced infrared

absorption intensity for chlorine in benzene solution should be obtained







as an appropriate statistical average over all intermolecular orienta-

tions, and not just for one orientation, as assumed by Hanna et al.

Using the same argument as Hanna and associates (30,.311, Kettle

and Price (33) applied the theory of collision-induced far infrared

absorption (46-50) to interpret quantitatively the observed results

of their studies on solutions of iodine and bromine in benzene. They

reported that the intensities of the far-infrared absorption of iodine

and bromine in benzene solutions could be adequately explained by con--

sidering only quadrupole-induced dipole moments, but they had to

assume different values for the parameters from those given by Hanna

and Williams (31).

Meanwhile, a Raman spectroscopic study of iodine in benzene solu-

tion had been carried out by Klaeboe (27). He observed only one Ramian

band in the iodine solution, and did not see a Raman shift for the

uncomplexed iodine. Later, Rosen, Shen andStenman (29, 32) made a

more systematic study of the Raman spectrum of iodine in benzene solu-

tion. They observed a uniform change in frequency of the Raman shift

for iodine as the benzene was increasingly diluted by the addition of

the inert solvent; e.g., n-hexane. No change in band shape was ob-

served on dilution. They concluded that the reason for not resolving

two Raman peaks, one for the completed iodine and the other for an

uncomplexed one, was the weakness of the charge-transfer interaction

between iodine and benzene, so that iodine could interact with more

than one donor. If the observed single Raman band for iodine in

benzene is due to the weak charge-transfer complex, then the weaker

charge-transfer complex of chlorine with benzene may exhibit the

same uniform change in vibrational frequency with dilution for both








Raman and infrared spectra.

SAfter reviewing these previous studies of complexes of halogens

with benzene, we see there is considerable conflict in the interpreta-

tion of the observations of infrared absorption of halogens in benzene.

In order to understand better the difference in the interpretations

of the spectroscopic phenomena associated with the complexes of halo-

gens with benzene, we decided to re-investigate the benzene-chlorine

system. We remeasured the infrared intensity of the complex of

chlorine with benzene under carefully controlled experimental condi-

tions, and also studied the infrared absorption spectrum of chlorine

in carbon tetrachloride, which is not expected to form a charge-trans-

fer complex with chlorine, in order to compare it with the one in

benzene. On the other hand, we re-examined the theory of induced in-

frared absorption more carefully. With the improved liquid structure

theory (51, 52) recently available, we applied the collision-induced

infrared absorption theory of Van Kranendonk (43) and Fahrenfort (44)

in order to determine whether intensities observed for chlorine in both

the benzene and carbon tetrachloride solutions could be explained

quantitatively by this theory alone, without any charge-transfer effect.

Secondly, we extended the work of Rosen, Shen and Stenman (29, 32)

by studying the Raman spectrum of chlorine in benzene-carbon tetra-

chloride solutions in order to understand better the nature of weak

charge-transfer complexes of halogens with benzene. There are three

reasons for our choice of chlorine instead of bromine or iodine for

the Raman work: (1) the complex of chlorine with benzene is much weaker

than a complex of iodine with benzene (6), so that the negative results

for benzene-iodine could be even worse for benzene-chlorine, (2) the








chlorine solution absorbs less of the Raman exciting line because the

solution is more transparent, so it could be observed easier in the

Perkin-Elmer LR-1 spectrometer, and (3) the infrared absorption of

chlorine is in a region which can be studied with less difficulty (13,

17) than for the benzene-iodine solutions.

We repeated the study of the ultraviolet spectrum reported by

Andrews and Keefer (6) for two reasons: first, we wanted to see if the

equilibrium constant of the complex of chlorine with benzene changes

with concentration of chlorine, since the Raman and infrared experi-

ments required a high.concentration of chlorine, while the equilibrium

constant obtained by Andrews and Keefer was presumably determined in a

dilute solution (they did not report their concentrations); secondly,

error analysis (53, 54) of the determination of equilibrium constants

for weak molecular complexes has shown that equilibrium constants as

small as that reported for chlorine with benzene cannot be determined

with any meaningful accuracy. For a complex with saturation function

(s, the fraction of completed Cl2 in the solution) between 0.01 and

0.1, the relative error in both the equilibrium constant and absorptiv-

ity (E) will vary between + 10 and + 100%, respectively (52a). It is

thus of interest to compare equilibrium constants obtained from these

three different methods (ultraviolet, Raman, and infrared spectra) in

order to see the order of agreement that can be achieved.













CHAPTER II


GENERAL EXPERIMENTAL PROCEDURES


Introduction

In this chapter we shall discuss the experimental procedures that

were common to all of the different spectroscopic studies. These in-

clude the discussion of the source and purity of-reagents, the prepara-

tion and handling of chlorine solutions, and the cells used, including

a description of the specially constructed infrared cells. In the

following chapters we shall then describe in detail the special experi-

mental procedures for each different (ultraviolet, Raman arid infrared)

spectral study.

Source of Reagents

The reagents used for all experiments in this work are listed in

Table I. All the solvents were used without further purification. How-

ever, these solvents did not have impurities detectable at the conditions

of our spectral studies. The two different grades of chlorine gas did

not show any differences in our spectra.

Preparation of Chlorine Solutions

The chlorine solutions for all the different spectral studies were

prepared in the same way. Chlorine gas was introduced into the solution

through a gas dispersion tube connected by Tygon tubing to a trap filled

with glass wool to filter any solid impurity and then to the flask of

chlorine. The flow rate of the chlorine gas was not regulated by a




















Material


TABLE I


SOURCE AND PURITY OF THE REAGENTS



Purity


chlorine gas


benzene and
carbon tetrachloride


chloroform


sodium thiosulf-ate
(Na2S203 5H20)



potassium iodate
(KIO3)



Potassium iodide
(KI)


research or ultra-high
purity grade


(1) spectrophometric grade (1)


(2) spectro-quality reagent (2)


analytical reagent


analytical reagent




analytical reagent




reagent grade


Source


Matheson Gas
Products


Mallinchrodt
Chemical Works

Matheson Cole-
man and Bell


Allied Chemical



Fisher Scientific
Company



Fisher Scientific
Company



Fisher Scientific
Company


deionized.


University of
Florida


water








regulator, but was controlled in such a way that the concentration of

the chlorine was around 0.1 M after bubbling Cl for five minutes,
2
around 0.2 M after 10 minutes, and so on. It may be safe to say that

this flow rate is about 5 bubbles per second. The bubbling process

usually took 5 to 30 minutes depending on the concentration desired.

As will be discussed in more detail later, the most serious difficulty

with the chlorine solution was preventing the formation of photochemical

product. Since this product does not absorb ultraviolet light nor

have Raman scattering in the same spectral region as does the completed

chlorine, a small amount does not interfere with those studies. How-

ever, it does absorb near the Cl-Cl infrared-absorption and the im-

purity is especially bothersome there.

The chlorine solutions were prepared under ordinary room lights,

and the flow rate adjusted as described above during the ultraviolet

and Raman experiments. With the experience gained from these two.

experiments, it was easy to work in the dark in order to prepare

chlorine solutions for the infrared experiments, where the photochemical

product interfered more seriously. However, when the solutions were

exposed to light, we could easily detect formation of large amounts of

photochemical product, since the solution would first become a little

cloudy, clearing again with time, because the product is very soluble

in benzene and in carbon tetrachloride. If this cloudiness was detected,

we would then discard the solution and use a freshly prepared one. In

the dark, we could monitor the solution by feeling the flask to detect

the solution heating up, since we believe that heating was always an

indication of extensive photochemical reaction.

Because of this well-known (55) photochemical reaction between








chlorine and benzene, occurring in daylight or under fluorescent lights,

it was necessary to keep the room as dark as possible. Actually, we had

found that the chlorine concentration in the benzene solution under or-

dinary fluorescent lights decreased by about 8% in 2 hours when the

stock solution was about 0.2 M. The reason for the decreasing concen-

tration of chlorine was partly due to the photochemical reaction, but

possibly was also due to chlorine gas escaping from the flask even

though the flask was stoppered. After evaporating benzene solutions of

chlorine that had been exposed to light, the solid residue was dissolved

in carbon tetrachloride. The NMR spectrum of this solution showed the

residue was mainly hexachlorocyclohexane (CH C1 6) because of the peak

at 4.7 ppm (see Fig. 1).

To make sure the Raman spectrum and the infrared spectrum that were

observed for the chlorine solution were actually due to the chlorine

molecule and not to any compound formed between chlorine and the sol-

vent, we removed the chlorine gas from the solvent after running the

spectrum either by bubbling nitrogen through the solution in the case

of Raman experiments, or by pumping out the chlorine gas (from the

solution in the cell) through a vacuum line, in the case of infrared

experiments. Following this treatment the spectrum of the clear

solution was then taken, so that absorption by the photochemical pro-

duct could be detected.

We have mentioned briefly earlier that the photochemical product

(C6H6C16) gives more serious problems for the infrared experiment. The
-l
absorption of the hexachlorocyclohexane near 510 cm could distort

the spectrum of chlorine by overlapping the two bands. Therefore, ex-

treme care is necessary to avoid exposing the sample to light. However,





















Q)

N

.Q
0
































0
QL


































S0 u
-H




0'-



















'-m
S-4
0


r*-










O





na
0r





0) .
(-1 *
(U














R M


N C0
, ooo

0 a


4.J* *n


S a <


*rc 0-a 0


0 r4
(-) P.4
4 *( 0
r-- ur
4-4 ri ofl


















Si
















it
.-







*I


o



































O
0

C4






0


















*
Ct

















O0


0




0








0


-3







one method which can inhibit the formation of C6 H6C6 was to add some

oxygen gas in the solvent before chlorine gas was introduced. Oxygen

was reported to be a radical quencher (56). Nevertheless, we could not

completely inhibit the photochemical reaction by this procedure.

Every chlorine solution was freshly prepared for each experiment.

The concentration of chlorine was determined by withdrawing a 5 ml

portion of chlorine solution from the stock solution and transferring

it into a prepared solution containing excess potassium iodide. The

iodine released by the reaction with chlorine was titrated with standard

aqueous thiosulfate. The analysis of this stock solution was done

before and after the Raman and infrared spectra were taken. As a check,

occasionally, a 1 ml portion of chlorine solution from the sample cell

was withdrawn after its spectrumhad been taken, and its concentration

was determined. The concentrations of the chlorine solutions in the

two cases (from the cell or from the stock) were not significantly

different, but the concentrations after the experiment were about 5-6%

lower than at the beginning.

Liquid Cells

We used a set of matched silica cells with a pathlength of 1 cm

for the ultraviolet spectroscopic study of chlorine solutions at low

concentration (about 1.0 x 10-3 M), and a silica cell with light path-

length of 0.1 mm for studying chlorine solutions of higher concentration

(about 1.0 x 10-1 M). The 1 cm ultraviolet absorption cells were rec-

tangular ones with ground-glass stoppers, while the 0.1 mm one was con-

structed with platinum and tantalum parts, with silica windows, and

assembled with teflon spacers. All of them were supplied by Beckman.

A standard 2.5 ml Raman liquid cell from Perkin-Elmer was used








for the Raman experiments.

.For the infrared experiments, specially constructed liquid cells

were made. In order to eliminate the solvent spectrum, we built two

fairly well-matched sets of liquid cells, one with a pathlength of 3 mm

and the other with 6 mm pathlength; potassium bromide windows (25 mm

in diameter and 3 mm thick) were used. Chlorine did not react very

rapidly with KBr in contrast with the solvent we used. This was tested

by placing the windows in the chlorine solution for one hour. They

did not show a significant change in their infrared spectrum from the

original KBr background. However, when we tried intentionally to -ex-

tend the window contact with the chlorine solution to 24 hours, the

baseline did change and we saw actual corrosion of the KBr salt plate.

We had tried to use AgC1 windows of 1.5 mm thickness, and found the

thin windows were too soft to resist the pressure difference on evacua-

tion of the cell.

The infrared liquid cell is shown in Fig. 2. The spacer was made

of teflon. Between the KBr window and the thick spacer, we

inserted a thin Teflon spacer in order to avoid damage by the rigid

contact with the KBr window and the Teflon spacer and in order to mini-

mize leaking of the chlorine solution from the cell. To prevent the

KBr windows from cracking when they were fastened by two brass tubes

to form the liquid cell, an 0-ring was placed between the brass tubing

and the KBr window. Finally, we compressed all these components by

the two outer brass plates, each with four drilled holes, and tightened

them with bolts. A hole of the exact dimension of the glass tubing

adaptor to the vacuum line was cut into the side of the Teflon spacer.

The filled 3 mm pathlength liquid cell contained 2.5 or 3.0 ml of

solution.















































*r-1

4r




cr



LD

4*
41 41- 0


O -0
cd


000 I 0C

04 wa00m r-44
o o 00



1 Cd CO 4 rid -
E r-1 0 w r0)


C
0
*r-i cl cn o
o o-^

tfl
6 d















CHAPTER III


ULTRAVIOLET SPECTROSCOPIC STUDIES
OF CHLORINE IN BENZENE SOLUTIONS


Experimental Procedures

The ultraviolet spectrum of the complex of chlorine with benzene

dissolved in carbon tetrachloride was studied as a function of benzene

concentration at two different chlorine concentrations, one on the order

of 0.001 M, and the other in a short path cell (0.1 mm) for solutions

around 0.1 M. Five different benzene-carbon tetrachloride mixtures

were prepared, ranging from pure benzene to pure carbon tetrachloride,

and the chlorine was dissolved in each.

For the chlorine solutions with concentration around 0.001 M, a

fairly well-matched set of silica cells was used in the spectral

studies. Before any solution was prepared, the Cary Model 15 ultra-

violet spectrophotometer was turned on and allowed to warm up. At

this point, we started preparing 50 ml of aqueous potassium iodide

solution (containing 2 grams of KI) necessary for the titration of the

chlorine solution, and the different preparations of solvent needed

to dilute the stock chlorine solution. The chlorine solution around

0.1 M was prepared as described in Chap. II. The time was recorded

when a 5 ml stock solution was pipetted into the flask containing excess

potassium iodide solution; immediately following, we pipetted a 10 ml

stock solution into a 125 ml flask containing 90 ml of the same solvent.

This solution was diluted to 1/10 the original concentration by adding








10 ml of this solution to a 125 ml flask containing 90 ml of the sol-

vent.* Three more dilutions were made to form three different final

solutions ranging in concentrations from 0.0005 M to 0,0001 M in

chlorine, each with final volume of solution around 60 ml. Each flask

containing a chlorine solution was stoppered properly with a glass

stopper. At this point, we recorded the baseline of the solvent vs.

solvent with the double beam spectrometer. The spectrum (from 320 to

250 nm)' of each chlorine solution was then recorded, proceeding from

higher to lower concentration, recording the time at the beginning of

each spectrum. We repeated each measurement at least three times,

proceeding from higher to lower concentration by refilling the sample

cell solution from the flask. When all spectra were obtained, the

chlorine stock solution already added to the potassium iodide solution

was then titrated.

Spectra of chlorine dissolved in pure benzene for several different

concentrations of chlorine (each studied as a function.of time) are

shown in Fig. 3. The time interval between recording any two successive

spectra of the same solution was about 20 minutes. The concentration

of chlorine indicated for solutions A, B, and C are the values deter-

mined by titration of the stock solution, combined with the known

volume ratios on dilution, but those values are probably not correct

concentrations for the solutions at the time the spectra were taken.

From measurements of the baseline (D in Fig. 3) before and after all

spectra of the chlorine solutions were taken, we notice that the

spectrum is not reliable below 280 nm, where absorption by pure benzene

in the sample and reference beams reduces the signal to zero. Each

sample spectrum shown in Fig. 3 was measured in a fresh solution formed








by refilling the sample cell from the flask as described above. The

decrease in absorbance of each chlorine solution with time (for

example, from A-l to A-3) was most probably due to the changing

chlorine concentration, not because of the photochemical reaction

between chlorine and benzene (in such dilute solutions), but rather

because of the escape of the chlorine gas from the solution into the

vapor phase in the flask.

The normalized absorbance at 280 nm (defined as the observed
0
absorbance A divided by the concentration of chlorine CA) of each

chlorine solution was plotted as a functicnof time. The functions

were quite linear as can be seen in Fig. 4. There is a considerable

uncertainty in the extrapolated values of the normalized absorbance

at time zero because of the long extrapolation. The non-uniform

slope for different chlorine solution plots could be due to the diffi-

culty in defining uniquely the procedure for handling the chlorine

solutions. When we repeated some measurements for one chlorine solu-

tion from freshly prepared solutions, a different slope of the plot

was obtained. The best least-squares line through the data in Fig. 4

was used to obtain the extrapolated values of A /CA at time zero. The

results are shown in Table II. These values are then analyzed by the

Benesi-Hildebrand or Scott method (as described below) to obtain the

formation constant K, and the molar absorptivity e for the complex.
280
For the more concentrated chlorine solutions (around 0.1 M), we

used a single silica cell (described in Chap. II) of 0.1 mm pathlength,

measuring against air as the reference. Since these solutions were

prepared directly without successive dilution as described before, we

modified the procedure slightly from the one previously described.

























Fig. 3. --


Ultraviolet spectra of chlorine in benzene taken at
different concentrations and at different times.
(A) 0.00053 M, (B) 0.00027 M, (C) 0.00013 M (all in
C12), (D) baseline; (1), (2), and (3) are the order
of successive measurements on fresh solutions (see
text).
















4... \


I- ,, 1
I



S\
4i


(C)


/


-' \


(3)

Nt.\ (1)



Ss-- (2)
.. (3)


before any spectrum was taken

(D) e
./ after all spectra were taken
.-*


I[ --- "


260


280


WAVELENGTH (nm)


\\


\ "9'


0.2 L


0.0


\\\

~\


q


~


~


N


320































C>
00
0





44 O
oo
o






0g 0
o
00




a
$4-H >f > >










U Q 0 0
0 0






0 0 0 0

0 u0





0- 4 '0 '0
0000
0 U0


















04
C)4
*w : i
60l~9OO
Tl ~ r)~







































































0


( C-OTx) aNV IOSWV QaZITIVWr ON













TABLE II


EXTRAPOLATED VALUES AT TIME ZERO OF
THE NORMALIZED ABSORBANCE (A /CA) FOR
DIFFERENT CHLORINE SOLUTIONS


Concentration of
Benzene (M)


11.30


9.03


6.78


Extrapolated Valuesa
Absorbance at 280 nm


of Normalized
(Ac/CA) x 10-


2.47


2,09


1.68


1.19


0.57


4.52


2.26


a. Values obtained from the intercept (in Fig. 4) of the best least-
squares line. The uncertainty of each value is + 4% (twice the
standard deviation).







This time the concentration of chlorine in the cell could be determined

at a time much closer to that of the spectral measurement since the

concentration was high enough to be accurately determined. When the

sample cell was filled up each time with the syringe and placed in the

sample compartment of the spectrometer for the measurement, a 5 ml por-

tion of the chlorine solution was withdrawn within one minute and

pipetted into the flask containing excess potassium iodide solution.

The measurement was repeated three to four times with fresh solutions

from the flask. As before, we measured the baseline before and after

the sample spectrum was obtained. Three spectra of chlorine solutions

of different concentrations in a 30% (v/v) C6H6, 70% (v/v) CC4 solvent

are shown in Fig. 5. The spectrum A was for a 0.105 M chlorine solu-

tion, spectrum B for 0.053 M chlorine, and spectrum C for a 0.026 M

chlorine solution; spectra D were taken of the solvent in the cell

before and repeated after the spectrum of one of those chlorine solu-

tions was measured. A replotted.spectrum for 0.027 M chlorine solution

in a 30% (v/v) C6H6, 70% (v/v) CC4 mixture is shown in Fig. 6. The

spectrum is uncertain below 275 nm due to solvent absorption, so that

a clear determination of the wavelength of maximum absorbance cannot

easily be made, although it appears from Fig. 6 to be near 275 nm.

Analysis of the Ultraviolet Spectroscopic Data from Chlorine-Benzene
Solutions

The data at 280 nm from both dilute and concentrated chlorine

solutions were analyzed using the Scott equation (14),


CAC /A = C/E280 + 1/KE280 (3-1)


Here Z is the pathlength in cm, CD is the initial donor concentration
























Fig. 5. --


Ultraviolet spectra of chlorine solutions in a 30% (v/v)
CH6 and 70% (v/v) CC1I solvent. (A) 0.105 M, (B) 0.053 M,
( ) 0.027 M in C12, (D) baseline (solvent vs. air) path-
length = 0.1 mm.























































0.0


300


WAVELENGTH (nm)




















0.2











0.1










0.0


260


275


290


320


WAVELENGTH (nm)




Fig. 6. -- Replotted spectrum of 0.027 M chlorine solution in 30%
(v/v) C6H6 and 70% (v/v) CC14 mixture (0.1 mm path-
length).


-1 I' ~-----I







0
(M), CA is the initial acceptor concentration (M), Ac is the absorbance

of the complex at 280 nm, e280 is the molar absorptivity of the complex

at 280 nm and K is the equilibrium constant. We assumed the absorption

at 280 nm is due to the charge-transfer absorption of the one-to-one

complex of chlorine with benzene. The reason absorbance at 280 nm

is studied is because that wavelength is the closest to the maximum

absorbance that can be studied before the solvent absorption becomes

too great.

For the data obtained from the dilute solution in the 1 cm path-
0
length cell, we used the extrapolated values of Ac/CA at time zero

(Table II) for the Scott plot, while for those obtained from the con-

centrated solutions in the short (0.1 mm) pathlength cell, we used the

direct absorbance readings and concentrations for the plot. At the

same time, we re-analyzed Andrews and Keefer's ultraviolet data (6)

by the same Scott plot. The three different sets of the ultraviolet

data were plotted on the same graph, and shown in Fig. 7. The error

bars for points obtained from the long pathlength cell were estimated

from the standard deviation of the least-squares fit to the extrapola-

tion plot (Fig. 4), and from the uncertainty involved in the concentra-

tion determination. The error bars for the points obtained from the

short pathlength cell are the standard deviations of three to four

repeated measurements. There was no way to estimate the uncertainties

from Andrews and Keefer's data since they did not report their experi-

mental conditions.

From Fig. 7 we can say that for chlorine solutions of low concen-

tration in chlorine ( 0.001 M) the agreement between Andrews and

Keefer's result and ours is quite good. In particular, we have the















6.0 -








-"
0<-





o(.

2.0








0.0 I
0.0 5.0 10.0


0
CD (M)






Fig. 7. -- Scott plots of the complex of chlorine and benzene.
O and for 1 cm pathlength, D and --for 0.1 mm
pathlength cell, A and -- for Andrews and Keefer's
data (Ref. 6).






35





^*s


Boo o
4 uoo 0
00
0 t 0


8 +1 o a
0 o U )
o0 0 0 d
Ss -~- i. 0
S. w 0 *+-4




oQ 'I
O E4 41-C o



H C- 44
r-4 C
0 0
M a m

Q b .0 0
O 0 -t 00 0
[ Cto oou
0 60 aa ,t t
44 C s r-O Cn r-i
E- O a



M oo i4
W4 0 0
1 W40 0a ,o + 0 *-



M O 0- 1 *4 44


pu a *- oc +4
0 0 H N P4 (1 )





O E- E -'4-
.aO e N 3
cMoo ( >C < o >

COa

4. a 414
0 U 00 4J T* 0
OE- 00 0 H- 4

O 00 00 ar C
d N ** C
i-3> 00 C 1-4
> 3 u cun + co U m
M ( r-H +1 0 N N 0 0)
C0 6 N c
04 00 rl 0 r-1
0 N r1 O H)

E-O0l -4
rM 4-4 00
Cn *-4 a 1

U S


I 0
I I MH




0 N) ao U ) C

Ii C-)N N 0 00
0 0 0 E EH 01







same intercepts of the straight lines which determine the product K280

The difference between the plots of the low and the high concentrations

of chlorine solutions may not be significant even though the factor of

the activity coefficients for solutions of different concentrations

could be different (57). However, the experimental uncertainties

were so large, we are not in a position to give any definite conclu-

sions about this point.

The values of Ke280, K, and E280 from the Scott plots for the

three different sets of ultraviolet data from chlorine solutions are

shown in Table III. For each set, the constants were calculated from

the best least-squares line. The upper and lower limits of uncer-

tainties listed for each constant were twice the calculated standard

deviations.

Despite the fact that the experimental uncertainties were large,

the equilibrium constant K of the chlorine-benzene complex is believed

to be 0.025 + 0.015 liter mole-1. The large uncertainty in the value

of K is also expected theoretically (53, 54). Nevertheless, the

order of the magnitude of K indicates this complex is indeed a very

weak one. It is worthwhile to note that the saturation fractions

(defined as s = Cc/CA, where CA is the concentration of completed C12)

are between 0.1 to 0.25 in benzene for the above K values.

It has been suggested by Deranleau (54a) that the Scatchard plot

is a better method for the analysis of spectral data from weak molecu-

lar complexes. In order to check the reliability of the values ob-

tained from the Scott plot, we also used Scatchard's method to analyze

the short pathlength ultraviolet data and Andrews and Keefer's data.

The reason for not analyzing the long pathlength cell data was








because the values of the parameters Ks280,' 280' and K of this system

were within the range of those obtained from the short pathlength

cell data, and those from Andrews and Keefer's data.

The Scatchard equation is given (54a) by

0 0
A /CCD = K(280 Ac/C) (3-2)
c AD 280 c A

0
Here CD is the equilibrium concentration of the donor, (C = CD, the

total concentration of the donor for solutions with excess donor), k,
O
CA, Ac K and E280 are the same as defined for Eq. 3-1. We calculated
o o o o
Ac/ACCD and Ac/RCA for each CA at a particular CD and plotted Ac/kCACD
0
vs. A /ZC for the five different values of C The results are shown
- c A D

in Fig. 8. For the 0.1 mm (short pathlength) cell data, we obtained
0 0 0
the average values of A /CACD and A /kCA by averaging all A /CACC
C A D A c A D
0
and A /AC values, respectively, at each C The error bars in Fig.8
c A D
were obtained from the scatter of the measurements about the average
o o
value. There were five sets of (A /C ACD, A /CA ) values at each of
c AD' c A
the five different C values. We estimated K and K280 from the slope
D 280
and the intercept of the best least-squares line through these points.

We applied the same technique to analyze Andrews and Keefer's data

to estimate K, KE278 and E278. The calculated parameters of the

Scatchard plots are shown in Table IV. The upper and lower limits

were twice the calculated standard deviations.

When we compare Table III and IV, we see that the values of KE ,

K and e are not significantly different. Again, the value of K from

the short pathlength cell may be lower than the value from the more

dilute solutions. However, a line can be drawn through the error bars

for these data (Fig. 8) that includes the value of K from the long













3.0









2.0
C"







1.0








0o 1 I I I
0 5.0 10.0 15.0 20.0 25.0


A /ICA (x 102)
c A









Fig. 8. -- Scatchard plots for the complex of chlorine
with benzene. (1) 0.1 mm short pathlength
data; (2) 0 from Andrews and Keefer's data













TABLE IV



VALUES OF Ke K AND E FOR
v v
CHLORINE SOLUTIONS FROM SCATCHARD PLOTS


Parameters


Short Pathlengtha
(0.1 mm)


228 + 8


b
Andrews and Keefer


269 + 12c


0.0064 + 0.0048c



35,000 + 100,000c
16,000


0.034 + 0.01c



7,300 + 4,400
1,300


Evaluated at v = 280 mm.

Evaluated at v = 278 mm.

The upper and lower limits were twice the calculated standard
deviations.


_ _





40

pathlength studies. We conclude that the value of Ke is 280 + 40,
280
with K = 0.025 + 0.015 liter mole-1 and E280 = 13,000, possibly from

values as low as 5,000 to values as high as 35,000 liter cm-lmole-.

In concentrated solutions, K may possibly be somewhat smaller. It

is not possible to reach more definite conclusions about these values

from this very weak complex (54).











CHAPTER IV


RAMAN SL'ECTlOSCOP'IC STUDIES
OF CHLORINEE IN BENZEIJE SOLUTIONS


Introduction

We are particularly interested in studying the Raman frequency

shifts and the Raman intensity change of chlorine in solution as the

composition of the solvent is gradually changed from benzene by the

addition of carbon tetrachloride. The spectral profiles of the CI-Cl

stretching vibration as a function of the composition of the mixture

C6H6-CCI4 were carefully examined in order to understand more about the

nature of the complex of chlorine with benzene. As a check of the

reliability of the equilibrium constant of the complex determined from

the ultraviolet spectroscopic measurements, we analyzed the Raman in-

tensity data both by the method of Rosen, Shen and Stenman (32) to

estimate the equilibrium constant and also by the method of Bahnick and

Person (58). The absolute Raman intensity of chlorine in carbon tetra-

chloride was carefully determined.

Experimental Procedure

For this study, a Perkin-Elmer LR-1 Raman spectrometer was used with

a Ne-He laser with a minimum out-put of 2.7 mw. The Raman shift (A cm-)

is proportional to the grating position read in mechanical units (called

drum numbers) from the linear spectrometer scale. The actual Raman

shift was obtained from a calibration curve of wavenumbers vs. drum

number using the known wavenumbers of the emission lines of a Ne lamp.

41






-l
Three lines at 650.669 nm, 653.308 nm and 659.918 nm (or 433.1 cm ,

495.1 cm and 648.5 cm from the Raman exciting line at 15,802.7 cm

or 632.8 nm) were chosen for this purpose because they had been well

studied (59). The Ne lamp source was a Pen-Ray quartz lamp operated

with a 115 volt 60 cycle/second power supply (Model No. SCT2, with

maximum current of 4 amperes from Ultra Violet Products, Inc., San

Gabriel, California). In practice, we placed the lamp in the sample

cell position in the sample compartment of the Raman spectrometer,

opened the mechanical slit to 5 microns and recorded the spectrum just

as though we were making a Raman measurement except the laser was not

turned on. As mentioned in Chap. II, the standard Perkin-Elmer 2.5 ml

multiple-path cell was used.

Because of the chemical instability of the chlorine solution, it

was desirable to work with low chlorine concentrations (around 0.1 M)

and to scan the spectrum quite rapidly. In order to obtain a spectral

resolution of 7.5 cm-1 at a 5% peak-to-peak noise level, the spectral

scan rate was about 6 cm- per minute, or 15 to 20 minutes to measure
-1 -I
a complete chlorine Raman spectrum from 480 cm to 600 cm.

Before studying the Raman spectra of chlorine solutions, we investi-

gated the solvent background in the region where the Raman band of

chlorine would appear. The Raman spectrum for the solvent mixture

of C6H6-CC14-CHC13 in a 6:3:1 ratio is shown in Fig. 9. The Raman

shift for chlorine is expected to appear between the two bands (vl of
-l
carbon tetrachloride at 461 cm on the low frequency side and v18 of
-lo
benzene at 606 cm- on the high frequency side) with only slight over-

lap with these two solvent bands. Nevertheless, that overlap results

in the loss of most of the spectral information from the wings of the






























O

O
*l

















CI
-t









r-4
o




0


*r
!4
0




















a-'
TXJ
3:






re
ul








M-












































































0 o o 0 0
co 0 -It C4


SlINfI av1mIaxv








chlorine band. The extent of the overlap of the chlorine band with the

two solvent bands is shown in Fig. 10, where the spectrum was obtained

from a 0.12 M chlorine solution in the mixture of C6H -CCI -CHCI3 at a

ratio of 8:1:1.

Secondly, since we knew that it was very difficult to prevent the

photochemical reaction from occurring, especially when the chlorine

solution was irradiated by the laser in order to obtain the Raman spec-

trum, we studied the Raman spectrum of the photochemical product

(C6H6C16) in order to determine its interference with the chlorine

band. We found that the hexachlorocyclohexane (and also any other

unidentified photochemical products) did not have any observed Raman

shift near the chlorine band. This was done by an experiment in which

we let the chlorine solution (around 0.5 M) in a 6:4 C6 H-CC14 mixture

stand under the fluorescent room lights for several hours before tak-

ing the Raman spectrum of the solution. Afterwards we eliminated the

chlorine by bubbling N gas through the same solution (but not from

the sample cell solution) and measured the Raman spectrum of the result-

ing chlorine-free stock solution. We knew that the photochemical pro-

duct did form in the experiment, since the solid residue after evaporat-

ing the solvent was dissolved in carbon tetrachloride and the NMR spec-

trum showed its existence. The Raman spectrum of this particular

chlorine solution (approximately 0.5 M) in the C6H6-CC14 mixture at a

ratio of 6:4 is shown -in Fig. 11. The Raman spectrum of the chlorine-

free stock solution at the same experimental condition is shown in

Fig. 12. The apparent reduction in the Raman intensity, both for v18

of benzene and v of carbon tetrachloride bands in the chlorine solu-
tion (Fig. 11) compared to the intensities in the colorless solution
tion (Fig. 11) compared to the intensities in the colorless solution




























Cr

r-4
U



U
I


.0
0

*-4
U







cc

o
"- 4)-
0 *
o


4-1
0


4-h
11)1
0 "
s*


CM
e-4
* 0

0K
0 l
I- -
I
e





























































SIINI xiw ) ImIv









100%






80%







S60%7
E-4






40%


Si8 of C6H6



20% C_ 2
band





0%
579 490

RAMAN SHIFT (A cm-1)





Fig. 11. -- Raman spectrum of 0.5 M chlorine in 6:4
C6H6-CC4 .








(Fig. 12), is most probably due to the absorption of the existing or

scattered light in the dark-colored solution. Within the experimental

error we can say that there is no observable Raman band due to photo-

chemical products in this spectral region (between v of CC4 and v18

of C6H6).

At this point we were ready to measure the Raman spectra of chlorine

solutions. We warmed up the spectrometer for one hour. During this

period, we prepared 100 ml of solvent, which always contained 10 ml of

chloroform. When the spectrometer was ready, we bubbled chlorine into

the solvent for 5 minutes (to prepare a solution about 0.1 M in

chlorine). A 5 ml sample of the chlorine solution was withdrawn for

titration and the Raman liquid cell was immediately filled with the

chlorine solution and placed in the spectrometer. After the Raman

spectrum of that chlorine solution was recorded, a 5 ml sample of solu-

tion was again withdrawn from the stock solution for concentration

determination. We also determined (once only) the chlorine concen-

tration for some solution taken directly from the Raman cell after its

Raman spectrum had been recorded. The result was the same as the

concentration from the stock solutions within the experimental error.

The depolarization ratio (p) of the Raman band of chlorine was

measured for three different chlorine solutions (one of chlorine in

pure C H6, one in a 1:1 C6H6- CC14 mixture, and one in pure CC14). The

concentrations of these chlorine solutions were not determined but they

were believed to be around 0.2 M. For these measurements, we used an

Ahrens prism placed between the sample housing and the monochromator

as described in the Perkin-Elmer manual (60). The spectral resolution

was the same as before. The intensity of the parallel component was








100%






80%


60% L


40%


20%






0%


Fig. 12. --


V18

of


C6H6


CCl
4


I I


579

RAMAN SHIFT (A cm-1)







Raman spectrum of the chlorine-free 6:4
solution.


490


C6H6-CC14
6 6 4


- ---- ------- ---- ---








measured first by adjusting the experimental parameters so that the

maximum Raman scattering of this component was around 70% on the

chart paper scale. (We did not turn the gain higher because we

wanted to keep the peak-to-peak noise level less than 10%.) Then we

measured the intensity of the perpendicular component. In order to

compensate for the fluctuation of the laser power and the change in

chlorine concentration during the measurement, we measured again the

intensity of the parallel component immediately after we had measured

the perpendicular one. To obtain the depolarization ratio, we divided

the band area of the perpendicular component by the average band area

of the two measurements of the parallel component. Because the Raman

band of chlorine was weaker as more carbon tetrachloride was added to

the solvent mixture, the peak-to-peak noise level was higher for Cl
2
in CC1 As we tried to increase the amplifier gain in order to obtain

a comparable signal for different chlorine solutions, the depolariza-

tion ratio of the Raman band of chlorine had larger uncertainty (for

solutions containing more CC1 ). In particular, the noise level was

so high that the intensity of the perpendicular component could not

be measured with certainty for the chlorine solution in pure carbon

tetrachloride. Hence, only an upper limit can be given for p for Cl
2
dissolved in pure CC1 .

Results of the Raman Measurements on Chlorine Solutions
-1
The Raman shifts (in cm ) observed for chlorine solutions are

shown in Table V as a function of the benzene concentration. The
-1
values listed here are believed to be accurate within + 0.5 cm and

were obtained from the positions of the band maxima. The concentration

of benzene was estimated from a knowledge of the volume of benzene













00
J C H -







41

'rC





OH 000 0 0 0 0
Sq r-i
OH 44 C oc o C)
1 HC) +1 +1 +1 +I +1 +1 +1

U W ( *

u r- rr-rr r r4

ELH-4O
H z

HE



IO c
44

C1s 4' cfC .0 P r 0 l

Co 00
Ho co o o o vi o :
m + + 1 +1 +i



* m O 6


H H <

H 4 h
M En 4J
1 o 0
I 0 0
EI "- 0 -

cU3 H c 00. C' 1o o rC1 o L N m
z M cS 0 C 0'4 0 C4 Cf Q0
HH (0 *0






E- C,)
S( c o 0 Z p C



03



H
Cd
414


O H
0 0
4- a 0 e
0 E


u0 -c N cm '
t 4 rl J0 r* *5 01 CM i







added, and the total volume of the solvent. The concentration of pure

liquid benzene was taken to be 11.3 M at room temperature. The concen-

tration of benzene in the solvent mixture was calculated by multiplying

this number by the volume fraction of benzene in the mixture (assuming

no volume change as benzene was dissolved in CC1 ).

-i
At our rather poor spectral resolution of 7.5 cm we could not

observe (for any solvent mixture) two clearly separated Raman peaks,

one for completed chlorine and the other for the uncomplexed molecule,

so we examined the spectral profile of the chlorine band as a whole.

The half-band widths of the chlorine solutions were measured and are

also shown in Table V. The corresponding values are plotted vs. the

concentration of benzene in Fig. 13, where we see clearly the broaden-

ing of the chlorine Raman band that occurs as the ratio of C6H6 to CC14

approximates 1:1. This behavior may be an indication of two overlapping

bands, one for completed chlorine and the other for the uncoriplexed

chlorine.

The relative integrated intensity IR(v) of the Raman band of

chlorine was defined as given by Bahnick and Person (58),


I =I/I M
R(v) V RlefM (4-1)


Here I is the band area of the chlorine band, I is the band area
v Ref
-l
of the 366 cm chloroform reference band (an internal standard, always at

10% by volume), and M is the total molar concentration of chlorine.

The band area was measured by a planimeter (Keuffel and Esser Co.).

The most difficult thing in defining the band area was the decision

on how to draw a baseline. We estimated by different assumed baselines
















C4
S20.0 ---T--f --- p
iI 20.0 -



15.0 -



S 0.0




5.0



0.0
5.0 10.0

CD (M)






Fig. 13. -- Plot of the Raman spectral half-band width of
chlorine vs. the concentration of benzene (C ).







that the choice of the baseline might lead to an uncertainty of + 5-10%

in band area. In general, we drew a baseline through the average back-

ground noise level in the two wings of the band. The relative inte-

grated intensities obtained according to Eq. 4-1 for chlorine solutions

are shown in column 5 of Table IV. The corresponding values of I
R(v)
are plotted in Fig. 14 as a function of benzene concentration.

The uncertainties in the values of the relative intensities of

chlorine were estimated by propagation of errors. From Eq. 4-1 the

relative error is given by

2 2 -2 1/2
61R() /I = [(I /I ) + (I /I +(6M/M)
R(v) R(v) v v ref ref
(4-2)
From the scatter in measurements, we estimated that the individual

error is + 4.3% for (61 /I ), + 6.8% for (Iref/Iref) and 4.6% for

(6M/M), so that the uncertainty in the relative intensity (I6R /IR()
R(v) R(v)
was then found from Eq. 4-2 to be + 9.3%.

From Fig. 14 we see that there is a drastic intensification of the

relative Raman intensity of the C1-C1 stretching vibration of chlorine

as the solvent is changed from pure CC4 to pure benzene. The en-

hancement in intensity is found to be approximately by a factor of 5

based on a total chlorine concentration or by a factor of 20 based on

the concentration of completed chlorine. (Note: The fraction of

chlorine in pure benzene solution that is completed is about 0.2 of

the total concentration, based on a value for the equilibrium constant

of 0.03 liter mole-1.) There appear to be only two possible explana-

tions for this dramatic intensity increase -- one due to the non-

specific solvent effects and the other due to the effects from the

formation of the charge-transfer complex. A more detailed discussion

























Fig. 14. --


The relative Raman intensity of chlorine IR(v)
as function of the benzene concentration
(M).


E3 Measured values


Calculated values from K and I determined
fTom Rosen plot and measured value of
IR(v)

















15.0











10.0


5.0


0.0


0.0


C (M)


5.0


10.0








will be given in Chap. VII.

Rosen, Shen and Stenman (32) have derived an equation which can

be used to analyze the Raman spectroscopic data from the complex, which

may not necessarily be a charge-transfer complex. Their equation was

derived from a statistical mechanical treatment assuming that the

properties of the acceptor are a statistical average over all possible

configurations between acceptors and donors weighed by an appropriate

distribution function. For a one-to-one complex, the Benesi-Hildebrand

type equation for Raman intensity data of the acceptor was found by

Rosen, Shen, and Stenman to be

I 0 a
/[(IR IR()] = BIRK B + I/IR (4-3)


Here I is the total relative intensity of the Raman band of the
R(v)
acceptor at some particular donor concentration, I is the relative
R(v)
intensity of the acceptor Raman band at zero donor concentration (i.e.,

the pure CC4 solution), PB is the molar concentration of the pure donor,
0
PB is the molar concentration of the donor in the solvent mixture, IR

is the Raman intensity statistically averaged over all possible orienta-

tions of the one-to-one interactions between donor and acceptor, and
I 0
K /pB ( = K) is the statistically averaged "equilibrium constant" over

all the one-to-one interactions.

In applying Eq.4-3, we assumed that only one-to-one interactions

between chlorine and benzene have a significant effect on the Raman

spectrum. Using the relative Raman intensity data for chlorine in

this system, reported in the last column of Table IV, a plot of Eq. 4-3

is shown in Fig. 15, where the error bar for each point indicated the

uncertainty of the measured relative Raman intensity of chlorine. The




































Vi-

0
o




0






o.






v
) 0













H


O C
;>
o ,









L, r










H
60
4 1


(Ur













*~
C>
FrH






60




















o



o
o











a







-4
IW---I








o



-*0-1











I I I. I
a


*
o o 0 0 0




I







0
constant IR is found from the intercept of Fig. 15, by a least-squares

+ C
fit to be 54.7 3 7 (the upper limit is undefined because the standard

deviation is larger than the magnitude of the intercept), and the con-
I o 0
stant K IR/PB is calculated from the slope to be 1.2 + 0.15. Taking
I o
the ratio, we estimated that the equilibrium constant K (= K /pB) is

0.022 + 0.055 liter mole-1 (the lower limit is undefined because the
0.02
O
upper limit of I is undefined). The undertainties here are the
R
standard deviations. Even though the uncertainty in K is large, its

value (0.022 liter mole-1) is almost identical with the equilibrium

constant determined from the ultraviolet spectroscopic measurements

given earlier in Chap. III.

In order to gain some confidence in our measured relative Raman

intensities of chlorine in different benzene solutions, we substituted
0 I 0
the values found here for IR and K /pB back into Eq. 4-3 together with
1-1
the measured value for I (2.75 liter mole ) to obtain values for
R(v)

IR(v) vs. PB to be compared in Fig. 14 with the measured values of

IR(v). Comparing these calculated values of IR() 's with the observed
RR(v)

ones, we see that the measured I ('s are reasonably good.
R(v)
Earlier, Bahnick and Person (58) had derived a different expression

for the analysis of the Raman spectroscopic data of a complex to obtain

the formation constant. By analogy to the derivation of the method

for analysis of ultraviolet spectroscopic data by Tamres (61), they

obtained an equation for a one-to-one complex (assumed to be in a

particular configuration):
1 I 0 1
pB/R(v) -R(v =(P + CA -C)/[I IR + /KR R(v)
R (4-4)

e I ), a the same as hose defined fr E. 4-3
Here I -R I -R(W I are the same as those defined for Eq. 4-3; p B is
K^V/ K.W/ RB







0
still the molar concentration of the donor and C is the total molar
A
concentration of the acceptor, while C is the molar concentration of

the complex (or the molar concentration of the completed acceptor for

the one-to-one complex). The difference between Eq. 4-3 and Eq. 4-4

is that the former is equivalent to the Benesi-Hildebrand equation (2),

while the latter is similar to the Scott equation (14).

In order to apply Eq. 4-4, a trial value of K has to be assumed,

and C is then computed for each solution. The left-hand side of Eq. 4-4

is then plotted vs. (pg + CA C), and the best straight line is

fitted to the points by least squares. The value of K calculated from

this line was used to recompute C and so on until K converges to a

constant value (for more detailed procedure, see Ref. 58). Since C for

the complex of chlorine with benzene is very small (since it was found

from the ultraviolet spectroscopic data that the equilibrium constant
0 0
was very small), (pB + CA C) is almost equal to (pB + CA), so we

used the value of K (0.022 liter mole-1) obtained from the plot of

Eq. 4-3 to calculate C and then made a least-squares fit to the points
0
calculated. The formation constant K and the values of I were then

estimated from this best straight line (as shown in Fig. 16) to be

0.034+ 0.045 liter mole-1 and 38.9 180.0 respectively.
0.03 15.0
Thus both methods for analyzing the Raman intensity data gave

almost the same equilibrium constant K for the complex of chlorine with

benzene and nearly equal values for the relative molar Raman intensity
0 0
IR for the completed chlorine. The slight differences in K and IR

obtained from the two methods could be due just to the differences

between the two procedures (Benesi-Hildebrand and Scott), since the

two methods weigh the experimental points differently.








The results of the depolarization ratio measurements (p) for the

C1-C1 stretching vibration measured in these different chlorine-

benzene solutions are shown in Table VI. p was estimated from the ratio

of the band area of the perpendicular component to that of the parallel

one. As mentioned in the experimental procedures section, the perpen-

dicular band of chlorine in carbon tetrachloride was weak and the

noise level was so high that it was impossible to obtain a reliable

value of p in this solvent. We believe these results show a tendency

for the depolarization ratio to increase as the benzene concentration

increases, possibly because more chlorine molecules are completed as

more benzene is added. However, we cannot make a definite conclusion

about whether any real increase in the depolarization ratio occurs as

benzene is added, since the value of p for chlorine in carbon tetra-

chloride could not be determined accurately. In order to give some

indication as to what the value of p for chlorine in carbon tetrachlo-

ride might be, we listed the gas phase value in Table VI.

Absolute Raman Intensity of Chlorine in Carbon Tetrachloride

It is possible to obtain the absolute Raman intensity and hence

the values of the average polarizability derivative a' and of the

anisotropic polarizability derivative y' from the measured relative

Raman intensity. This had been demonstrated first by Bernstein and

Allen (62) and confirmed later by Long, Gravenor and Milner (63). In

order to calculate a' and y' we have to know both P (which will be

defined in the following) and the depolarization ratio p of the band

at v. Bernstein and Allen (61) showed that a standard intensity P

(for a Raman band at v) of a compound could be defined by comparing





























- 2.0
I-i


1.0
C-4



0.0
0.


I


0


5.0


10.0


0
(pB + c C)


Fig. 16. --


I 0
Plot of p /[(I R( I ()] vs. (p + C C) for
Eq. 4-4.) B A
Eq. 4-4.


_~I ~I III(_~~
















TABLE VI


DEPOLARIZATION RATIO OF
CHLORINE IN DIFFERENT CHLORINE SOLUTIONS


Concentration of
Benzene (M)


11.3


Depolarization
of chlorine


0.27 + 0.03


0.25 + 0.04


< 0.22c+ 0.04


5.65


gas phase


0.14


a. p = band area of perpendicular component divided by band area of
parallel component.

b. In carbon tetrachloride.

c. It was difficult to measure the perpendicular band of chlorine
in this solvent with certainty, so the upper limit is listed
(see text).


d. See Ref. 63, 64, 65 and others.


(p)a








this band with the measured intensity of the.459 cm- band of carbon

tetrachloride in the pure liquid:

s [ 2 ,2 compound '2 ,2 CC14
P = [45a + 7y 2 /45a + 7y ] (4-5)
Vv 459
,2 (2 CC1
By taking arbitrarily the value of [45a + 7y ] 4 to be 1,
459
s -1
PS of the v = 366 cm- chloroform band was estimated to be 0.28 by Long
v
Gravenor and Milner (63). From our measurement, we obtained the rela-

tive molar intensity of chlorine in carbon tetrachloride with respect
-1
to the 366 cm band of 1.25 M chloroform to be I = 2.75 + 0.26 (as
R
given in Table V Analytically, this means that

[ 2 ,2 C12 ,2 ,2 CHC13
[45a + 7y ] /[45a + 7y ]3 =
543 366

(2.75 + 0.26) x 1.25 = 3.46 + 0.30 (4-6)


From the value of PS for chloroform (63) and the results in Eq. 4-6,
366
we then obtained the standard Raman intensity of the C1-C1 stretching
-1
vibration at 543 cm to be:

s [452 2 C12 ,'2 ,2 CC14
P = [45a + 7y ] /[45a + 7y ] = 0.969 + 0.084.
543 543 459 (4-7)
,2 --
Often in the literature, y2 of the 459 cm band of carbon tetra-

chloride has been assumed to be zero [for example, Long, Gravenor and
5 2
Milner (63)] defined Ps explicitly with the assumption that (y') is 0

for this band. We verified the reasonableness of this assumption by
'2
calculating (y ) 2 from Bernstein's value 0.015 for p, finding that
v2
7y contributed only 2% to the total intensity of this particular

band. Therefore, we can assume in practice that:








[45a2 + 72 CC14 = [452 1 CC14 (4-8)
[45a'2 + 7y245 = [45a 45
459 459
,2 CC14
The value of [45a ] had been measured in liquid CC1 and found (64)
459 4
to be (33.71 + 9.63)x 10-8 cm /g. From this value and Eq. 4-7 we obtain


[45a2 + 7y2] 12 = (32.3 + 10.0) x 10 cm /g (4-9)
543

(Here the major uncertainty is in the value for the absolute intensity

of the CC4 band.)

As has been mentioned, the depolarization ratio of chlorine in

carbon tetrachloride was difficult to determine with our spectrometer.

However, the gas phase value (p = 0.14) (65) for chlorine is most probably

the lower limit for the values (see Table VI). Using this value, we

then obtained

,2 ,2 v2
p = 3y /(45a + 4y )= 0.14 (4-10)


Solving Eqs. 4-9 and 4-10, we find that the absolute intensity of chlo-

rine is given by

,22
a2 = (0.512 + 0.159) x 10-8 cm4/g = [(3a/3 ) ] (4-11a)

w2 -8 4 2
y = (1.32 + 0.41) x 108 cm /g = [(y/B ) ] (4-1lb)
10
4 4 ,2 ,2
We may convert from unit of cm /g to cm by multiplying a and y
-24
each by the reduced mass of chlorine (29.426 x 10 g). When this was

done, we found

,2 -30 4 2
a = (0.15 + 0.047) x 10 cm = [(/a/Dr ) ] (4-12a)
1 0
,2 -30 4 2
Y = (0.39 + 0.12) x 10- cm = [(y/r ) ]2 (4-12b)
1 0








or

a = (3.9 + 0.6) x 1016 cm2 (4-13a)

-16 2
y = (6.2 + 0.9) x 1016 cm (4-13b)


However, the depolarization ratio of chlorine in benzene was measured

to be 0.27 (see Table VI) which may be an upper limit for p for chlorine

in carbon tetrachloride. With this value we found

-16 2
a= (3.3 + 0.46) x 1016 cm (4-14a)


y = (8.2 + 1.2) x 10 cm (4-14b)


We believe that the depolarization ratio of chlorine in carbon

tetrachloride may be much closer to the value found for the gas phase

than it is to the value obtained in benzene solution, since carbon

tetrachloride is expected to be a relatively inert solvent. Therefore

the values of a and y for chlorine in carbon tetrachloride given by

Eqs. 4-13a and 4-13b are expected to be more reliable, although the

range of possible values for these parameters allowed by the uncertain-

ties in p (compare Eq. 4-13 to Eq. 4-14) is not very large.













CHAPTER V


INFRARED SPECTROSCOPIC STUDIES OF
CHLORINE IN BENZENE SOLUTIONS


Experimental Procedure

The concentrations of chlorine solutions required for infrared

studies (0.3 M to 0.9 M) were higher than those for ultraviolet and

Raman studies. At these concentrations, we found that the photochemical

reaction occurs very easily. When we exposed the solution of chlorine

in benzene to fluorescent light, and determined the infrared spectrum

as a function of the time after it was prepared, an increase in the

concentration of photochemical product was observed as illustrated in

Fig. 17. Since it was impossible to prepare the solution and to fill

the sample cell in complete darkness, there was no way to prevent the

photochemical reaction from occurring. At last we tried adding oxygen

gas to the solution to act as a radical quencher (56). As a result,

the photochemical reaction was inhibited considerably, if not completely.

A small amount of iodine in addition to oxygen was reported to be even

more effective in quenching the radicals (56). Since iodine itself

forms a stronger complex with benzene than does the chlorine, we did

not try to use iodine as radical quencher in our studies for fear of

further complicating the system.

The infrared spectrometer we used was a Perkin-Elmer Model 621.

In order to minimize the change in chlorine concentration during the

69























0


r-4
0

to
r0

00 7-
M *r- -A



) 0 0o

0 ,C
t 41 r)



0000
0 0
.0 0

(3 4-4 4)

04 0




0 41
C 0 4)
0T CO











$O P


0 m
4 i


u r0
(o <
a) i


o)
0 0

o o
40

0 0
4. 4!1


m0 00
4-1 r4
x u

4l 1.1




w o
S 0 0)
S 44

- oi o
0 U 0)

3 4-1 4-1
r--O


S0 0

01 0 0
S0 0

o V :

a) 0 0

0 3
0) 0 0
04 *}
0 0

3 p






m -, u






























O
o
iLA
Vn


















Cll




rvar
















o
-I
0,


So 00
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course of recording the spectrum and the growth of the photochemical

product sufficient to distort the absorption band from the C1-C1

stretching vibration, we chose to sacrifice the signal-to-noise ratio

(S/N), reducing it to around 125, with a spectral resolution of about

2 cm-1. The total scan time for each measurement from 650 cm1 to

350 cm-1 was about 15 to 20 minutes.

Before the preparation of the chlorine solution, we warmed up the

spectrometer and covered the sample compartment with a black.polyethy-

lene sheet. The baseline was recorded beforehand to give the apparent

transmittance of solvent vs. solvent in the matched cells described

earlier in Chap. II. At this point, we prepared the chlorine solution,

withdrew a 5 ml portion for determination of the chlorine concentration,

and immediately filled the liquid cell with the chlorine solution using

a micropipette (5 3/4 inches long, P5205-1 Scientific Products, Evans-

ton, Illinois). The sample cell was carried to the spectrometer .in a

box covered with a black polyethylene sheet. All lights in the room

were turned off (note the sample preparation room was separated from

the laboratory containing the spectrometer), since the light emitted

from the infrared glower source was sufficient to permit the alignment

of the cells in the sample compartment. A special holder was made to

fit the sample compartment so that we could reproducibly align the

sample each time with little light. After the spectrum of the chlorine

solution was taken, the sample cell was placed in the box mentioned

before, and connected to the vacuum line in order to pump out the

chlorine. The chlorine solution always filled the cell up to the top

of the glass tubing, so that the pumping process did not reduce the

liquid level below the upper edge of the light path. It usually took







about half an hour to eliminate the chlorine gas from the solution.

The baseline spectrum of clear solution vs. solvent was then recorded.

The baseline always changed a little from that recorded at the begin-

ning but not enough to affect the total band area of the chlorine ab-

sorption by as much as 2%. Most importantly, if enough of the photo-

chemical product was present in the original chlorine solution, we

could detect it by its infrared absorption spectrum in the second clear

solution after the chlorine was removed. If that product was detected,

then we would have to repeat the measurement. Occasionally, instead

of pumping out the chlorine gas in the sample cell, we withdrew a 1 ml

portion of the chlorine solution and determined the concentration of

chlorine by titration to find out how much had been lost by both the

photochemical reaction and the escape of chlorine gas from the cell.

We had actually tried three liquid cells with different path-

lengths. The 1 mm liquid cell was made specially of tantalum metal

in our machine shop. Its construction was not much different from an

ordinary standard round liquid cell with Teflon spacer (Barnes cell

# 0004-035) such as that used to take the spectrum shown in Fig. 17.

Since the intensity of the chlorine absorption (spectrum B in Fig. 17)

with this 1 mm pathlength cell was so small, it was difficult to

observe especially the very weak absorption by chlorine in benzene

solutions diluted very much with carbon tetrachloride. Furthermore,

it was difficult to distinguish between the baseline shift due to the

photochemical reaction and the absorption by the chlorine. The 6 mm

pathlength liquid cell described in Chap. II also had been used to

measure the absorption by chlorine, but the benzene absorption in this

long path cell was so high in this region, and the actual signal-to-








noise ratio was so low, that we could not measure a reliable chlorine

absorption band with this 6 mm cell. Hence, the 3 mm pathlength liquid

cell (also described in Chap. II) was the most suitable for this kind

of measurement. The pathlength (3 mm) was obtained by measuring the

thickness of the Teflon spacer with a micrometer. Since the absorp-

tion by carbon tetrachloride was less than that by benzene in the

infrared region near the chlorine absorption band, we were able to

measure the absorption by chlorine dissolved in carbon tetrachloride

in the 6 mm pathlength liquid cell by making a special effort (more

discussion will be given later in this chapter).

The spectrum of 0.33 M chlorine in benzene in the 3 mm cell is

shown in Fig. 18 (recorded vs. pure benzene in the reference beam in

a matched cell), where it is compared with the spectrum of benzene in

that same cell, recorded with air in the reference beam, and with a

baseline of benzene vs. benzene. Benzene absorbs almost totally above

575 cm-1 and below 410 cm-1, so that we lost all the spectral informa-

tion for the chlorine-benzene solution outside the region from 410 to
-1
575 cm However, within that spectral region, we were able to work

at quite a good signal-to-noise ratio (a ratio of 125), and so we

could obtain a reliable spectrum. (The spectra were recorded in the

transmittance mode rather than in the absorbance mode because opera-

tion of our Perkin-Elmer 621 in the absorbance mode was not reliable

at the time of the experiment.)

Spectra of chlorine solutions in benzene diluted by carbon

tetrachloride are shown in Figs. 18-21. As benzene was gradually

diluted by the addition of carbon tetrachloride, less solvent absorp-

tion was found above 575 cm-1, so that more spectral information was





















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unveiled concerning the high frequency wing of the chlorine absorption

band. However, the'strong absorption by carbon tetrachloride in the

3 mm cell below 500 cm-1 made it difficult to observe the low frequency

wing of the chlorine absorption band. This situation is illustrated in

Fig. 20 and Fig. 21. The weak absorption band near 510 cm-1 in Fig. 20B

was due to the hexachlorocyclohexane.

One of the most exciting things in this work was the observance of

the infrared absorption band of chlorine in carbon tetrachloride shown

in Fig. 21. To the author's knowledge, this was the first time that

the infrared absorption by chlorine has been observed for a chlorine

solution in a solvent whose molecules have tetrahedral symmetry. This

spectrum is quite different from that of chlorine in benzene (Fig. 18)

or those of chlorine in different benzene-carbon tetrachloride mixtures

(Figs. 19-20). It is very broad and weak. If one did not use a long

pathlength liquid cell, this broad and weak absorption could easily be

confused with some baseline shift of unknown origin. To make clear that

the absorption in Fig. 21B is due to chlorine in carbon tetrachloride,

we measured this absorption band at several different concentrations

of chlorine, as shown in Fig. 22. The dependence of the absorption on

the concentration of chlorine was clearly demonstrated. To be more

convincing, the spectrum of 0.33 M chlorine in carbon tetrachloride was

measured with the longer pathlength (6 mm) cell. The spectrum obtained

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Full Text

STUDIES OF MOLECULAR COMPLEXES
By
TZE C.HI JAO
A DISSERTATION PRESENTED TO THE GRADUATE
COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1974

To my parents
and
my wife Carmen
« * i

ACKNOWLEDGEMENTS
Special thanks are for Dr. Willis B. Person for his wise counsel,
constant enthusiasm, and encouragement throughout the entire project.
I should also like to express thanks for their help to Dr. Keith E.
Gubbins, Dr. Yngue Ohrn, Dr. Thomas M. Reed and Dr. John R. Sabin.
I am grateful to the University of Puerto Rico (Mayagliez Campus)
for financial support of my graduate studies, at the University of
Florida and also for support from the National Science Foundation
(Research Grant No. GP 17818).
Support of computing expenses by the College of Arts and Sciences
of the University of Florida is gratefully acknowledged.
I should like to express my sincere thanks to Dr. Shigeo Kondo,
Mr. Robert Levine, Mr. James H. Newton, Mr. Gary Peyton and Miss
Barbara Zilles for their friendship and assistance.
Finally, I express my appreciation to Mrs. James H. Newton for
her patience in typing this manuscript.
iii

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
LIST OF TABLES vii
LIST OF FIGURES ix
ABSTRACT xii
CHAPTER
I. INTRODUCTION • 1
II. GENERAL EXPERIMENTAL PROCEDURES 11
Introduction 11
Source of Reagents 11
Preparation of Chlorine Solutions 11
Liquid Cells 17
III. ULTRAVIOLET SPECTROSCOPIC STUDIES OF CHLORINE IN
BENZENE SOLUTIONS 21
Experimental Procedures 21
Analysis of the Ultraviolet Spectroscopic Data from
Chlorine-Benzene Solutions 29
IV. RAMAN SPECTROSCOPIC STUDIES OF CHLORINE IN BENZENE
SOLUTIONS 41
Introduction 41
Experimental Procedure 41
Results of the Raman Measurements on Chlorine Solutions 51
Absolute Raman Intensity of Chlorine in Carbon
Tetrachloride 63
iv

Chapter
Page
V. INFRARED SPECTROSCOPIC STUDIES OF CHLORINE IN
BENZENE SOLUTIONS 69
Experimental Procedure 69
Analysis of the Experimental Results 88
VI. COLLISION-INDUCED INFRARED INTENSITY OF CHLORINE IN
BENZENE AND IN CARBON TETRACHLORIDE SOLUTIONS 107
Introduction 107
General Expression for the Integrated Collision-
Induced Absorption Intensity 108
N^2> The Number of Collision Pairs 108
Evaluation of | Jl* * H * | 113
Explicit Expression for the Integrated Collision-
Induced Absorption Intensity 116
Evaluation of ) F + a„ (9F /3E ) ]2\ for
\ 110 / / 110 /r
the "Axial" Chlorine-Benzene Pair ; 116
Actual Calculation of the Infrared Intensity of Chlorine
in Benzene Solution for Collision Pairs in Different
Orientations
Evaluation of
< K
F2 + “2 FU
Carbon Tetrachloride Collision Pairs
for Chlorine-
120
125
VII.CALCULATIONS OF THE RAMAN INTENSITY ENHANCEMENT FOR
CHLORINE IN BENZENE AND IN CARBON TETRACHLORIDE
SOLUTIONS 130
Introduction 130
Theory of the Raman Intensity Enhancement Caused by
Electrostatic Interaction (Bernstein's Collision-
Complex Theory) 131
Calculation on the Raman Intensity Enhancement for
Chlorine-Benzene and Chlorine-Carbon Tetrachloride
Pairs in Different Solute-Solvent Orientations 138
Discussion 146
v

Chapter
Page
Theory of the Pre-Resonance Raman Effect 148
Application of the Pre-Resonance Raman Effect Theory
to the Interpretation of the Raman Intensity Data
of Chlorine in Benzene Solutions 152
APPENDIX 157 '
REFERENCES 163
BIOGRAPHICAL SKETCH 168
vi

LIST OF TABLES
Table
I. Source and Purity of the Reagents
II. Extrapolated Values at Time Zero of the Normalized
Absorbance (A /C.) for Different Chlorine Solutions
c A
III.The Values of K^gQ) K, and ^or T^ree Different Sets
of Ultraviolet Data from Chlorine-Benzene Solutions
Obtained from the Scott Plot
Page
12 ’
28
35
IV. Values of Ke , K, and e for Chlorine Solutions from
v* v
Scatchard Plots 39
V. Observed Raman Shifts, Half-Band Widths and Relative
Intensities of Chlorine Solutions in C,H -CC1. Solvent
6 6 4
Mixtures as a Function of Benzene Concentration 52
VI. Depolarization Ratio of Chlorine in Different Chlorine
Solutions 65
VII.Integrated Infrared Molar Absorption Coefficients (A) and
the Parameters of the Lorentzian Functions for the Cl-Cl
Vibration of Chlorine in Benzene Solutions 100
VIII.Parameters Used for the Calculation of the Collision-
Induced Infrared Intensity of Chlorine in Benzene or
Carbon Tetrachloride Solutions 121
IX. Calculated Collision-Induced Infrared Intensity for
Chlorine-Benzene Pairs in Different Orientations 122
X. Calculated Collision-Induced Infrared Intensity of Chlorine-
Carbon Tetrachloride Pairs in Two Different Orientations .. 127
XI. Coefficients of the 1/R Terms in the Expressions for
i 2 '2
A(a ) and A(y.„) (Eqs. 7-21a and 7-21b) for Several
ab 'ab h
Different Solute-Solvent (AB) Orientations 143
XII.The Calculated Values of {A(aAB} X’ (A(YAB} }r>
N /N , and the Enhancement of Intensity (AP)
12 A
145

Table
Page
A-l. Parameters Used for the Calculations of the Pair-
Correlation Functions of Chlorine-Benzene and
Chlorine-Carbon Tetrachloride Pairs 160
A-2. The Potential Function u (R., „, u. , oj„)/kT for Chlorine-
3 12 1 2
Benzene Pairs as a Function of Relative Orientation
(at T = 298°K) 161
A-3. The Potential Function u (R , w, , m0)/kT for Chlorine-
a Id -L d 0
Carbon Tetrachloride Pairs (at T = 298 K) 162
viii

LIST OF FIGURES
Figure
1. The NMR spectrum of the residue (redissolved in CC1 )
after benzene solutions were evaporated
2. Schematic diagram of the infrared liquid cell
3. Ultraviolet spectra of chlorine in benzene taken at
different concentrations and at different times
4. Plots of the normalized absorbance of chlorine at 280 nm
vs. time for different chlorine solutions (around 0.001 M).
5. Ultraviolet spectra of chlorine solutions in a 30% (v/v)
C,H. and 70% (v/v) CC1 solvent
6 6 4
6. Replotted spectrum of 0.027 M chlorine solution in 30%
(v/v) C,,Fh and 70% (v/v) CC1, mixture (0.1 mm path-
length)6.^ *
7. Scott plots of the complex of chlorine and benzene
8. Scatchard plots for the complex of chlorine with benzene..
9. Raman spectrum of the C,H,-CC1 -CHC10 mixture at a ratio of
6:3:1 6.6....^ 3.
10. Raman spectrum of 0.12 M chlorine in a C^H^-CCl -CHC1
mixture at a ratio of 8:1:1 ?....
11. Raman spectrum of 0.5 M chlorine in 6:4 C H -CC1
6 6 4
12. Raman spectrum of the chlorine-free 6:4 C H -CC1
solution
13. Plot of the Raman spectral half-band width of chlorine vs.
the concentration of benzene (C^)
14. The relative Raman intensity of chlorine I . . as a
function of the benzene concentration (M)
» 0
15. Plot of 1/[I ^ - IR(v) ^ VS‘ PB^PB ^°r c^-*-or^ne in
benzene solutions
Page
16
20
25
27
31
32
34
38
44
47
48
50
54
57
60

Figure Page
f O
16. Plot of p /[(I -I] vs. (p + C - C) for
B R(v) R(v) B A
Eq. 4-4 64
17. Infrared spectra of chlorine (about 0.6 M) in benzene
solutions as a function of the exposure to fluorescent
lights 71
18. Infrared spectra of 0.33 M chlorine in benzene. The path-
length of the cells for all studies is 3 nnn 76
19. Infrared spectrum of chlorine in 60% (v/v) benzene and
50% (v/v) carbon tetrachloride. The pathlength is 3 mm
for all spectra 78
20. Infrared spectrum of chlorine solution in 20% (v/v)
benzene and 80% (v/v) carbon tetrachloride. Pathlength
is 3 mm 80
21. Spectrum of chlorine in carbon tetrachloride. Path-
length is 3 mm for all spectra 82
22. Infrared spectra of chlorine in carbon tetrachloride. The
pathlength is 3 mm for all measurements 85
23. Infrared spectrum of chlorine in carbon tetrachloride solu¬
tion with the 6 mm pathlength liquid cell 87
24. Replotted infrared spectra of chlorine in benzene solutions;
the concentration of chlorine in each solution is 0.5 M
and the pathlength is 3 mm 90
25. Lorentzian curve (F) fitted to the observed absorption
spectrum of chlorine in benzene (I) 93
26. Lorentzian curve (F) fitted to the observed absorption
band (I) of chlorine in 60% (v/v) benzene and 40% (v/v)
carbon tetrachloride 95
27. Lorentzian curve (F) fitted to the observed absorption
band (I) of chlorine in carbon tetrachloride 97
28. Scott plot of the infrared data for the complex of
chlorine with benzene (neglecting the intensity of "free"
chlorine in the presence of carbon tetrachloride)......... 103
29. Scott plot of chlorine complex with benzqne, using a
recalculated intensity of chlorine, as given by Eq. 5-9,
and described in the text 105
x

Figure Page
30. Coordinate system used in defining the orientation of
linear molecules 110
31. Coordinate system used in defining the orientation of
chlorine and carbon tetrachloride 126
32. Coordinate system and symbols used for deriving the
electrostatic potential due to a dipole 132'
33. The relative orientation between cartesian coordinates
(x, y, z) and the polar coordinate unit vectors
xi

Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy
STUDIES OF MOLECULAR COMPLEXES
By
Tze Chi Jao
March, 1974
Chairman: Willis B. Person
Major Department: Chemistry
Molecular complexes of chlorine in benzene solutions were studied
by ultraviolet, Raman and infrared spectroscopic techniques. Ultra¬
violet spectroscopic studies verify the order of magnitude of the
previously reported equilibrium constant for the assumed benzene-
chlorine 1:1 complex. Its value, K = 0.025 + 0.015 liter mole \
agrees quite well with values obtained from Raman and infrared spectro¬
scopic data.
Careful experimental measurements were made of the absolute Raman
and infrared intensities of the Cl-Cl stretching vibration of chlorine
in solutions of benzene in carbon tetrachloride. Specially designed
infrared long path liquid cells, inert to chlorine, were constructed
and used to obtain the absorption spectra of chlorine in the mixtures
of benzene and carbon tetrachloride. The resulting infrared studies
xii

were more acurate than previous work, and the collision-induced infrared
absorption spectrum of in CCl^ could also be observed.
The v -venumber of the Raman band of shifts uniformly from
530 cm ^ benzene solution to 543 cm ^ in carbon tetrachloride solu¬
tion, alt.h >ugh the half band width clearly broadens at a 1:1 ratio of
benzene to carbon tetrachloride. The infrared absorption by chlorine
shifts slightly from 527 cm ^ in pure benzene to 532 cm ^ in 2.26 M
benzene in CCl^; with a big jump to 545 cm ^ for chlorine in pure
carbon tetrachloride. This difference between the Raman and infrared
spectra for chlorine in benzene solutions suggests that the infrared
absorption is from only the complexed chlorine, while the Raman band
is a composite of two unresolved bands, one for the complexed chlorine
and the other from free chlorine. The absolute infrared intensity and
the relative Raman intensity for the Cl-Cl vibration of chlorine both
increase approximately by a factor of five from those for the Cl^
solution in carbon tetrachloride to the solution in benzene.
In order to interpret these observed Raman and infrared spectra,
theoretical calculations were made of the effect on the Raman and
infrared intensities from direct electrostatic interactions. The basic
theory of collision-induced infrared absorption intensity by Van
Kranendonk and Fahrenfort and of the Raman intensity enhancement by
Bernstein was applied, using statistical mechanics of liquid structures
with angularly dependent pair-correlation functions of chlorine in
benzene solutions. The isotropic and anisotropic effects were taken
into consideration for the calculations of both Raman and infrared
intensities. The calculated intensities were then compared with the
xiii

experimentally measured values.
The electrostatic effect predicts a maximum Raman intensity
enhancement of 100% for chlorine from gas phase to solution in CCl^,
and 134% for solution in benzene, compared with an observed enhancement
of more than 400% from solution in carbon tetrachloride to solution in
benzene. The contribution of the electrostatic effect to the infrared
intensity of chlorine in benzene was predicted to be, at most, 50% of
the total measured intensity of 333 cm mmole ^. The vibronic charge-
transfer effect may be responsible for the intensification of infra-
Raman effect involving the charge-
the enhancement of the Raman band.
red absorption while a pre-resonance
transfer absorption band may explain
xiv

CHAPTER I
INTRODUCTION
Complexes of halogens with benzene have been studied quite
intensively in the last two decades by both experimental and theoretical
methods (1-34). The general subject of molecular complexes has been
reviewed by several authors (35-40). The experimental studies include
those by ultraviolet, visible, Raman and infrared spectroscopic techni¬
ques, while the theoretical studies are concerned with the mechanism
of the interaction and the theory of the associated experimental
phenomena, and particularly the relative importance of the electro¬
static and charge-transfer effects. The complexes of iodine with
aromatic donors have been studied quite thoroughly by these methods.
Less attention has been paid to the complexes of bromine and chlorine
with benzene or other aromatic donors, because the latter are more
reactive.
In the first careful study by Andrews and Keefer (6) the complex
of chlorine with benzene was found to exhibit an additional strong ul¬
traviolet adsorption band near 278 nm, which is absent in the spectrum
of each individual constituent solution. From their ultraviolet data,
they found by the Benesi-Hildebrand method (2) that the equilibrium
constant of the complex is about 0.033 liter mole ^ with a maximum
, . -1-1
absorptivity e for the complex at 280nm of 9090 liter mole cm .
max
The equilibrium constant for the complex of iodine with benzene
1

2
was found (2) to be about 0.17 liter mole ^, with z of about 15000
max
liter mole ‘'"cm , so that the complex of chlorine with benzene is
weaker than that for iodine with benzene, in agreement with the expect¬
ed Lewis acid strengths of chlorine and iodine.
In an attempt to explain the results of these ultraviolet spectro¬
scopic studies (1, 2) of iodine with benzene, Mulliken (11) introduced
the "charge-transfer" resonance structure theory. This theory described
the ground state electronic wavefunction of a donor-acceptor
complex approximately by a combination of two resonance structure
functions ¥ and ¥ :
0 1
¥ (D*A) = a¥Q(D,A) + b¥1(D - A )
(no-bond) (dative)
(1-D
Here a_ and b_ are the coefficients of the no-bond and dative structures,
respectively. In the ground state of a weak complex, a is expected
to be approximately 1.0 and b^ expected to be less than about 0.1. The
stability of the complex depends on the extent of the mixing between
the wavefunctions of the no-bond and dative structures.
If the ground state structure of a complex is given by ¥ , then
N
according to the "charge-transfer" theory, there is an excited state
Â¥^ which is called a charge-transfer state, given by
Â¥ - - b*Â¥Q(D,A) + a*Â¥^(D+ - A~) .
(1-2)
* *
The coefficients b^ and a are determined by the quantum theory require¬
ment that the excited state wavefunction be orthogonal to the ground
state function:
j¥„¥ dx = 0.
N V

3
The electronic absorption frequency of the new band formed in the
complex corresponds to the energy difference between the ground state
(N) and this charge-transfer excited state (V ) of the complex. The
charge-transfer theory also explains the characteristically high in¬
tensity of the electronic absorption band of the complex (for
further discussion see Ref. 37).
The first infrared study of the complex of chlorine with benzene
was made by Collin and D'Or (13). A new weak and relatively broad
absorption band was observed near 526 cm-'*’ for solutions of chlorine
35
dissolved in benzene. The Raman shift for chlorine ( C]^) in carbon
tetrachloride was known (22) to be at 548 cm”*'. More quantitative
studies of the infrared spectrum of chlorine in benzene were carried
out by Person and associates (18, 21).
An attempt was made by Friedrich and Person (26) to interpret the
changes in vibrational frequency and intensity of the halogen-halogen
stretching vibration when the halogen molecule, an aa acceptor (37),
complexes with benzene, a bir donor (37) (or with other electron donor
molecules) in terms of charge transfer theory (11). They postulated
that a relationship existed between the vibrational frequency shift
(Av) and b the coefficient of the dative wavefunction:
Fin = (b2 + absoi} “ Ak/ko = 2Av/v0 • (1-3)
2
Here F„ is the weight of the dative structure in ¥ (F = b + 2abS )
IN N IN or
S is the overlap integral between T and f , k is the force constant
01 0 1
and Vq is the vibrational wavenumber of the isolated molecule, while
Ak and Av are the changes (kQ - k or v^ - v, respectively) in the
complex.

4
In the following, we shall summarize some of the material from
Ref. 41 relating to the theories of charge-transfer and of electro¬
static effects for the interpretation of the changes in infrared
intensity of halogens forming complexes with benzene. The experi¬
mental absolute infrared intensity (A ) of the ith normal vibrational
i
mode of any molecule can be related to the dipole moment derivative
(3p/9C1) by (41)
2 2 2
A. = NTrg./3c (9p/2£.) = K(3p/H ) • (1-4)
xi i 1
Here is the Avogadro's number, g. is the degeneracy of the ith
normal vibration at wavenumber v , (9p/9£ ) is the magnitude of the
i i
dipole moment derivative for the ith normal vibration with respect
to normal coordinate (E, ) . The integrated molar absorption coeffi-
i
cient A is defined experimentally by:
i
A = (l/n£)/i,n(I /l)dv
1 0
(1-5)
Here n is the concentration of the absorbing molecules in liter mole ,
is the pathlength in cm, I and I are the transmitted and incident
intensities of monochromatic light at wavenumber v..
Based on charge-transfer theory (11), Friedrich and Person (26)
argued that the dipole moment derivative for the Cl-Cl stretching
vibration in the complex is given by
9p/3£ “ m + (2b)(9b/9C )|y - y |
i N i i 1 0
(1-6)
Here 9^/95. represents the magnitude of change in the Cl-Cl dipole
N i
moment of the uncomplexed Cl molecule when the Cl-Cl coordinate (?)
changes; |y^ - y^| is the difference between the dipole moment in the

5
dative state y^ and that in the no-bond state Vq, and is approximately
equal to the electronic transition moment for the charge-transfer
absorption band. The second term (9b/3£ ) is the change in the coeffi-
i
cient b_ as the Cl-Cl bond length changes (£.) and gives the vibronic
charge-transfer effect.
The derivative (9p/9£ ) is related to the derivatives with
i
respect to the internal coordinates (R ) by:
j
9p/9£. = l L .(3p/9R )
1 j J1 j
(1-7)
Or conversely,
-1. â– *.
3p/9R = EL Op/9C )
3 i ij i
(1-8)
Here L . is the iith coefficient from the normal coordinate transfórma¬
la —
-1
tion, while L is the corresponding element from the inverse transfor-
ji
mation. In analogy with Eq. 1-6 we have
9p/9R = 9y /9R + (2b)(3b/9R ) y - y I
J N i 3 1 0
(1-9)
Assuming 9y /9R. is not different from the dipole moment derivative
N J
of the free molecule, it has been shown (41) from Eq. 1-9 that the
f
vibronic contribution (M ) to the infrared intensity change, for the
d
special case R = R , the stretching coordinate of the X-Y bond of a
j 1
complexed halogen molecule, can be obtained from the following equation:
- (9p/8^) - Oj/aRp » - <2F0NV<3EI/3y/i|í1 -^O1 •
(1-10)
Here F„ is the weight of the no-bond structure in f (F = a + abS ) ,
ON 6 N ON 01 *
and is related to by F + F^ = 1; A is the difference between the
energies of the dative and no-bond structures and eY is the vertical
A

6
electron affinity of the acceptor, and appears because b depends on E ,
v A
so that 3b/3R is related to 3E /3R . The comparison between the
1 A i
calculated M and the observed values is shown in Table 1,8 of Ref.
d
41. The agreement is qualitatively good, but the calculated values
in some cases are larger than experimental by a factor of 2 to 5.
The defect of the model of Friedrich and Person arises from two
sources: one is the oversimplified assumption that 3y /3R can be
N 1
0 .
approximated by 3p /3R , the dipole moment derivative of the free
v
molecule, the other is because 3E /3R (and, to a lesser extent, the
A 1
other parameters such as F, ) cannot be obtained a priori.
IN ~
In an alternative treatment, Hanna and associates (30, 31) attempt¬
ed to interpret the change in the infrared intensity of halogens in
benzene as a purely electrostatic effect. They estimated an induced
dipole for chlorine in a complex arising from the interaction of the
field along the six-fold z-axis from the benzene molecule with the
polarizable halogen molecule:
y = (1/2) a" (E + E )
i 1 2
(1-11)
Here a^is the polarizability of the halogen parallel to its axis (in
the z^ direction); E^ is the field from the benzene at the nearest
halogen atom (X), and E^ is the field at the halogen atom (Y) further
away from the benzene. Taking the derivative of Eq. 1-11 with respect
to the internal coordinate R^ of the halogen,
(3y /3R ) = (1/2) (3a///3R ) (E + E )
i 1 1 1 2
+ (1/2) a'[(3E /3R ) + (3E /3R )] .
11 2 1
(1-12)

7 •
The calculated infrared intensity for the halogen complexed with benzene
froTQ Eq. 1-12 is compared with the observed values (31). Again the
agreement is good (within a factor of 2).
The values from the model of Hanna and associates (30, 31) appear
to be the right order of magnitude, but the parameters needed for this
calculation are not easy to determine. For example, the polarizability
derivative (So/'VSR ) of chlorine was estimated from the semi-empirical
1
Lippincott model (42); the experimental studies reported here (Chap. IV)
found that this estimate is too large. There is also some considerable
uncertainty in the parameters chosen for E and E since estimation of
1 2
the correct values requires quite good molecular wavefunctions of the
benzene molecule.
The subject of electrostatic "collision-induced" infrared
absorption is an old one, having been studied by Van Kranendonk (43),
Fahrenfort (44) and others (45) . In the original formulation of
collision-induced infrared absorption given by Van Kranendonk (43)
and Fahrenfort (44) , homonuclear diatomic molecules or nonpolar linear
molecules under high pressure are predicted to have induced infrared
absorption due to (a) an atomic distortion effect and (b) a quadrupole
distortion effect. The former arises from mutual repulsion of electron
clouds at small intermolecular separation, while the latter comes from
the interaction between one polarizable molecule and the electric
field generated by the quadrupole moment of the other molecule. Hanna
and associates (30, 31) have considered the second effect in the
benzene-halogen case. In line with the correct collision-induced in¬
frared absorption theory (43, 44), the estimated induced infrared
absorption intensity for chlorine in benzene solution should be obtained

8
as an appropriate statistical average over all intermolecular orienta¬
tions, and not just for one orientation, as assumed by Hanna et al.
Using the same argument as Hanna and associates (30, 31), Kettle
and Price (33) applied the theory of collision-induced far infrared
absorption (46-50) to interpret quantitatively the observed results
of their studies on solutions of iodine and bromine in benzene. They
reported that the intensities of the far-infrared absorption of iodine
and bromine in benzene solutions could be adequately explained by con¬
sidering only quadrupole-induced dipole moments, but they had to
assume different values for the parameters from those given by Hanna
and Williams (31).
Meanwhile, a Raman spectroscopic study of iodine in benzene solu¬
tion had been carried out by Klaeboe (27). He observed only one Raman
band in the iodine solution, and did not see a Raman shift for the
uncomplexed iodine. Later, Rosen, Shen andStenman (29, 32) made a
more systematic study of the Raman spectrum of iodine in benzene solu¬
tion. They observed a uniform change in frequency of the Raman shift
for iodine as the benzene was increasingly diluted by the addition of
the inert solvent; e.g., n-hexane. No change in band shape was ob¬
served on dilution. They concluded that the reason for not resolving
two Raman peaks, one for the complexed iodine and the other for an
uncomplexed one, was the weakness of the charge-transfer interaction
between iodine and benzene, so that iodine could interact with more
than one donor. If the observed single Raman band for iodine in
benzene is due to the weak charge-transfer complex, then the weaker
charge-transfer complex of chlorine with benzene may exhibit the
same uniform change in vibrational frequency with dilution for both

9
Raman and infrared spectra.
After reviewing these previous studies of complexes of halogens
with benzene, we see there is considerable conflict in the interpreta¬
tion of the observations of infrared absorption of halogens in benzene.
In order to understand better the difference in the interpretations
of the spectroscopic phenomena associated with the complexes of halo¬
gens with benzene, we decided to re-investigate the benzene-chlorine
system. We remeasured the infrared intensity of the complex of
chlorine with benzene under carefully controlled experimental condi¬
tions, and also studied the infrared absorption spectrum of chlorine
in carbon tetrachloride, which is not expected to form a charge-trans¬
fer complex with chlorine, in order to compare it with the one in
benzene. On the other hand, we re-examined the theory of induced in¬
frared absorption more carefully. With the improved liquid structure
theory (51, 52) recently available, we applied the collision-induced
infrared absorption theory of Van Kranendonk (43) and Fahrenfort (44)
in order to determine whether intensities observed for chlorine in both
the benzene and carbon tetrachloride solutions could be explained
quantitatively by this theory alone, without any charge-transfer effect.
Secondly, we extended the work of Rosen, Shen and Stenman (29, 32)
by studying the Raman spectrum of chlorine in benzene-carbon tetra¬
chloride solutions in order to understand better the nature of weak
charge-transfer complexes of halogens with benzene. There are three
reasons for our choice of chlorine instead of bromine or iodine for
the Raman work: (1) the complex of chlorine with benzene is much weaker
than a complex of iodine with benzene (6), so that the negative results
for benzene-iodine could be even worse for benzene-chlorine, (2) the

10
chlorine solution absorbs less of the Raman exciting line because the
solution is more transparent, so it could be observed easier in the
Perkin-Elmer LR-1 spectrometer, and (3) the infrared absorption of
chlorine is in a region which can be studied with less difficulty (13,
17) than for the benzene-iodine solutions.
We repeated the study of the ultraviolet spectrum reported by
Andrews and Keefer (6) for two reasons: first, we wanted to see if the
equilibrium constant of the complex of chlorine with benzene changes
with concentration of chlorine, since the Raman and infrared experi¬
ments required a high concentration of chlorine, while the equilibrium
constant obtained by Andrews and Keefer was presumably determined in a
dilute solution (they did not report their concentrations); secondly,
error analysis (53, 54) of the determination of equilibrium constants
for weak molecular complexes has shown that equilibrium constants as
small as that reported for chlorine with benzene cannot be determined
with any meaningful accuracy. For a complex with saturation function
(s, the fraction of complexed Cl^ in the solution) between 0.01 and
0.1, the relative error in both the equilibrium constant and absorptiv¬
ity (E) will vary between + 10 and + 100%, respectively (52a). It is
thus of interest to compare equilibrium constants obtained from these
three different methods (ultraviolet, Raman, and infrared spectra) in
order to see the"order of agreement that can be achieved.

CHAPTER II
GENERAL EXPERIMENTAL PROCEDURES
Introduction
In this chapter we shall discuss the experimental procedures that
were common to all of the different spectroscopic studies. These in¬
clude the discussion of the source and purity of reagents, the prepara¬
tion and handling of chlorine solutions, and the cells used, including
a description of the specially constructed infrared cells. In the
following chapters we shall then describe in detail the special experi¬
mental procedures for each different (ultraviolet, Raman and infrared)
spectral study.
Source of Reagents
The reagents used for all experiments in this work are listed in
Table I. All the solvents were used without further purification. How¬
ever, these solvents did not have impurities detectable at the conditions
of our spectral studies. The two different grades of chlorine gas did
not show any differences in our spectra.
Preparation of Chlorine Solutions
The chlorine solutions for all the different spectral studies were
prepared in the same way. Chlorine gas was introduced into the solution
through a gas dispersion tube connected by Tygon tubing to a trap filled
with glass wool to filter any solid impurity and then to the flask of
chlorine. The flow rate of the chlorine gas was not regulated by a
11

12
SOURCE
Material
chlorine gas
benzene and
carbon tetrachloride
chloroform
sodium thiosulfate
(Na SO *5H 0)
2 2 3 2
potassium iodate
(kio3)
Potassium iodide
(KI)
TABLE I
AND PURITY OF THE REAGENTS
Purity
research or ultra-high
purity grade
(1) spectrophometric grade (1)
(2) spectro-quality reagent (2)
analytical reagent
analytical reagent
analytical reagent
reagent grade
Source
Matheson Gas
Products
Mallinchrodt
Chemical Works
Matheson Cole¬
man and Bell
Allied Chemical
Fisher Scientific
Company
Fisher Scientific
Company
Fisher Scientific
Company
water
deionized
University of
Florida

13
regulator, but was controlled in such a way that the concentration of
the chlorine was around 0.1 M after bubbling Cl^ for five minutes,
around 0.2 M after 10 minutes, and so on. It may be safe to say that
this flow rate is about 5 bubbles per second. The bubbling process
usually took 5 to 30 minutes depending on the concentration desired.
As will be discussed in more detail later, the most serious difficulty
with the chlorine solution was preventing the formation of photochemical
product. Since this product does not absorb ultraviolet light nor
have Raman scattering in the same spectral region as does the complexed
chlorine, a small amount does not interfere with those studies. How¬
ever, it does absorb near the Cl-Cl infrared-absorption and the im¬
purity is especially bothersome there.
The chlorine solutions were prepared under ordinary room lights,
and the flow rate adjusted as described above during the ultraviolet
and Raman experiments. With the experience gained from these two
experiments, it was easy to work in the dark in order to prepare
chlorine solutions for the infrared experiments, where the photochemical
product interfered more seriously. However, when the solutions were
exposed to light, we could easily detect formation of large amounts of
photochemical product, since the solution would first become a little
cloudy, clearing again with time, because the product is very soluble
in benzene and in carbon tetrachloride. If this cloudiness was detected,
we would then discard the solution and use a freshly prepared one. In
the dark, we could monitor the solution by feeling the flask to detect
the solution heating up, since we believe that heating was always an
indication of extensive photochemical reaction.
Because of this well-known (55) photochemical reaction between

14
chlorine and benzene, occurring in daylight or under fluorescent lights,
it was necessary to' keep the room as dark as possible. Actually, we had
found that the chlorine concentration in the benzene solution under or¬
dinary fluorescent lights decreased by about 8% in 2 hours when the
stock solution was about 0.2 M. The reason for the decreasing concen¬
tration of chlorine was partly due to the photochemical reaction, but
possibly was also due to chlorine gas escaping from the flask even
though the flask was stoppered. After evaporating benzene solutions of
chlorine that had been exposed to light, the solid residue was dissolved
in carbon tetrachloride. The NMR spectrum of this solution showed the
residue was mainly hexachlorocyclohexane (C^H^Cl^) because of the peak
at 4.7 ppm (see Fig. 1).
To make sure the Raman spectrum and the infrared spectrum that were
observed for the chlorine solution were actually due to the chlorine
molecule and not to any compound formed between chlorine and the sol¬
vent, we removed the chlorine gas from the solvent after running the
spectrum either by bubbling nitrogen through the solution in the case
of Raman experiments, or by pumping out the chlorine gas (from the
solution in the cell) through a vacuum line, in the case of infrared
experiments. Following this treatment the spectrum of the clear
solution was then taken, so that absorption by the photochemical pro¬
duct could be detected.
We have mentioned briefly earlier that the photochemical product
(C^H^Cl^) gives more serious problems for the infrared experiment. The
absorption of the hexachlorocyclohexane near 510 cm ^ could distort
the spectrum of chlorine by overlapping the two bands. Therefore, ex¬
treme care is necessary to avoid exposing the sample to light. However,

Fig. 1. -
The NMR spectrum of the residue (redissolved in CCl^) after benzene
solutions were evaporated.
filter bandwidth: 4 Hz
R.F. field: 0.05 mG
sweep time: 1000 second
spectrum amplitude: 80

(9) Wdd
O'T
O’Z
0*E
0*V
r
^aVj"/,i'v.'->7>^v»'ir‘syV'vv^iirr> v'fPiSI f I* p i ‘^•■'1
T

17
one method which can inhibit the formation of C H Cl was to add some
6 6 6
oxygen gas in the solvent before chlorine gas was introduced. Oxygen
was reported to be a radical quencher (56). Nevertheless, we could not
completely inhibit the photochemical reaction by this procedure.
Every chlorine solution was freshly prepared for each experiment.
The concentration of chlorine was determined by withdrawing a 5 ml
portion of chlorine solution from the stock solution and transferring
it into a prepared solution containing excess potassium iodide. The
iodine released by the reaction with chlorine was titrated wTith standard
aqueous thiosulfate. The analysis of this stock solution was doné
before and after the Raman and infrared spectra were taken. As a check,
occasionally, a 1 ml portion of chlorine solution from the sample cell
was withdrawn after its spectrum had been taken, and its concentration
was determined. The concentrations of the chlorine solutions in the
two cases (from the cell or from the stock) were not significantly
different, but the concentrations after the experiment were about 5-6%
lower than at the beginning.
Liquid Cells
We used a set of matched silica cells with a pathlength of 1 cm
for the ultraviolet spectroscopic study of chlorine solutions at low
concentration (about 1.0 x 10 J M), and a silica cell with light path-
length of 0.1 mm for studying chlorine solutions of higher concentration
(about 1.0 x 10 ^ M). The 1 cm ultraviolet absorption cells were rec¬
tangular ones with ground-glass stoppers, while the 0.1 mm one was con¬
structed with platinum and tantalum parts, with silica windows, and
assembled with teflon spacers* All of them were supplied by Beckman.
A standard 2.5 ml Raman liquid cell from Perkin-Elmer was used

18
for the Raman experiments.
For the infrared experiments, specially constructed liquid cells
were made. In order to eliminate the solvent spectrum, we built two
fairly well-matched sets of liquid cells, one with a pathlength of 3 mm
and the other with 6 mm pathlength; potassium bromide windows (25 mm
in diameter and 3 mm thick) were used. Chlorine did not react very
rapidly with KBr in contrast with the solvent we used. This was tested
by placing the windows in the chlorine solution for one hour. They
did not show a significant change in their infrared spectrum from the
original KBr background. However, when we tried intentionally to ex¬
tend the window contact with the chlorine solution to 24 hours, the
baseline did change and we saw actual corrosion of the KBr salt plate.
We had tried to use AgCl v/indows of 1.5 mm thickness, and found the
thin windows were too soft to resist the pressure difference on evacua¬
tion of the cell.
The infrared liquid cell is shown in Fig. 2. The spacer was made
of teflon. Between the KBr window and the thick spacer, we
inserted a thin Teflon spacer in order to avoid damage by the rigid
contact with the KBr window and the Teflon spacer and in order to mini¬
mize leaking of the chlorine solution from the cell. To prevent the
KBr windows from cracking when they were fastened by two brass tubes
to form the liquid cell, an O-ring was placed between the brass tubing
and the KBr window. Finally, we compressed all these components by
the two outer brass plates, each with four drilled holes, and tightened
them with bolts. A hole of the exact dimension of the glass tubing
adaptor to the vacuum line was cut into the side of the Teflon spacer.
The filled 3 mm pathlength liquid cell contained 2.5 or 3.0 ml of
solution.

Fig. 2. — Schematic diagram of the infrared liquid cell.
A glass tubing adaptor
B Teflon spacer (3 or 6 mm)
C Teflon spacer (0.001 mm)
D KBr window
E 0-ring
F brass tubing
G brass plate
H bolt

20

CHAPTER III
ULTRAVIOLET SPECTROSCOPIC STUDIES
OF CHLORINE IN BENZENE SOLUTIONS
Experimental Procedures
The ultraviolet spectrum of the complex of chlorine with benzene
dissolved in carbon tetrachloride was studied as a function of benzene
concentration at two different chlorine concentrations, one on the order
of 0.001 M, and the other in a short path cell (0.1 mm) for solutions
around 0.1 M. Five different benzene-carbon tetrachloride mixtures
were prepared, ranging from pure benzene to pure carbon tetrachloride,
and the chlorine was dissolved in each.
For the chlorine solutions with concentration around 0.001 M, a
fairly well-matched set of silica cells was used in the spectral
studies. Before any solution was prepared, the Cary Model 15 ultra¬
violet spectrophotometer was turned on and allowed to warm up. At
this point, we started preparing 50 ml of aqueous potassium iodide
solution (containing 2 grams of KI) necessary for the titration of the
chlorine solution, and the different preparations of solvent needed
to dilute the stock chlorine solution. The chlorine solution around
0.1 M was prepared as described in Chap. II. The time was recorded
when a 5 ml stock solution was pipetted into the flask containing excess
potassium iodide solution; immediately following, we pipetted a 10 ml
stock solution into a 125 ml flask containing 90 ml of the same solvent.
This solution was diluted to 1/10 the original concentration by adding
21

22
10 ml of this solution to a 125 ml flask containing 90 ml of the sol¬
vent. Three more dilutions were made to form three different final
solutions ranging in concentrations from 0.0005 M to 0.0001 M in
chlorine, each with final volume of solution around 60 ml. Each flask
containing a chlorine solution was stoppered properly with a glass
stopper. At this point, we recorded the baseline of the solvent vs.
solvent with the double beam spectrometer. The spectrum (from 320 to
250 nm) of each chlorine solution was then recorded, proceeding from
higher to lower concentration, recording the time at the beginning of
each spectrum. We repeated each measurement at least three times,
proceeding from higher to lower concentration by refilling the sample
cell solution from the flask. When all spectra were obtained, the
chlorine stock solution already added to the potassium iodide solution
was then titrated.
Spectra of chlorine dissolved in pure benzene for several different
concentrations of chlorine (each studied as a function of time) are
shown in Fig. 3. The time interval between recording any two successive
spectra of the same solution was about 20 minutes. The concentration
of chlorine indicated for solutions A, B, and C are the values deter¬
mined by titration of the stock solution, combined with the known
volume ratios on dilution, but those values are probably not correct
concentrations for the solutions at the time the spectra were taken.
From measurements of the baseline (D in Fig. 3) before and after all
spectra of the chlorine solutions were taken, we notice that the
spectrum is not reliable below 280 nm, where absorption by pure benzene
in the sample and reference beams reduces the signal to zero. Each
sample spectrum shown in Fig. 3 was measured in a fresh solution formed

23
by refilling the sample cell from the flask as described above. The
decrease in absorbance of each chlorine solution with time (for
example, from A-l to A-3) was most probably due to the changing
chlorine concentration, not because of the photochemical reaction
between chlorine and benzene (in such dilute solutions), but rather
because of the escape of the chlorine gas from the solution into the
vapor phase in the flask.
The normalized absorbance at 280 nm (defined as the observed
O
absorbance A divided by the concentration of chlorine C.) of each
c A
chlorine solution was plotted as a function of time. The functions
were quite linear as can be seen in Fig. 4. There is a considerable
uncertainty in the extrapolated values of the normalized absorbance
at time zero because of the long extrapolation. The non-uniform
slope for different chlorine solution plots could be due to the diffi¬
culty in defining uniquely the procedure for handling the chlorine
solutions. When we repeated some measurements for one chlorine solu¬
tion from freshly prepared solutions, a different slope of the plot
was obtained. The best least-squares line through the data in Fig. 4
O
was used to obtain the extrapolated values of A /C at time zero. The
c A
results are shown in Table II. These values are then analyzed by the
Benesi-Hildebrand or Scott method (as described below) to obtain the
formation constant K, and the molar absorptivity e for the complex.
For the more concentrated chlorine solutions (around 0.1 M), we
used a single silica cell (described in Chap. II) of 0.1 mm pathlength,
measuring against air as the reference. Since these solutions were
prepared directly without successive dilution as described before, we
modified the procedure slightly from the one previously described.

Fig. 3. — Ultraviolet spectra of chlorine in benzene taken at
different concentrations and at different times.
(A) 0.00053 M, (B) 0.00027 M, (C) 0.00013 M (all in
CI2), (D) baseline; (1), (2), and (3) are the order
of successive measurements on fresh solutions (see
text).

ABSORBANCE
25
WAVELENGTH (nm)

Fig. 4.
Plots of the normalized absorbance of chlorine at 280 nm vs. time
for different chlorine solutions (around 0.001 M) .
A
C6H6
0
00
o
O^S
(v/v)
C6H6 *
20%
(v/v)
CC1
©
60%
(v/v)
w
40%
(v/v)
CC1
(
O
40%
(v/v)
C6H6’
60%
(v/v)
CC1
P
20%
(v/v)
C6H6*
80%
(v/v)
CC1

_3
NORMALIZED ABSORBANCE (xlO )
LZ

28
TABLE II
EXTRAPOLATED VALUES AT TIME ZE$0 OF
THE NORMALIZED ABSORBANCE (A /C^> FOR
DIFFERENT CHLORINE SOLUTIONS
Concentration of
Benzene (M)
£
Extrapolated Values of Normalized
Absorbance at 280 nm (Ac/C^) x 10
11.30
2.47
9.03
2.09
6.78
1.68
4.52
1.19
2.26
0.57
a.
Values obtained from the intercept (in Fig. 4) of the best least-
squares line. The uncertainty of each value is + 4% (twice the
standard deviation).

29
This time the concentration of chlorine in the cell could be determined
at a time much closer to that of the spectral measurement since the
concentration was high enough to be accurately determined. When the
sample cell was filled up each time with the syringe and placed in the
sample compartment of the spectrometer for the measurement, a 5 ml por¬
tion of the chlorine solution was withdrawn within one minute and
pipetted into the flask containing excess potassium iodide solution.
The measurement was repeated three to four times with fresh solutions
from the flask. As before, we measured the baseline before and after
the sample spectrum was obtained. Three spectra of chlorine solutions
of different concentrations in a 30% (v/v) CkH^, 70% (v/v) CCl^ solvent
are shown in Fig. 5. The spectrum A was for a 0.105 M chlorine solu¬
tion, spectrum B for 0.053 M chlorine, and spectrum C for a 0.026 M
chlorine solution; spectra D were taken of the solvent in the cell
before and repeated after the spectrum of one of those chlorine solu¬
tions was measured. A replotted spectrum for 0.027 M chlorine solution
in a 30% (v/v) , 70% (v/v) CCl^ mixture is shown in Fig. 6. The
spectrum is uncertain below 275 nm due to solvent absorption, so that
a clear determination of the wavelength of maximum absorbance cannot
easily be made, although it appears from Fig. 6 to be near 275 nm.
Analysis of the Ultraviolet Spectroscopic Data from Chlorine-Benzene
Solutions
The data at 280 nm from both dilute and concentrated chlorine
solutions were analyzed using the Scott equation (14),
^aS^c = CD//e280 + 1^Ke280 * ^3-1^
O
Here Z is the pathlength in cm, is the initial donor concentration

Fig. 5. — Ultraviolet spectra of chlorine solutions in a 30% (v/v)
C.H6 and 70% (v/v) CC14 solvent. (A) 0.105 M, (B) 0.053 M,
(C) 0.027 M in Cl?, (D) baseline (solvent vs. air) path-
length = 0.1 mm.

absorbance
31
WAVELENGTH (nm)

ABSORBANCE
32
WAVELENGTH (nm)
Fig. 6. Replotted spectrum of 0.027 M chlorine solution in 30%
(v/v) C¿H¿ and 70% (v/v) CC1. mixture (0.1 mm path-
length) .

33
O
(M), C is the initial acceptor concentration (M), A is the absorbance
A c
of the complex at 280 nm, e is the molar absorptivity of the complex
2o0
at 280 nm and K is the equilibrium constant. We assumed the absorption
at 280 nm is due to the charge-transfer absorption of the one-to-one
complex of chlorine with benzene. The reason absorbance at 280 nm
is studied is because that wavelength is the closest to the maximum
absorbance that can be studied before the solvent absorption becomes
too great.
For the data obtained from the dilute solution in the 1 cm path-
length cell, we used the extrapolated values of A /C. at time zero
C Pi
(Table II) for the Scott plot, while for those obtained from the con¬
centrated solutions in the short (0.1 mm) pathlength cell, we used the
direct absorbance readings and concentrations for the plot. At the
same time, we re-analyzed Andrews and Keefer's ultraviolet data (6)
by the same Scott plot. The three different sets of the ultraviolet
data were plotted on the same graph, and shown in Fig. 7. The error
bars for points obtained from the long pathlength cell were estimated
from the standard deviation of the least-squares fit to the extrapola¬
tion plot (Fig. 4), and from the uncertainty involved in the concentra¬
tion determination. The error bars for the points obtained from the
short pathlength cell are the standard deviations of three to four
repeated measurements. There was no way to estimate the uncertainties
from Andrews and Keefer's data since they did not report their experi¬
mental conditions.
From Fig. 7 we can say that for chlorine solutions of low concen¬
tration in chlorine ( ~ 0.001 M) the agreement between Andrews and
Keefer's result and ours is quite good. In particular, we have the

34
CD (M)
Fig- 7. — Scott plots of the complex of chlorine and benzene.
O and ■—• for 1 cm pathlength, □ and -—for 0.1 mm
pathlength cell, A and —• for Andrews and Keefer's
data (Ref. 6).

TABLE III
THE VALUES OF Ke280, K> AND e280 F0R DIFFERENT
SETS OF ULTRAVIOLET DATA FROM CHLORINE-BENZENE SOLUTIONS OBTAINED
FROM THE SCOTT PLOT
Parameters
Ke280
2 -l -2
(liter cm mole )
Long Pathlength Cell
(1 cm)
275
4- 32b
- 26
28°-l -1
(liter cm mole )
13,000
+ 23,000b
- 5,000
(liter mole
-1
)
0.022
+ 0.012b
- 0.015
Short Pathlength Cell
(0.1 mm)
Andrews and Keefer's
data (probably 1 cm cell)
321 + 4b
270 + llb
25,000
+ 21,000b
- 8,000
8,000
+ 2,200b
- 1,400
0.01 + .005
b
0.034 + 0.009
a.These values are for v = 278 nm, not 280 nm.
b. These upper and lower uncertainty limits were twice the calculated standard deviations.
c. The temperature for all measurements of equilibrium constant was 300 K.
LO
Ln

36
same intercepts of the straight lines which determine the product Ke^gQ»
The difference between the plots of the low and the high concentrations
of chlorine solutions may not be significant even though the factor of
the activity coefficients for solutions of different concentrations
could be different (57). However, the experimental uncertainties
were so large, we are not in a position to give any definite conclu¬
sions about this point.
The values of Ke , K, and e„ from the Scott plots for the
zoU zou
three different sets of ultraviolet data from chlorine solutions are
shown in Table III. For each set, the constants were calculated from
the best least-squares line. The upper and lower limits of uncer¬
tainties listed for each constant were twice the calculated standard
deviations.
Despite the fact that the experimental uncertainties were large,
the equilibrium constant K of the chlorine-benzene complex is believed
to be 0.025 + 0.015 liter mole ^. The large uncertainty in the value
of K is also expected theoretically (53, 54). Nevertheless, the
order of the magnitude of K indicates this complex is indeed a very
weak one. It is worthwhile to note that the saturation fractions
(defined as s = C^/C^, where is the concentration of complexed C^)
are between 0.1 to 0.25 in benzene for the above K values.
It has been suggested by Deranleau (54a) that the Scatchard plot
is a better method for the analysis of spectral data from weak molecu¬
lar complexes. In order to check the reliability of the values ob¬
tained from the Scott plot, wTe also used Scatchard's method to analyze
the short pathlength ultraviolet data and Andrews and Keefer's data.
The reason for not analyzing the long pathlength cell data was

37
because the values of the parameters Ke^ggj e280’ anc* ^ °f this system
were within the range of those obtained from the short pathlength
cell data, and those from Andrews and Keefer's data.
The Scatchard equation is given (54a) by
O o
A /AC C = K(e - A /AC )
c A D 280 c A
(3-2)
Here C is the equilibrium concentration of the donor, (C = C^,, the
D ’ D D’
total concentration of the donor for solutions with excess donor), A,
O
C , A , K and e__. are the same as defined for Eq. 3-1. We calculated
A c* 280 M
o ® o o
A /AC C and A /AC. for each C, at a particular C^ and plotted A /AC C
c AD c A A D ^ c AD
O
vs. A /AC for the five different values of C . The results are shown
— c A D
in Fig. 8. For the 0.1 mm (short pathlength) cell data, we obtained
o o O
the average values of A and Ac/£C^ by averaging all A /AC^C^
O ^
and A /AC values, respectively, at each C . The error bars in Fig.8
c A D
were obtained from the scatter of the measurements about the average
O o
value. There were five sets of (A /ACC , A /AC ) values at each of
c A D c A
the five different C values. We estimated K and Ke from the slope
D 280 ^
and the intercept of the best least-squares line through these points.
We applied the same technique to analyze Andrews and Keefer's data
to estimate K, ^273 and e278' calculated parameters of the
Scatchard plots are shown in Table IV. The upper and lower limits
were twice the calculated standard deviations.
When we compare Table III and IV, we see that the values of Ke ,
K and are not significantly different. Again, the value of K from
the short pathlength cell may be lower than the value from the more
dilute solutions. However, a line can be drawn through the error bars
for these data (Fig. 8) that includes the value of K from the long

A ¡%c
38
A flC°. (x 102)
c A
Fig. 8. — Scatchard plots for the complex of chlorine
with benzene. (1) © 0.1 mm short pathlength
data; (2) © from Andrews and Keefer's data

39
TABLE IV
VALUES OF Ke , K AND £ FOR
v v
CHLORINE SOLUTIONS FROM SCATCHARD PLOTS
Parameters
a
Short Pathlength
(0.1 mm)
Andrews and Keefer
Kev
228 + 8C
269 + 12c
K
0.0064 + 0.0048C
0.034 + 0.01C
£
V
35,000
+ 100,000c
- 16,000
7,300
+ 4 ,400°
- 1,300
a. Evaluated at v = 280 mm.
b. Evaluated at v = 278 mm.
c. The upper and lower limits were twice the calculated standard
deviations.

40
pathlength studies. We conclude that the value of Ke is 280 + 40,
2oU
with K = 0.025 + 0.015 liter mole ^ and e9gQ = 13,000, possibly from
values as low as 5,000 to values as high as 35,000 liter cm ^mole
In concentrated solutions, K may possibly be somewhat smaller. It
is not possible to reach more definite conclusions about these values
from this very weak complex (54).

CHAPTER IV
RAMAN SPECTROSCOPIC STUDIES
OF CHLORINE IN BENZENE SOLUTIONS
Introduction
We are particularly interested in studying the Raman frequency
shifts and the Raman intensity change of chlorine in solution as the
composition of the solvent is gradually changed from benzene by the
addition of carbon tetrachloride. The spectral profiles of the Cl-Cl
stretching vibration as a function of the composition of the mixture
C^Hg-CCl^ were carefully examined in order to understand more about the
nature of the complex of chlorine with benzene. As a check of the
reliability of the equilibrium constant of the complex determined from
the ultraviolet spectroscopic measurements, we analyzed the Raman in¬
tensity data both by the method of Rosen, Shen and Stenman (32) to
estimate the equilibrium constant and also by the method of Bahnick and
Person (58). The absolute Raman intensity of chlorine in carbon tetra¬
chloride was carefully determined.
Experimental Procedure
For this study, a Perkin-Elmer LR-1 Raman spectrometer was used with
a Ne-He laser with a minimum out-put of 2.7 mw. The Raman shift (A cm ^)
is proportional to the grating position read in mechanical units (called
drum numbers) from the linear spectrometer scale. The actual Raman
shift was obtained from a calibration curve of wavenumbers vs. drum
number using the known wavenumbers of the emission lines of a Ne lamp.
41

42
Three lines at 650.669 nm, 653.308 nm and 659.918 nm (or 433.1 cm \
495.1 cm and 648.5 cm ^ from the Raman exciting line at 15,802.7 cm ^
or 632.8 nm) were chosen for this purpose because they had been well
studied (59) . The Ne lamp source was a Pen-Ray quartz lamp operated
with a 115 volt 60 cycle/second power supply (Model No. SCT2, with
maximum current of 4 amperes from Ultra Violet Products, Inc., San
Gabriel, California). In practice, we placed the lamp in the sample
cell position in the sample compartment of the Raman spectrometer,
opened the mechanical slit to 5 microns and recorded the spectrum just
as though we were making a Raman measurement except the laser was not
turned on. As mentioned in Chap. II, the standard Perkin-Elmer 2.5 ml
multiple-path cell was used.
Because of the chemical instability of the chlorine solution, it
was desirable to work with low chlorine concentrations (around 0.1 M)
and to scan the spectrum quite rapidly. In order to obtain a spectral
resolution of 7.5 cm ^ at a 5% peak-to-peak noise level, the spectral
scan rate was about 6 cm ^ per minute, or 15 to 20 minutes to measure
-1 -1
a complete chlorine Raman spectrum from 480 cm to 600 cm
Before studying the Raman spectra of chlorine solutions, we investi¬
gated the solvent background in the region where the Raman band of
chlorine would appear. The Raman spectrum for the solvent mixture
of C^H^-CCl^-CHCl^ in a 6:3:1 ratio is shown in Fig. 9. The Raman
shift for chlorine is expected to appear between the two bands (v-^ of
carbon tetrachloride at 461 cm ^ on the low frequency side and v^g of
benzene at 606 cm ^ on the high frequency side) with only slight over¬
lap with these two solvent bands. Nevertheless, that overlap results
in the loss of most of the spectral information from the wings of the

- Raman spectrum of the CgHg-CCl^-CHCl-j mixture at a ratio of 6:3:1.
Fig. 9. -

arbitrary units

chlorine band. The extent of the overlap of the chlorine band with the
two solvent bands is shown in Fig. 10, where the spectrum was obtained
from a 0.12 M chlorine solution in the mixture of C H.-CC1.-CHC1„ at a
6 6 4 3
ratio of 8:1:1.
Secondly, since we knew that it was very difficult to prevent the
photochemical reaction from occurring, especially when the chlorine
solution was irradiated by the laser in order to obtain the Raman spec¬
trum, we studied the Raman spectrum of the photochemical product
(C,H,C1¿) in order to determine its interference with the chlorine
bo o
band. We found that the hexachlorocyclohexane (and also any other
unidentified photochemical products) did not have any observed Raman
shift near the chlorine band. This was done by an experiment in which
we let the chlorine solution (around 0,5 M) in a 6:4 C-H,-CC1. mixture
6 6 4
stand under the fluorescent room lights for several hours before tak¬
ing the Raman spectrum of the solution. Afterwards we eliminated the
chlorine by bubbling N gas through the same solution (but not from
the sample cell solution) and measured the Raman spectrum of the result¬
ing chlorine-free stock solution. We knew that the photochemical pro¬
duct did form in the experiment, since the solid residue after evaporat¬
ing the solvent was dissolved in carbon tetrachloride and the NMR spec¬
trum showed its existence. The Raman spectrum of this particular
chlorine solution (approximately 0.5 M) in the C^H^-CCl^ mixture at a
ratio of 6:4 is shown in Fig. 11. The Raman spectrum of the chlorine-
free stock solution at the same experimental condition is shown in
Fig. 12. The apparent reduction in the Raman intensity, both for v
lo
of benzene and v of carbon tetrachloride bands in the chlorine solu¬
tion (Fig. 11) compared to the intensities in the colorless solution

Fig.
— Raman spectrum of 0.12 M chlorine in a C^H^-CCl^-CHCl^
mixture at a ratio of 8:1:1.
10.

ARBITRARY UNITS
579 490
-1
RAMAN SHIFT (A cm )
â– c-

ARBITRARY UNITS
48
Fig. 11.
Raman spectrum of 0.5 M chlorine in 6:4
C,H,-CC1. .
DO 4

49
(Fig. 12), is most probably due to the absorption of the existing or
scattered light in the dark-colored solution. Within the experimental
error we can say that there is no observable Raman band due to photo¬
chemical products in this spectral region (between of CCl^ and v^g
of C6H6).
At this point we were ready to measure the Raman spectra of chlorine
solutions. We warmed up the spectrometer for one hour. During this
period, we prepared 100 ml of solvent, which always contained 10 ml of
chloroform. When the spectrometer was ready, we bubbled chlorine into
the solvent for 5 minutes (to prepare a solution about 0.1 M in
chlorine). A 5 ml sample of the chlorine solution was withdrawn for
titration and the Raman liquid cell was immediately filled with the
chlorine solution and placed in the spectrometer. After the Raman
spectrum of that chlorine solution was recorded, a 5 ml sample of solu¬
tion was again withdrawn from the stock solution for concentration
determination. We also determined (once only) the chlorine concen¬
tration for some solution taken directly from the Raman cell after its
Raman spectrum had been recorded. The result was the same as the
concentration from the stock solutions within the experimental error.
The depolarization ratio (p) of the Raman band of chlorine was
measured for three different chlorine solutions (one of chlorine in
pure , one in a 1:1 CgHg- CCl^ mixture, and one in pure CCl^). The
concentrations of these chlorine solutions were not determined but they
were believed to be around 0.2 M. For these measurements, we used an
Ahrens prism placed between the sample housing and the monochromator
as described in the Perkin-Elmer manual (60). The spectral resolution
was the same as before. The intensity of the parallel component was

ARBITRARY UNITS
50
Fig. 12. —
Raman spectrum of the chlorine-free 6:4
solution.
C,H,-CC1,
6 6 4

51
measured first by adjusting the experimental parameters so that the
maximum Raman scattering of this component was around 70% on the
chart paper scale. (We did not turn the gain higher because we
wanted to keep the peak-to-peak noise level less than 10%.) Then we
measured the intensity of the perpendicular component. In order to
compensate for the fluctuation of the laser power and the change in
chlorine concentration during the measurement, we measured again the
intensity of the parallel component immediately after we had measured
the perpendicular one. To obtain the depolarization ratio, we divided
the band area of the perpendicular component by the average band area
of the two measurements of the parallel component. Because the Reiman
band of chlorine was weaker as more carbon tetrachloride was added to
the solvent mixture, the peak-to-peak noise level was higher for Cl ^
in CCl^. As we tried to increase the amplifier gain in order to obtain
a comparable signal for different chlorine solutions, the depolariza¬
tion ratio of the Raman band of chlorine had larger uncertainty (for
solutions containing more CC1 ). In particular, the noise level was
4
so high that the intensity of the perpendicular component could not
be measured with certainty for the chlorine solution in pure carbon
tetrachloride. Hence, only an upper limit can be given for p for Cl
2
dissolved in pure CC1,.
4
Results of the Raman Measurements on Chlorine Solutions
-1
The Raman shifts (in cm ) observed for chlorine solutions are
shown in Table V as a function of the benzene concentration. The
values listed here are believed to be accurate within +0.5 cm \ and
were obtained from the positions of the band maxima. The concentration
of benzene was estimated from a knowledge of the volume of benzene

TABLE V
OBSERVED RAMAN SHIFTS, HALF-BAND WIDTHS AND
RELATIVE INTENSITIES OF CHLORINE SOLUTIONS IN CgHg-CCl.
SOLVENT MIXTURES AS A FUNCTION OF BENZENE CONCENTRATION
Concentration of
Benzene (M)
Concentration of
Chlorine (M)
a
Raman Shift
(cm-1)
Raman Half-Band Width
(cm~^-)
Relative
Raman Intensity
10.7
0.138
530.2
19.3 + 0.3
13.7 ’
9.04
0.123
531.2
18.3 + 0.7
11.0
6.78
0.181
533.2
19.3 + 0.4
8.4
4.52
0.102
535.6
18.6+0.3
7.1
2.26
0.123
539.7
17.8 + 0.4
6.3
1.13
0.205
542.0
15.5 + 0.3
3.7
0.0
0.129
543.3
12.4 + 0.5
2.75
a) The uncertainty is about +0-5 Cm
b)
As defined in Eq. 4-1; the uncertainty is about + 9.3%

53
added, and the total volume of the solvent. The concentration of pure
liquid benzene was taken to be 11.3 M at room temperature. The concen¬
tration of benzene in the solvent mixture was calculated by multiplying
this number by the volume fraction of benzene in the mixture (assuming
no volume change as benzene was dissolved in CC1.).
4
At our rather poor spectral resolution of 7.5 cm , we could not
observe (for any solvent mixture) two clearly separated Raman peaks,
one for complexed chlorine and the other for the uncomplexed molecule,
so we examined the spectral profile of the chlorine band as a whole.
The half-band widths of the chlorine solutions wTere measured and are
also shown in Table V. The corresponding values are plotted vs. the
concentration of benzene in Fig. 13, where we see clearly the broaden¬
ing of the chlorine Raman band that occurs as the ratio of (RH^ to CCl,
6 6 4
approximates 1:1. This behavior may be an indication of two overlapping
bands, one for complexed chlorine and the other for the uncomplexed
chlorine.
The relative integrated intensity I , . of the Raman band of
chlorine was defined as given by Bahnick and Person (58),
IR(v) 3VIRefM ‘
Here I is the band area of the chlorine band, I is the band area
v Ref
of the 366 cm chloroform reference band (an internal standard, always at
10% by volume), and M is the total molar concentration of chlorine.
The band area was measured by a planimeter (Keuffel and Esser Co.).
The most difficult thing in defining the band area was the decision
on how to draw a baseline. We estimated by different assumed baselines

HALF-BAND WIDTH (Av
54
Fig. 13. Plot of the Raman spectral half-band width o£
chlorine vs. the concentration of benzene (C )•

55
that the choice of the baseline might lead to an uncertainty of + 5-10%
in band area. In general, we drew a baseline through the average back¬
ground noise level in the two wings of the band. The relative inte¬
grated intensities obtained according to Eq. 4-1 for chlorine solutions
are shown in column 5 of Table IV. The corresponding values of I
R(v)
are plotted in Fig. 14 as a function of benzene concentration.
The uncertainties in the values of the relative intensities of
chlorine were estimated by propagation of errors. From Eq. 4-1 the
relative error is given by
‘WV) ■ [<5VV2 + (5Iref/Iref)2 + («‘/«V'2 •
(4-2)
From the scatter in measurements, we estimated that the individual
error is + 4.3% for (6I /I ) + 6.8% for (61 /I ) and 4.6% for
— v v — ref ref
(ÓM/M), so that the uncertainty in the relative intensity (61 , ./I , .
R(v) R(v)
was then found from Eq. 4-2 to be + 9.3%.
From Fig. 14 we see that there is a drastic intensification of the
relative Raman intensity of the Cl-Cl stretching vibration of chlorine
as the solvent is changed from pure CCl^ to pure benzene. The en¬
hancement in intensity is found to be approximately by a factor of 5
based on a total chlorine concentration or by a factor of 20 based on
the concentration of complexed chlorine. (Note: The fraction of
chlorine in pure benzene solution that is complexed is about 0.2 of
the total concentration, based on a value for the equilibrium constant
of 0.03 liter mole ^.) There appear to be only two possible explana¬
tions for this dramatic intensity increase — one due to the non¬
specific solvent effects and the other due to the effects from the
formation of the charge-transfer complex. A more detailed discussion

Fig. 1A. —
The relative Raman intensity of chlorine I . .
as function of the benzene concentration
(M).
Ej Measured values
® Calculated values from K and I
fyom Rosen plot and measured
TR(v)
O
determined
value of

â– R(v)
57
CD

58
will be given in Chap. VII.
Rosen, Shen and Stenman (32) have derived an equation which can
be used to analyze the Raman spectroscopic data from the complex, which
may not necessarily be a charge-transfer complex. Their equation was
derived from a statistical mechanical treatment assuming that the
properties of the acceptor are a statistical average over all possible
configurations between acceptors and donors weighed by an appropriate
distribution function. For a one-to-one complex, the Benesi-Hildebrand
type equation for Raman intensity data of the acceptor was found by
Rosen, Shen, and Stenman to be
1/[ R
(4-3)
Here I is the total relative intensity of the Raman band of the
R(v)
acceptor at some particular donor concentration, I is the relative
R(v)
intensity of the acceptor Raman band at zero donor concentration (i.e.,
the pure CC1 solution), p„ is the molar concentration of the pure donor,
4
O
p„ is the molar concentration of the donor in the solvent mixture, I
D K
is the Raman intensity statistically averaged over all possible orienta¬
tions of the one-to-one interactions between donor and acceptor, and
I o
K /pg ( = K) is the statistically averaged "equilibrium constant" over
all the one-to-one interactions.
In applying Eq. 4-3, we assumed that only one-to-one interactions
between chlorine and benzene have a significant effect on the Raman
spectrum. Using the relative Raman intensity data for chlorine in
this system, reported in the last column of Table IV, a plot of Eq. 4-3
is shown in Fig. 15, where the error bar for each point indicated the
uncertainty of the measured relative Raman intensity of chlorine. The

Fig. 15. — Plot of 1/[I^ ^ - 1^ ] vs. P^/Pg for chlorine in
benzene solutions.

R(v) R(v)
pb^pb

61
constant ID is found from the intercept of Fig. 15, by a least-squares
fit to be 54.7 * 3 7 (the upper limit is undefined because the standard
deviation is larger than the magnitude of the intercept), and the con-
I O o
stant K Ip/pn is calculated from the slope to be 1.2 + 0.15. Taking
K D —
t O
the ratio, we estimated that the equilibrium constant K (= K /pR) is
0.022 q’q2J li-ter mole-^ (the lower limit is undefined because the
O
upper limit of I is undefined). The undertainties here are the
standard deviations. Even though the uncertainty in K is large, its
value (0.022 liter mole ^) is almost identical with the equilibrium
constant determined from the ultraviolet spectroscopic measurements
given earlier in Chap. III.
In order to gain some confidence in our measured relative Raman
intensities of chlorine in different benzene solutions, we substituted
O f O
the values found here for I and K /p back into Eq. 4-3 together with
K B
' -1
the measured value for I , (2.75 liter mole ) to obtain values for
R(v)
I vs. p„ to be compared in Fig. 14 with the measured values of
R(v) a
I„, .. Comparing these calculated values of I , N's with the observed
R(v) R(v)
ones, we see that the measured I ^'s are reasonably good.
Earlier, Bahnick and Person (58) had derived a different expression
for the analysis of the Raman spectroscopic data of a complex to obtain
the formation constant. By analogy to the derivation of the method
for analysis of ultraviolet spectroscopic data by Tamres (61), they
obtained an equation for a one-to-one complex (assumed to be in a
particular configuration):
vbr(v) - -s+ cl -c>/v w+i/k[i* - w.
(4-4)
i w
Here IR^ . , IR^ , IR are the same as those defined for Eq. 4-3; pR is

62
still the molar concentration of the donor and C is the total molar
A
concentration of the acceptor, while C is the molar concentration of
the complex (or the molar concentration of the complexed acceptor for
the one-to-one complex). The difference between Eq. 4-3 and Eq. 4-4
is that the former is equivalent to the Benesi-Hildebrand equation (2),
while the latter is similar to the Scott equation (14).
In order to apply Eq. 4-4, a trial value of K has to be assumed,
and C is then computed for each solution. The left-hand side of Eq. 4-4
O
is then plotted vs. (pj> + C - C) , and the best straight line is
fitted to the points by least squares. The value of K calculated from
this line was used to recompute C and so on until K converges to a
constant value (for more detailed procedure, see Ref. 58). Since C for
the complex of chlorine with benzene is very small (since it was found
from the ultraviolet spectroscopic data that the equilibrium constant
O O
was very small), (p + C. - C) is almost equal to (p + C.), so we
BA BA
used the value of K (0.022 liter mole-') obtained from the plot of
Eq. 4-3 to calculate C and then made a least-squares fit to the points
O
calculated. The formation constant K and the values of I were then
R
estimated from this best straight line (as shown in Fig. 16) to be
0.034 q ^ liter mole and 38.9 ^ ^ respectively.
Thus both methods for analyzing the Raman intensity data gave
almost the same equilibrium constant K for the complex of chlorine with
benzene and nearly equal values for the relative molar Raman intensity
O O
1^ for the complexed chlorine. The slight differences in K and Ip
obtained from the two methods could be due just to the differences
between the two procedures (Benesi-Hildebrand and Scott), since the
two methods weigh the experimental points differently.

63
The results of the depolarization ratio measurements (p) for the
Cl-Cl stretching vibration measured in these different chlorine-
benzene solutions are shown in Table VI. p was estimated from the ratio
of the band area of the perpendicular component to that of the parallel
one. As mentioned in the experimental procedures section, the perpen¬
dicular band of chlorine in carbon tetrachloride was weak and the
noise level was so high that it was impossible to obtain a reliable
value of p in this solvent. We believe these results show a tendency
for the depolarization ratio to increase as the benzene concentration
increases, possibly because more chlorine molecules are complexed as
more benzene is added. However, we cannot make a definite conclusion
about whether any real increase in the depolarization ratio occurs as
benzene is added, since the value of p for chlorine in carbon tetra¬
chloride could not be determined accurately. In order to give some
indication as to what the value of p for chlorine in carbon tetrachlo¬
ride might be, we listed the gas phase value in Table Vi.
Absolute Raman Intensity of Chlorine in Carbon Tetrachloride
It is possible to obtain the absolute Raman intensity and hence
the values of the average polarizability derivative a' and of the
anisotropic polarizability derivative y' from the measured relative
Raman intensity. This had been demonstrated first by Bernstein and
Allen (62) and confirmed later by Long, Gravenor and Milner (63). In
g
order to calculate a' and y' we have to know both (which will be
defined in the following) and the depolarization ratio p^ of the band
g
at v. Bernstein and Allen (61) showed that a standard intensity P
v
(for a Raman band at v) of a compound could be defined by comparing

64
Fig. 16.
Plot °f P /[(i
B R(v)
Eq. 4-4.
XR(V)J vs- (pw + c°
13 A
~ C) for

65
TABLE VI
DEPOLARIZATION RATIO OF
CHLORINE IN DIFFERENT CHLORINE SOLUTIONS
Concentration of
Benzene (M)
11.3
5.65
o.ob
gas phase0*
Depolarization (p)
of chlorine
0.27 + 0.03
0.25 + 0.04
< 0.22C+ 0.04
0.14
a. p = band area of perpendicular component divided by band area of
parallel component.
b. In carbon tetrachloride.
c. It was difficult to measure the perpendicular band of chlorine
in this solvent with certainty, so the upper limit is listed
(see text).
d. See Ref. 63, 64, 65 and others.

66
this band with the measured intensity of the 459 cm ^ band of carbon
tetrachloride in the pure liquid:
= [45a + 7y’-]— /[45a' + 7y ]
»2 t2 compound '2 '2 CCl^
v 459
.2 ,2
(4-5)
CC1,
By taking arbitrarily the value of [45a + 7y ] 4 to be 1,
459
S “1
P" of the v = 366 cm chloroform band was estimated to be 0.28 by Long
v
Gravenor and Milner (63). From our measurement, we obtained the rela¬
tive molar intensity of chlorine in carbon tetrachloride with respect
to the 366 cm band of 1.25 M chloroform to be I = 2.75 + 0.26 (as
R -
given in Table V . Analytically, this means that
• 2
>2CU
,2 CHC13
[45a + 7y ^/^a + 7y ] ^
(2.75 + 0.26) x 1.25 = 3.46 + 0.30 .
(4-6)
From the value of P for chloroform (63) and the results in Eq. 4-6,
366
we then obtained the standard Raman intensity of the Cl-Cl stretching
-1
vibration at 543 cm to be:
.2 *2 Cl
.2 CC1,
c iz. ix ux-1 12 ' uex/
P = [45a + 7y ] V[45a + 7y ] = 0.969 + 0.084.
543 543 459 (4-7)
.2 -1
Often in the literature, y of the 459 cm band of carbon tetra¬
chloride has been assumed to be zero [for example, Long, Gravenor and
s , 2
Milner (63)] defined P explicitly with the assumption that (y ) is 0
for this band. We verified the reasonableness of this assumption by
. 2
calculating (y ) from Bernstein's value 0.015 for p, finding that
.2
7y contributed only 2% to the total intensity of this particular
band. Therefore, we can assume in practice that:

67
r/1. .2 ^ _ ’2 CC14 _ -2 CC14
t45a + i4594 - £4ja ]459 •
(4-8)
The value of [45a ] 4 had been measured in liquid CC1 and found (64)
459 4
_ Q 4
to be (33.71 + 9.63)x 10 ° cm /g. From this value and Eq. 4-7 we obtain
12 12 Cl 9 —8 4
[45a + 7y ] 2 = (32.3 + 10.0) x 10 cm /g
543 ~~
(4-9)
(Here the major uncertainty is in the value for the absolute intensity
of the CC1 band.)
4
As has been mentioned, the depolarization ratio of chlorine in
carbon tetrachloride was difficult to determine with our spectrometer.
However, the gas phase value (p = 0.14) (65) for chlorine is most probably
the lower limit for the values (see Table VI). Using this value, we
then obtained
12 12 12
p = 3y /(45a 4- 4y )= 0.14 . (4-10)
Solving Eqs. 4-9 and 4-10, we find that the absolute intensity of chlo¬
rine is given by
2 2
a' = (0.512 + 0.159) x 10-8 cm4/g = [ (3a/3C )Q] *" (4-lla)
y ^ = (1.32 + 0.41) x 10 ^ cm /g = [(3y/3£ ) ] . (4-llb)
1 0
4 4 12 »2
We may convert from unit of cm /g to cm , by multiplying a and y
-24
each by the reduced mass of chlorine (29.426 x 10 g). When this was
done, we found
i2 _30 4 2
a = (0.15 + 0.047) x 10 cm = [(3a/3r ) ]
10
(4-12a)
y’2 = (0.39 + 0.12) x 10 30 cm4 = [(3y/3r ) ]2
— 1 0
(4-12b)

63
or
a = (3.9 + 0.6) x 10 ^ cm2 (4-13a)
y' = (6.2 +0.9) x 10-16 cm2 . (4-13b)
However, the depolarization ratio of chlorine in benzene was measured
to be 0.27 (see Table VI) which may be an upper limit for p for chlorine
in carbon tetrachloride. With this value we found
a = (3.3 + 0.46) x 10 ^ cm (4-l4a)
y' = (8.2 + 1.2) x 10-16 cm2 . (4-14b)
We believe that the depolarization ratio of chlorine in carbon
tetrachloride may be much closer to the value found for the gas phase
than it is to the value obtained in benzene solution, since carbon
tetrachloride is expected to be a relatively inert solvent. Therefore
i i
the values of a and y fot chlorine in carbon tetrachloride given by
Eqs. 4-13a and 4-13b are expected to be more reliable, although the
range of possible values for these parameters allowed by the uncertain¬
ties in p (compare Eq. 4-13 to Eq. 4-14) is not very large.

CHAPTER V
INFRARED SPECTROSCOPIC STUDIES OF
CHLORINE IN BENZENE SOLUTIONS
Experimental Procedu' e
The concentrations of chlorine solutions required for infrared
studies (0.3 M to 0.9 M) were higher than those for ultraviolet and
Raman studies. At these concentrations, we found that the photochemical
reaction occurs very easily. When we exposed the solution of chlorine
in benzene to fluorescent light, and determined the infrared spectrum
as a function of the time after it was prepared, an increase in the
concentration of photochemical product was observed as illustrated in
Fig. 17. Since it was impossible to prepare the solution and to fill
the sample cell in complete darkness, there was no way to prevent the
photochemical reaction from occurring. At last we tried adding oxygen
gas to the solution to act as a radical quencher (56). As a result,
the photochemical reaction was inhibited considerably, if not completely.
A small amount of iodine in addition to oxygen was reported to be even
more effective in quenching the radicals (56) . Since iodine itself
forms a stronger complex with benzene than does the chlorine, we did
not try to use iodine as radical quencher in our studies for fear of
further complicating the system.
The infrared spectrometer we used was a Perkin-Elmer Model 621.
In order to minimize the change in chlorine concentration during the
69

Fig. 17. — Infrared spectra of chlorine (about 0.6 M) in benzene solutions
as a function of the exposure to fluorescent lights.
A baseline: benzene vs. benzene (pathlength, 1 mm)
B freshly prepared chlorine solution
C chlorine solution exposed to fluorescent lights for one hour
D chlorine solution exposed to fluorescent lights for two hours

TRANSMITTANCE (%)

72
course of recording the spectrum and the growth of the photochemical
product sufficient to distort the absorption band from the Cl-Cl
stretching vibration, we chose to sacrifice the signal-to-noise ratio
(S/N), reducing it to around 125, with a spectral resolution of about
2 cm \ The total scan time for each measurement from 650 cm-''" to
350 cm-'" was about 15 to 20 minutes.
Before the preparation of the chlorine solution, we warmed up the
spectrometer and covered the sample, compartment with a black polyethy¬
lene sheet. The baseline was recorded beforehand to give the apparent
transmittance of solvent vs. solvent in the matched cells described
earlier in Chap. II. At this point, we prepared the chlorine solution,
withdrew a 5 ml portion for determination of the chlorine concentration,
and immediately filled the liquid cell with the chlorine solution using
a micropipette (5 3/4 inches long, P5205-1 Scientific Products, Evans¬
ton, Illinois). The sample cell was carried to the spectrometer in a
box covered with a black polyethylene sheet. All lights in the room
were turned off (note the sample preparation room was separated from
the laboratory containing the spectrometer), since the light emitted
from the infrared glower source was sufficient to permit the alignment
of the cells in the sample compartment. A special holder was made to
fit the sample compartment so that we could reproducibly align the
sample each time with little light. After the spectrum of the chlorine
solution was taken, the sample cell was placed in the box mentioned
before, and connected to the vacuum line in order to pump out the
chlorine. The chlorine solution always filled the cell up to the top
of the glass tubing, so that the pumping process did not reduce the
liquid level below the upper edge of the light path. It usually took

73
about half an hour to eliminate the chlorine gas from the solution.
The baseline spectrum of clear solution vs. solvent was then recorded.
The baseline always changed a little from that recorded at the begin¬
ning but not enough to affect the total band area of the chlorine ab¬
sorption by as much as 2%. Most importantly, if enough of the photo¬
chemical product was present in the original chlorine solution, we
could detect it by its infrared absorption spectrum in the second clear
solution after the chlorine was removed. If that product was detected,
then we would have to repeat the measurement. Occasionally, instead
of pumping out the chlorine gas in the sample cell, we withdrew a 1 ml
portion of the chlorine solution and determined the concentration of
chlorine by titration to find out how much had been lost by both the
photochemical reaction and the escape of chlorine gas from the cell.
We had actually tried three liquid cells with different path-
lengths. The 1 mm liquid cell was made specially of tantalum metal
in our machine shop. Its construction was not much different from an
ordinary standard round liquid cell with Teflon spacer (Barnes cell
# 0004-035) such as that used to take the spectrum shown in Fig. 17.
Since the intensity of the chlorine absorption (spectrum B in Fig. 17)
with this 1 mm pathlength cell was so small, it was difficult to
observe especially the very weak absorption by chlorine in benzene
solutions diluted very much with carbon tetrachloride. Furthermore,
it was difficult to distinguish between the baseline shift due to the
photochemical reaction and the absorption by the chlorine. The 6 mm
pathlength liquid cell described in Chap. II also had been used to
measure the absorption by chlorine, but the benzene absorption in this
long path cell was so high in this region, and the actual signal-to-

74
noise ratio was so low, that we could not measure a reliable chlorine
absorption band with this 6 mm cell. Hence, the 3 mm pathlength liquid
cell (also described in Chap. II) was the most suitable for this kind
of measurement. The pathlength (3 mm) was obtained by measuring the
thickness of the Teflon spacer with a micrometer. Since the absorp¬
tion by carbon tetrachloride was less than that by benzene in the
infrared region near the chlorine absorption band, we were able to
measure the absorption by chlorine dissolved in carbon tetrachloride
in the 6 mm pathlength liquid cell by making a special effort (more
discussion will be given later in this chapter).
The spectrum of 0.33 M chlorine in benzene in the 3 mm cell is
shown in Fig. 18 (recorded vs. pure benzene in the reference beam in
a matched cell) , where it is compared with the spectrum of benzene in
that same cell, recorded with air in the reference beam, and with a
baseline of benzene vs. benzene. Benzene absorbs almost totally above
575 cm ^ and below 410 cm \ so that we lost all the spectral informa¬
tion for the chlorine-benzene solution outside the region from 410 to
575 cm 1. However, within that spectral region, we were able to work
at quite a good signal-to-noise ratio (a ratio of 125) , and so we
could obtain a reliable spectrum. (The spectra were recorded in the
transmittance mode rather than in the absorbance mode because opera¬
tion of our Perkin-Elmer 621 in the absorbance mode was not reliable
at the time of the experiment.)
Spectra of chlorine solutions in benzene diluted by carbon
tetrachloride are shown in Figs. 18-21. As benzene was gradually
diluted by the addition of carbon tetrachloride, less solvent absorp¬
tion was found above 575 cm-'*', so that more spectral information was

Fig. 18. — Infrared spectra of 0.33 M chlorine in benzene. The pathlength
of the cells for all studies is 3 mm.
A spectrum of benzene vs. air
B spectrum of chlorine (0.33 M) in benzene vs. benzene in a matched
cell
C baseline of pure-liquid benzene in matched cells

TRANSMITTANCE (%)
WAVENUMBER (cm 1)

Fig. 19. — Infrared spectrum of chlorine in 60% (v/v) benzene and 40% (v/v)
carbon tetrachloride. The pathlength is 3 mm for all spectra.
A spectrum of the solvent vs. air
B spectrum of 0.445 M chlorine vs. solvent
C baseline of solvent vs. solvent

TRANSMITTANCE (%)
WAVENUMBER (cm-1)
C/D

Fig. 20. — Infrared spectrum of chlorine solution in 20% (v/v) benzene and
80% (v/v) carbon tetrachloride. Pathlength is 3 mm. (Note scale
change from Fig. 18-19)
A spectrum of solvent vs. air
B spectrum of 0.99 M chlorine solution vs. solvent
C spectrum of 0.296 M chlorine solution vs. solvent
D baseline of solvent vs. solvent

TRANSMITTANCE (%)
00
o

Fig. 21. — Spectrum of chlorine in carbon tetrachloride. Pathlength is 3 mm
for all spectra.
A spectrum of carbon tetrachloride vs. air
B spectrum of 0.33 M chlorine in carbon tetrachloride vs. carbon
tetrachloride
C baseline of carbon tetrachloride vs. carbon tetrachloride

TRANSMITTANCE (%)
£ I L J
450 500 550 600 650
WAVENUMBER (cm-1)
00
ro

83
unveiled concerning the high frequency wing of the chlorine absorption
band. However, the strong absorption by carbon tetrachloride in the
3 mm cell below 500 cm made it difficult to observe the low frequency
wing of the chlorine absorption band. This situation is illustrated in
Fig. 20 and Fig. 21. The weak absorption band near 510 cm ^ in Fig. 20B
was due to the hexachlorocyclohexane.
One of the most exciting things in this work was the observance of
the infrared absorption band of chlorine in carbon tetrachloride shown
in Fig. 21. To the author's knowledge, this was the first time that
the infrared absorption by chlorine has been observed for a chlorine
solution in a solvent whose molecules have te.trahedral symmetry. This
spectrum is quite different from that of chlorine in benzene (Fig. 18)
or those of chlorine in different benzene-carbon tetrachloride mixtures
(Figs. 19-20). It is very broad and weak. If one did not use a long
pathlength liquid cell, this broad and weak absorption could easily be
confused with some baseline shift of unknown origin. To make clear that
the absorption in Fig. 21B is due to chlorine in carbon tetrachloride,
we measured this absorption band at several different concentrations
of chlorine, as shown in Fig. 22. The dependence of the absorption on
the concentration of chlorine was clearly demonstrated. To be more
convincing, the spectrum of 0.33 M chlorine in carbon tetrachloride was
measured with the longer pathlength (6 mm) cell. The spectrum obtained
is shown in Fig. 23 where the absorption is seen to be twice as large
(within experimental error) as that shown for the same solution in
Fig. 21 in a 3 mm cell.

Fig. 22. — Infrared spectra of chlorine in carbon tetrachloride. The pathlength
is 3 mm for all measurements. Compare these spectra also with Fig. 21
and Fig. 23.
A spectrum of carbon tetrachloride vs. air
B spectrum of 1.2 M chlorine in carbon tetrachloride vs. carbon tetrachloride
C spectrum of 0.66 M chlorine in carbon tetrachloride vs. carbon tetra¬
chloride
D baseline of carbon tetrachloride vs. carbon tetrachloride

o
W
O
H
H
oo
20
40
60
80
100
450
500
„L
550
WAVENUMBER
600
650
(cm 1)
Oo
Ln

Fig. 23. — Infrared spectrum of chlorine in carbon tetrachloride solution
with 6 mm pathlength liquid cell.
A spectrum of carbon tetrachloride vs. air
B spectrum of chlorine (0.31 M) vs. carbon tetrachloride
C
baseline of carbon tetrachloride vs. carbon tetrachloride

TRANSMITTANCE (%)
WAVENUMBER (cm"1)

88
Analysis of the Experimental Results
The absorption band of the chlorine solutions recorded on the trans¬
mittance scale was converted to a plot of absorbance vs. wavenumber in
a point-by-point replot by calculating the natural logarithm of the
ratio of the transmittance of the chlorine to that of the baseline.
Tha absorbance of chlorine in each solution was calculated at 0.5 M
chlorine by assuming the absorbance obeyed Beer's law semi-quantitative-
ly. The interval between any two points was 2 cm ; the total spectral
range was about 200 cm The spectra of chlorine in different ben¬
zene solutions were then replotted as absorbance vs. wavenumber by
Calcomp Plotter. All these were done in one computer program with
only one set of initial input data: the readings of the transmittance
of the chlorine solution and of the baseline. Some of the replotted
spectra are shown in Fig. 24. It can be seen in Fig. 24 that none of
the spectra were complete because the solvent absorption damaged the
determination of the spectral information in the wings of the chlorine
absorption band.
The incompleteness of the chlorine absorption band made it diffi¬
cult to measure directly the absorption intensity of the chlorine in
different benzene-carbon tetrachloride mixtures by measuring the band
area. To solve this problem, we tried to fit different known theoreti¬
cal curves to the measured absorption band contour. The first and most
successful theoretical curve we tried to fit was a Lorentzian function,
since most infrared absorption bands can be fit quite well by that
function (66-70). The Lorentzian function is
L(v) = a/[(v - b) “ + O
(5-1)

Fig. 24. — Replotted infrared spectra of chlorine in benzene solutions; the
concentration of chlorine in each solution is 0.5 M and the
pathlength is 3 mm.
This line indicates the wavenumber reading of 530 cm 1 in
order to observe the frequency shift easily.

ABSORBANCE ABSORBANCE
0.5
i
o
o

91
Here, a, b, and c are constants related to the infrared absorption band
by the following relationships (69):
a = S Avi^2/2'i7 , (5-2)
b = vQ , (5-3)
and
c = (1/2)(Av) . (5-4)
Here S is the total integrated intensity of the absorption band,
Av^/2 is the true half-band width and Vq is the wavenumber of the
absorption maximum. The nonlinear least-squares curve fit of Eq. 5-1
to the observed spectrum was carried out with Quantum Chemistry Ex¬
change Program No. 60 (71) at the Computing Center of the University
of Florida. We tried with at least five different sets of initial
parameters (a, b and c) for each curve fitting program. We selected
the set (a, b and c) generated by the program which gave the best fit.
In most of the cases, almost all of the initial parameters gave the same
final results. Some of the results of the Lorentzian curve fitting are
shown in Figs. 25-27. where the ordinate scale is linearly proportional
to the absorbancé. We obtained the recalculated absorbances (A ) in
each of Figures 25-27 by the equation
A = 5.3 A /(A )
cc co co max
(5-5)
Here A is the recalculated absorbance at wavenumber v, A is the
cc CO
observed absorbance at wavenumber v, (A ) is the maximum observed
’ co max
absorbance of chlorine in each chlorine solution. The factor 5.3 is
a scaling factor for the plot to utilize the full scale. The reason

Fig. 25. — Lorentzian curve (F) fitted to the observed absorption spectrum
of chlorine in benzene (I). Curve E is the difference (absolute
value) between I and F.
E ...
F
I
o o o

cc
O
5.0
/
V
a
4.0
3.0
1.0
0.0
2.0 _
p
/
/
/©
/
to
f
/ e
r
p*
o /
/
.E
\
01
l
\
o\
\
°\
Oi
\°0
\0O
\v0
\c°
s. coo I
oooso
N. 000°l>oooo„
•>»
I ••• ••
r r
560
520
480
440
WAVENUMBER (cm X)
VD
LO

Fig. 26. — Lorentzian curve (F) fitted to the observed absorption band (I) of
chlorine in 60% (v/v) benzene and 40% (v/v) carbon tetrachloride.
Curve E is the difference (absolute value) between I and F.
E ...
F

cc
i.O _
4.0
3.0 _
2.0
1.0
0.0
o /
/
rt f
/
/
/°
/
/
/ «
0
/•
/
/ 0
a
•T
y /
•i.**
\
e\
\
oV
\
o\
\
°V
*
\
0
°V
e
\
°\
S'..
\ o -r
\
S o000o
N
E .
• • a
•• l
560
520
480
440
WAVENUMBER (cm ^
\o

Fig. 27. — Lorentzian curve (F) fitted to the observed absorption band (I) of
chlorine in carbon tetrachloride. Curve E is the difference (absolute
value) between I and F.
E ...
F
I
o o o

cc
5.0 “
4.0
3.0
2.0
0 /
000 '
0 / V
o / F
/
oca *
s
os
/
t o
%o ®
/ O
/ o
f 0 O
tzoo
o /
1.0 - S00 0
-
0.0
00 9 0
• o
\
°o\
cA
o\
C
\
°\
O O
V O
\0
X
O N.
«7 \
«o V
00
.1 •
♦ „ • • -
620
580
540
500
WAVENUMBER (cm 1)
VO

98
for scaling was because it was easier then to see how good the curve
fitting was. In Fig. 25, the Lorentzian curve fits quite well to the
observed spectrum of chlorine in benzene near the maximum absorbance,
but the fit in the wings is not so good. Similar results are found for
Figs. 26 and 27. As it can be seen from these figures, the band area
from the Lorentzian curve is always an underestimate of the true band
area except for chlorine in carbon tetrachloride, since the wings of
the Lorentzian curve are lower than the observed ones. The underesti¬
mate in band area by this method was around 8-10% as estimated from
the integrated area of the difference between the calculated Lorentzian
curve and the observed spectrum shown as curv.e E in Figs. 25 and 26.
Since the agreement between the Lorentzian curves and the observed
ones is quite good for all the chlorine solutions we measured, we could
then estimate the absolute intensities of chlorine in different benzene
solutions from the values of the total absorption intensity S from the
following equation:
(5-6)
Here A (as defined in Eq. 1-5) is the absolute integrated molar
absorption coefficient in cm mmole '''of chlorine, n is the total
C12
molar concentration of chlorine (n = 0.5 M here), l is the path-
CJ-2
length of the liquid cell. The absolute integrated intensities of
the Cl-Cl stretching vibration for chlorine in benzene solutions are
shown in Table VI. The uncertainty in n was around + 8%, the un-
CI2
certainty in i was less than + 2%, and the uncertainty in S has been
discussed earlier; from these, the overall uncertainty for A was esti¬
mated to be + 13% or - 8%.

The intensity (A) of the chlorine absorption band increases by a
factor of five from the solution in pure carbon tetrachloride to the
solution in pure benzene. The enhancement in intensity for the chlorine
vibration for solutions in benzene has been interpreted on the basis
of two extreme theories — one is the vibronic coupling effect (26)
from the theory of charge-transfer complexes, and the other is the
quadrupole-induced dipole effect (30-31) of classical electrostatic
interaction theory. We shall discuss the relative contributions of
these two possible effects to the enhancement of the intensity of
chlorine in benzene after we present our investigation of this
electrostatic effect in Chap. VI.
Comparing the frequencies of the maxima of the infrared absorption
of chlorine solutions given in Table VII with the maxima of the Raman
band shifts reported in Table V (Chap. IV), we see clearly that there
is a significant difference in the frequency shift between infrared
and Raman spectra of chlorine solutions as the solvent is gradually
changed from benzene to carbon tetrachloride. The frequency maximum
of the infrared spectrum shifts slightly from 527 cm ^ for chlorine
in 11.3 M (pure) benzene to 532 cm ^ for chlorine in 2.26 M benzene
in CCl^; then suddenly there is a big jump to 5A5 cm ^ for chlorine
in pure carbon tetrachloride. On the other hand, the Raman frequency
maximum of chlorine apparently shifts smoothly from 530 cm ^ in pure
benzene to 5A3 cm ^ in pure carbon tetrachloride. These results may
indicate that the infrared absorption band of the chlorine solutions
in benzene is composed of only one band (from the complexed chlorine)
while the Raman band of the chlorine solutions in benzene is a composite
of two unresolved bands, one for the complexed chlorine and the other

TABLE VII
INTEGRATED INFRARED MOLAR ABSORPTION COEFFICIENTS (A) AND THE
PARAMETERS OF THE LORENTZIAN FUNCTIONS FOR THE Cl-Cl VIBRATION OF
CHLORINE IN BENZENE SOLUTIONS
Concentration of
•
Integrated Infrared Absorption
b
Parameters
of the
Lorentzian Curve
Benzene (M)
Intensity of Chlorine (A) (cm/(mmole)
c
S
v0(cm-1)
Av^icm-1)6
11.3
333.0
49.95
527.1
40.9
9.04
325.6
48.84
528.4
37.1
6.78
274.0
41.10
530.0
35.3
4.52
185.0
27.74
531.0
30.9
2.26
122.0
18.29
532.3
33.2
o.of
78.1
11.72
545.0
87.6
a. The values are believed to be reliable to + 13% or - 8% (see text) .
b. All parameters were obtained from curves normalized to 0.5 M (see text).
c. The values (except for chlorine in carbon tetrachloride) are believed to be underestimated by 8-10%.
d. The reliability of the frequency maximum (vq) is believed to be. + 0*5 cm--'-.
e. The half-band widths (Av-j^) are believed to be reliable to + 2 cm~l.
f. In carbon tetrachloride.
100

101
for free chlorine in CC1 . This may occur since the infrared spectrum
4
for a free homonuclear diatomic molecule like chlorine is forbidden,
but its Raman spectrum is allowed.
The half-band width of the infrared spectrum in benzene is twice
as small as that for chlorine in carbon tetrachloride as is shown in
column 5 of Table VII. We may estimate the lifetime of the "complex"
of chlorine with benzene (or with carbon tetrachloride), based on the
Heisenberg uncertainty principle:
or
AE • At < h
cAv At < 1
1/2
(5-7)
Here h and c are universal constants, Av ^ t^e true half-band
width, AE and At are uncertainties in energy and time, respectively.
We find from our data that the lifetime of the complex of chlorine with
-12
benzene may be about 0.83 x 10 sec and that of the complex of chlorine
-12
with carbon tetrachloride about 0.41 x 10 sec. Even though the
, -12
lifetimes in both cases are in the same order of magnitude (10 ) as
was found for the lifetime of the complex of iodine with benzene by
Kettle and Price (see Ref. 33 and the footnotes cited), they are
clearly different from each other, suggesting a difference in the inter-
molecular interactions for the two cases. Furthermore, the half-band
width of the infrared spectrum of chlorine in benzene is twice that
found for the Raman band of chlorine in benzene (see Table V). This
may relate to the difference in the time-correlation functions (72)
between the infrared absorption band and the Raman band. Since the
analysis of these data to obtain the time correlation functions requires

102
fairly complete measurements over the entire absorption band, we did
not attempt the analysis because of the incompleteness of the chlorine
spectra in both our Raman and infrared measurements, as described earli¬
er.
In principle, we could also analyze the complex formation of
chlorine with benzene from the infrared integrated intensity data,
using either the Benesi-Hildebrand method (2) or Scott method (14).
In order to use the same method as for the ultraviolet data and the
Raman data, we applied the Scott method here. We rewrote Eq. 3-1 for
the analysis of the infrared intensity data,
i C° C7A = (l/e)C + 1/Ke
D A c D
(5-8)
Here A /ZC is the absolute integrated infrared intensity of the
c A
chlorine in each chlorine solution (based on the total chlorine con¬
centration) , e is the absolute integrated infrared intensity (e = A)
O
for the completely complexed chlorine. Actually A /iC is not A of
c A
Eq. 5-6. We have to subtract the absorption intensity of "free" chlo¬
rine in the presence of carbon tetrachloride. However, it is difficult
to make the correction properly because the wings of the absorption of
chlorine were not complete (see Figs. 25 and 26).
Therefore, we analyzed the data in two ways, one without any
correction and the other with an estimated semi-quantitative correction.
O
In the first case, we assumed that A /£C is just the value of A
c A
0 o
from Eq. 5-6, and plotted C /A vs. as shown in Fig. 28. From
the best least-squares fit, we obtained the product of Ke from the
intercept to be 64 + 8 [liter * cm(mmole) ^ mole '*’)], e to be (6.608 +
3 -1
1.2) x 10 cm(mmole) from the slope, and K to be 0.09 + 0.04 liter

(x 10
103
C (M)
D
Fig. 28. — Scott plot of the infrared data for the complex of
chlorine with benzene (neglecting the intensity of "free"
chlorine in the presence of carbon tetrachloride).

104
mole . Here the uncertainties are the standard deviations. In the
second case, we made a trial-and-error estimate of how much absorption
intensity for free chlorine in carbon tetrachloride should be subtracted
from A in order to obtain an equilibrium constant closer to those we
obtained from analysis of the ultraviolet and Raman data and still give
a reasonably good linear plot for Eq. 5-8. We found a fairly good
linear plot of Eq. 5-8 by subtracting one-half of the absorption in¬
tensity for chlorine dissolved in pure carbon tetrachloride from the
value of A from Eq. 5-6. Thus we made the correction by:
A /£ C° = A - CL/2)X , AC12 . (5-9)
c A CC14 CC14
Here X^-,^ is the mole fraction of the carbon tetrachloride in benzene-
4 Cl2
carbon tetrachloride mixture, and A is the absolute intensity of
CC14
chlorine in carbon tetrachloride from Table VII. The factor of 2 is not
so unreasonable if we consider the amount of our underestimate for the
intensity (A) of chlorine in benzene solutions discussed above. After
making the correction with Eq. 5-9, we replotted Eq. 5-8 to obtain
Fig. 29. The best least-squares fit of it gave Ke to be 44 + 10
-2 3 -1
(liter cm mmole ), e to be (1.2 + 0.3) x 10 (cm mmole ), and K to
be 0.036 + 0.025 liter mole
From the above Scott analysis, we cannot say how well the equili¬
brium constant for the complex of chlorine with benzene has been
determined from the infrared data, but we can say with some confidence
that the absolute integrated molar absorption coefficient (e) for the
complex of chlorine with benzene (presumably a one-to-one complex) lies
between 660 and 1200 cm mmole
This value is to be compared with

(x 10
105
Fig. 29. — Scott plot of chlorine complex with benzene, using
a recalculated intensity of chlorine, as given by
Eq. 5-9, and described in the text.

106
the less accurately measured estimate of 153 cm mmole ^ (based on
total Cl^ concentration) for the intensity of this absorption band,
given by Person, Erickson and Buckles (21). The dramatically in¬
creased value of this intensity suggests that it would be desirable
to repeat accurately the other intensity estimates given earlier (21)
for the halogen complexes, with carefully determined equilibrium
constants.

CHAPTER VI
COLLISION-INDUCED INFRARED INTENSITY OF
CHLORINE IN BENZENE AND IN CARBON TETRACHLORIDE SOLUTIONS
Introduction
We have mentioned in Chap. I that there are two different inter¬
pretations for the observed infrared spectra of halogens in benzene
solution, and we have reported the observed infrared spectrum of
chlorine in both benzene and carbon tetrachloride solutions in the
preceeding chapters. The intermolecular interaction between chlorine
and carbon tetrachloride is not expected by the charge transfer theory
to result in any infrared absorption by the Cl^ so that the observed
band is more likely due to electrostatic effects. In order to estimate
the contribution of ordinary electrostatic effects to the infrared
absorption intensities of chlorine in benzene and in carbon tetrachlo¬
ride solutions, we carried out theoretical calculations of the colli¬
sion induced infrared absorption intensity, based on the theory develop¬
ed by Van Kranendonk (43) and Fahrenfort (44) , and on the related thoery
of collision-induced far infrared absorption intensity mentioned in
Chap. I. At first, we shall present calculations of the induced in¬
frared intensity of chlorine-benzene pairs or chlorine-carbon tetra¬
chloride pairs for definite, specific fixed orientations of the mole¬
cules, and then find a suitable way to obtain the value averaged over
all orientations.
107

General Expression for the Integrated Collision-Induced Absorption
Intensity
The integrated absorption coefficient is defined generally as
A = (l/ncl )/x(v)dv = (Br3N19v/3hcnpi ) | o * y * Y'0 dx
12
Cl9 12
12
(6-1)
Here A and n are the same as Eq. 5-6; k(v) is the absorption
C±2
coefficient, related to the incident light I and the emerging light
— K ( V ) Í
I through a medium of pathlength SL by the equation I = I^e ;
-1 '
v is the wavenumber (cm ) of the measured light; N is the number
12
3 '
of collision pairs per cm ; Y and ^2 are asso¬
ciated with the ground and excited states of the collision pair; y
is the (induced) dipole moment operator for the collision pair; h is
Planck's constant; c is the velocity of light; and ¡Jy " P * ¥
is the squared matrix element from the induced dipole moment matrix.
For a dilute gas with dipole moment operator y, the expression for
the integrated absorption coefficient A has the same form as Eq. 6-1,
except that N is the density of the pure gas and Y, „ in I ÍY ' y •
12 12 J i2
t - 2
! di| is replaced by Y, the wavefunction of the isolated molecule.
12
We will discuss more precisely these two important quantities (N
and 1/^2 ’ ^ * ^2 1^ as we proceed now to their calculation.
t
N , the Number of Collision Pairs
-12’
The number of collision pairs occurring with one particular
orientation of chlorine with respect to the solvent (either benzene
or carbon tetrachloride) in the solution may be estimated from the
—v
pair-correlation function G(R , u^) for the system. (See Reed
and Gubbins, Ref. 73, for a detailed discussion of pair correlation
functions.) We have adapted Fahrenfort's method (44) for calculating

109
N for a gas mixture with a slight modification in order to calculate
I
N in oar liquid mixture. In our case, the pair-correlation function
G(R.„, to , to„) is a function of both isotropic and anisotropic poten-
12 ^ 2
tials. The isotropic part is assumed to be a Lennard-Jones (6-12)
potential, while the anisotropic part is assumed to be just the elec¬
trostatic interaction energy; for the case of the chlorine and benzene
pair this electrostatic interaction energy will be t' e quadrupole-quad-
rupole interaction energy, and it will be the quadrupole-octapole
interaction energy for the chlorine and carbon tetrachloride pair,
since the first electric moment for carbon tetrachloride is the octa-.
pole moment. For different solute-solvent orientations, the expressions
for G(R , to , to ) have been derived and the results are shown in the
12 1 2
Appendix.
The differential probability of dP of finding a molecule of type B
(we shall label this molecule "2") in a given volume element dr near
B
a given molecule of type A (we shall label it molecule "1") anywhere
within the volume V is given by:
dP(R , to , to ) = (1/V) G(R , to , to ) dr
12 1 2 12 1 2 B
(6-2)
Here the magnitude of ^ is the distance between the type B molecule
12
and the type A molecule; to^ and to^ represent the orientations of
molecules 1 and 2 [co^ = (9^,^) and = (®2’^2^* ^i anc* ^or t^e
ith linear molecule are defined according to Fig. 30. Alternatively,
Fahrenfort (44) wrote
dP(R , to , to ) = (1/V)e ^ 12^ 1’ 2^ dr
±Z ± Z B
(6-3)

110
molecule 1
molecule 2
Fig. 30. — Coordinate system used in defining
the orientation of linear molecules
Here S is 1/kT, and R^ are the position coordinates of molecules 1
and 2, respectively, and 1^) is the pair potential energy.
The differential probability of finding the type B molecule within
a sphere around A defined by radius R and at a given solid angle d$ =
sin 0 d0 d<|>) is given by
^ 2
dp'(m , u ) = [ (1/V) J a G(R , cü u ) R dR] d$ . (6-4)
¿ R 12 l
0
Here R is the shortest allowed distance (the contact distance) between
0
the type B molecule and the type A molecule, and R is the radius of
cL
a sphere centered at the type A molecule containing the type B
molecule, and with volume V.
The probability per unit solid angle of finding the type B
molecule in a sphere of radius R is given by
a

Ill
I R 2
dP /d* = (l/v) JRa G(R12, wl? w ) R dR .
(6-5)
Finally, the total number of pairs formed at a particular orienta¬
tion (cu , új ) within the sphere of radius R is given by
11 a
n' = N N (dp'/d*) = (NN/V) / 3 G(R , u., u,) R2 dR . (6-6)
12 AB A B ; Rq 12 1 2
I
In order to illustrate the use of Eq. 6-6, let us calculate N
12
for collision pairs of chlorine and benzene in an orientation with
the symmetry axis of chlorine aligned along the six-fold symmetry axis
of benzene [the "axial" orientation (37)] at certain distance R apart.
Denote the chlorine molecule to be the type A molecule, and the benzene
molecule to be the type B molecule. Here the value of w gives the
orientation of the six-fold symmetry axis. If we consider the case
where the molar concentration (n ) of chlorine in the benzene solu-
cl2
tion is 0.4 M, and the concentration (n ) of benzene is 11.3 M (as
C6H6
in pure liquid benzene), then
20 3
N = n N /1000 = 2.48 x 10 molecules/cm ,
A Cl 0
2
and
, 20 3
N =n N /1000 = 68.026 x 10 molecules/cm .
B C H 0
6 6
Here N is Avogadro's number. From Eq. 6-6, we see that we have to
0 Ra 2
evaluate the integral / G(R , ^ > <0 R dR> where G(R , u , co„)
Rq i^- i ^ 12 i
is now the pair-correlation function for chlorine-benzene pairs in
this "axial" orientation. In order to evaluate the integral numerically,
we write:

112
4a «V V V r2 dR ■ °¡2 [JR* G<¿t12' "l’ “2* R‘2 ÍR‘] •
(6-7)
k
Here we have defined a set of "reduced coordinates," R to be
R/o^2 and 0^2 to + o9)/2, where and are the parameters of
O
the Lennard-Jones potential for chlorine (o = 4.AO A) and for benzene
, ° * *
(a = 5.27 A) (74). We chose R to be 0.84 and R to be 2.40 because
2 0 a
g
the factor 1/R , which appears in the squared-matrix element
l/’P " ^12 I » falls off very rapidly for R greater than 2.40.
eg* ->.* *2 *
The integral J a G(R^ > ^) R dR was evaluated numerically by
a computer program written for Simpson's numerical integration method,
"k
with the interval between any two successive values of R s taken to be
0.04. From Eq. 6-7 and the parameters given above, we found for the
"axial" orientation that:
R
-22
/ G(R , to , w ) R dR = 9.231 x 10 cm
R 12 1 2
0
»
Finally, the number of pairs N for chlorine and benzene pairs in this
"axial" orientation is
' -> 2 21 3
N = (N N /V) j G(R , a) , id ) R dR = 1.56 x 10 pairs/cm ,
12 A B rq 12 1 2
or
N /N =6.28
12 A
Here N /N given the average number of the axially oriented chlorine-
12 A 3
benzene pairs per cm per chlorine molecule. Since a pair is formed
2 -6
by two molecules, the unit "molecule cm " is equivalent to "pairs
3 i
per cm " . Note that the number of pairs (N ) here is physically
12
different from the "contact pairs" defined by Orgel and Mulliken (34).

Hie "contact pairs" are pairs in which the solvent molecules (benzene)
are in immediate contact with the solute molecule (chlorine), while
the N defined here is the number of solvent molecules which are at
12
a particular orientation with respect to the chlorine within the
electrostatic interaction distance (R < 2.40), but which are not
a
necessarily in physical contact.
, , -v * ,2
Evaluation of IjT ^ ^ I
To be exact, the wavefunction for the collision pair should be
written as a function of all normal coordinates of both molecule 1
and molecule 2: ¥ (£ , E, ,....). However, for a
12 Is la 4s 2a
weak intermolecular interaction the normal coordinates of each const!t
uent molecule are probably not appreciably perturbed; such is ex¬
pected to be the case for the pairs between chlorine and benzene (or
chlorine and carbon tetrachloride). We can approximate Y by:
Y.0(C , C , .... C9c, C9 , ....) = YU * •••) V (5, , C9
12 ls la 4s 2a 1 Is ls 2 2s 2
(6-8)
Here £ , £ , ... are the normal coordinates of molecule 1; C > C
ls la 2s 2a
are the normal coordinates of molecule 2; T U , C , ...) is the
1 ls la
wavefunction for an isolated molecule 1; and T (C , C , ...) is the
2 2s 2a
wavefunction for an isolated molecule 2. Then the squared induced
dipole matrix element can be rewritten as
1/^2 . y . ^ dt|2 = |JVz . £ • dx|2 . (6-9)
We are dealing with the case where only one of the molecules in
the pair undergoes a vibrational transition (the Cl-Cl vibration of
chlorine in benzene solution) and not the absorption by both chlorine

114
and benzene simultaneously,
mately the same, so that
For this case,
Â¥ and ^ are approxi-
l/y2 * y • \v'2 dTl = I/'i'i * y • ’1 d^l2 1/^2 dx2^2
-v 2
- I/?! • y • \ dx2| . (6-10)
The induced dipole y arising from the electrostatic fields of the
molecules in the collision pair was defined (43, 44) as
V = a, F„ + a F
1 2 2 1
(6-11)
Here a , a^ are the polarizability tensors of molecule 1 and molecule
2, respectively; F^ is the electrostatic field generated by molecule
1 at the center of mass of molecule 2, and F is the electrostatic
2
field generated by molecule 2 at the center of mass of molecule 1.
->â– 
We can also expand the induced dipole moment y in a Taylor series:
y
yn + (3y/3£ )n K + Oy/3)n K + (3y/3S ) +
0 Is 0 is la 0 la 2s q 2s
(3y/3£ ) Z +....+ higher order terms. (6-12)
2a U 2a
Since there is no permanent dipole moment either for the chlorine or
for the benzene molecule, y^ = 0. From the expansion of Eq. 6-12,
the term which contributes to the variation of y with the frequency
of the normal vibration v of molecule 1 is (3y/9£, ) £ . To
Is Is 0 Is
simplify the notation, from now on we write £ as C , so
Is 1
y = (3y/3C )Q l . (6-13)

115
More explicitly, we rewrite Eq. 6-13 as
y = [Oct ,/3£ ) + a (3F/35 ) ] 5,
1 102 2 1 10 1
(6-14)
When we substitute y from Eq. 6-14 into Eq. 6-10:
1/^2 • V • ^ di
12
= |/Â¥1U8a1/ac1)0 F2 + a2 O^/^lV 'V1 dxj
= [O^Vo ^2 + a2 (9V3V0] •/'‘'i ' C1 ' \ dTJ2 ’
(6-15)
r ' 1/2
Since T1 = + 1) /2y] > where v is the vibrational quantum
2
number, and y = 4tt v/h (see Appendix III of reference 75), and since
v = 0 for the fundamental vibration transition, =
(h/8TT^v)1^.
Finally,
1/^2 • y * vio dT
12
= [(3a1/8C1)Q F„ + a (aF^aC )Q]2 • (6-16)
In order to obtain an appropriate average value (designated by < >)
-y
over the radial distribution function G(R^2> w , w ), the value of
+ + 2
[Oct^/a£ )^ (aF^/a^)^ at a s^n^'*"e vaFue s^ouFd be
replaced by
R
/g(R12» “1» ^2} [ ( 9 0^1 / a ^i) Q F2 + a2(aF1/ag1)Q]2 R2 dR
2
Jg(R12, U)1, m2)R dR
(6-17)

116
Then Eq. 6-16 will be rewritten as
\¡\2 ‘V'\2 dT'2 = ([(3ctl/3Vo ^2 + 2 (3V ^^q]2)^/8^).
(6-18)
(Actually, the average should also be carried out over all
orientations, too, as we discuss later.)
Explicit Expression for the Integrated Collision-Induced Absorption
Intensity
Substituting Eq. 6-18 into Eq. 6-1,
A = l/ncl Jk(v)d\
or
■ (*4/3c2ncl,) <[(3“l/;,5l)0 f2 + °2 (3h/35l>o,2)R -(6-19a)
A = (trtt /3c nci ) ^Oy/3^)
R
(6-19b)
Note that Eq. 6-19b is equivalent to the usual expression for the
i
intensity of infrared absorption (76) , but with N /n„. correspond-
12
ing to N, the Avogadro's number, and ^ (3p/3^) \ ^ corresponding
^ 2
to (3^/35)^. the square of the dipole moment derivative with respect
to a particular normal mode vibration.
Evaluation of ^ [(30^/3^) Q F2 + a2 (9Fi/3^l^ } R f°r the MAxial"
Chlorine-Benzene Pair
The polarizability tensor or the polarizability derivative
tensor can be expressed in terms of its principal components (a ,
XX
t » f
a , azz or , a.^, a _) if the induced dipole is parallel to the
yy
xx yy zz
interacting electrostatic field direction, which is the case for the
particular coordinate system for this study. Now it is necessary
to evaluate the quantities (3F^/3£^) and for two axially symmetric

117
molecules such as chlorine and benzene. The electrostatic field
generated by molecule i_ at the center of mass of other molecule is
given by Buckingham (77) as
F. = F. e + F.. e. + F. e ,
i ir r 10 0 i<}>
where the components are
and
F = (3/2R4) Q. (3 cos¿ 0.-1) ,
ir i 1
F = (3/R ) Q (cos 0 sin 0.)
ie ill
F. = 0 .
id)
(6-20a)
(6-20b)
(6-20c)
Here Q is the quadrupole moment of molecule jl, R is the distance
i
between the two centers of mass (the same as R ), with 0. and R as
12 i
defined in Fig. 30. The electrostatic field expressed in the carte¬
sian coordinates defined in Fig. 30 is found after a transformation
of coordinates from (F. , F , F ) to (F. , F. , F ). (For details
ir i0 i ix iy iz
of this transformation see Ref. 73.) The results of the transforma¬
tion are:
IX
iy
Fiz
(3/R ) Q cos 0 sin 0 cos
i i i i
(3/R ) Q cos 0. sin 0 cos <|)
i i i i
4 2
(3/2R ) Q (3 cos 0 - 1)
i i
(6-21a)
(6-21b)
(6-21c)
In the expression for F , F. , F. the only quantity which
r ix iy iz
depends on the normal coordinate of molecule i_ is the quadrupole
moment Q , so that the derivative of F with respect to the normal
i i

118
coordinate 5^ is:
OF O? ) = F
lx x 0
xx
OF 05 ) = F
iy i 0 iy
Of. 05 ) = F
iz i 0 iz
(3/R )OQ 05 )A cos 6 sin 6 cos , (6-22a)
i i u i i i
(3/F ) OQ 05.) cos 9 sin 6 sin , (6-22b)
i i O i i i
4 2
(3/2R ) OQ /35 ) (3 cos 6 - 1) . (6-22c)
liO i
In particular for the "axial" chlorine-benzene pairs, 0^ and 9^
O â– > ->â– 
and 0 , so the only non-zero components of F^ (and also F ) and of the
» 4
derivative of F, are F (and also F„ ) and F, with F, = 30 /R ,
1 lz 2z lz lz
4 ' 4
F^ = 3Q^/R and F^ = (3/R )(9Q^/95^)^. Thus, substitution of
these values into Eq. 6-14 gives
IO«l/35i)0 F2 + a2 F2 + ^
=
,
a
lxx
0
0 \
F2*\
0
a
lyy
0
F,
2y
Vo
0
t
a
lzz /
a
2xx
0
0 \
KA
0
a
2yy
0
i
F
iy
\°
0
a2zzy
ihJ
= a F + ct F
lzz 2z zzz lz
(6-23)
Here we introduce the compact notation to stand for (9a^/95^)^,
etc.

119
More explicitly,
[(VsVo ?2+ “2 - (3/e4)[(o' ) Q + a (Q,)l
lzz 0 2 2zz 10
so
[«’ f2 + a2 ?’] = l*'Uz q2 + «2„CQ1)012 •
(6-24)
(6-25)
2
Therefore, the statistical average for [a F + a F ] over a radial
12 2 1
distribution for this particular orientation (eq. 6-17) is
2 v ' '2/8
<' "rl ¿ t ' ' ¿ / 0 \
[a F + a F ] \ = 9[a Q + a Q 1 ( 1/R )
12 2 1 / R lzz 2 2zz 1 \ /
(6-26)
Here
, s v / g(^2- V “2> dR
\ 1/R ) R ' ‘ ,Ra - ^ 2 ‘ ’ 3nd the
}R g(r12’ V W2) R dR
f
expression in Eq. 6-26 was so obtained because a (etc) is independent
of R. The value of /l/R^ \ was obtained numerically as in Eq. 6-7.
\ A
Substituting Eq. 6-26 into Eq. 6-19a, the integrated absorption
coefficient can then be expressed for axially oriented chlorine-
benzene pairs as:
A = (1/n ) Jtc(v)dv
Cl
= (TTN’^/3c2n^l ) ((3y/35,)
12 ci/ \'-^-'»1) y
= (irN /3c n ) • 9[(a ) Q + a (Q
12
Cl
lzz 0 2 2zz
• 2 / 8 \
W (1/R >
R
(6-27)
The expression for the contribution to the integrated intensity A from
other chlorine-benzene pairs with different orientation can be similarly
derived.

120
Actual Calculation of the Infrared Intensity of Chlorine in Benzene
Solution for Collision Pairs in Different Orientations
The parameters used for this calculation are listed in Table VIII
(and also in Table A-l) (79-80). To obtain the polarizability derivative
(80^/35^)^ or quadrupole moment derivative (3Q^/3£^)q of chlorine
from Table VIII, we simply multiply (3a^/3r^)g °r ^^l^^l^O
y , the square root of the reduced mass of chlorine (y = 29.43 x
values from our measurement of the Raman intensities for this calcu¬
lation, since we believe that the measured values are probably the
more reliable estimates, with the other estimates in Table VIII
indicating the potential range of uncertainty.
We have calculated the collision-induced infrared intensity for
four different chlorine-benzene orientations; the results are shown
in Table IX. In the axial chlorine-benzene orientation, the
values of (3o^/3C^)q is found to be the dominant term in the
expression for
although this is not necessarily
true for other orientations. We see from Table VIII that the
induced intensity for chlorine-benzene pairs comes predominantly
from one orientation; namely, the axial one. The other orientations
predict only a very small collision-induced infrared intensity for
these pairs.
Now the question is how to obtain the total collision-induced
infrared intensity expected for chlorine dissolved in benzene,
averaging over all the contributions for different orientations.
From Eq. 6-6, we see that we should now integrate over the entire

TABLE VIII
PARAMETERS USED FOR THE CALCULATION OF THE COLLISION-INDUCED INFRARED
INTENSITY OF CHLORINE IN BENZENE OR CARBON TETRACHLORIDE SOLUTIONS
Parameter
*
Value
Source of the value
polarizability derivative
of chlorine (x 10 cm )
K/3Vo
(1)
11.2
(1)
Ref. 31
b
(2)
8.04
(2)
our measurement
(3)
3.6
(3)
Ref. 79
<3“l/3ri)0
(1)
0.0
(1)
Ref. 42
(2)
1.804
(2)
b
our measurement
(3)
- 0.045
(3)
Ref. 79
polarizability of benzene
(x 1025 cm;
// a
a
635
Ref. 80
a
123.1
Ref. 80
quadrupole moment derivative
of chlorine (x 101 esu cm)
(3Wo
6.0
Ref. 79
polarizability of carbon
tetrachloride (x 10^5 cm )
a
105.0
Ref. 80
a. The parallel component (a ) is along the axial symmetry axis; the perpendicular component (a )
is thus perpendicular to this axis.
b. We converted the average and anisotropy polarizability derivatives (Chap. IV) to these values.
121

TABLE IX
CALCULATED COLLISION-INDUCED INFRARED INTENSITY
FOR CHLORINE-BENZENE PAIRS IN DIFFERENT ORIENTATIONS
(I)
(II)
(III)
(IV)
Clorine-benzene
orientation3
-Q-
0 °
I-G-
Coefficient of ^1/R y
in((3y/35 )q) (Eq. 6-27)
9[(<)'0 Q2
9[ - 1/2(“l>0 Q2
[3<“l)’o q2
9/4 [(a*)’
+ 4(q’) i2
2 1 o
+ v(QiV2
- 3/2 “Í (V0’2
+ “Í (Vo
Calculated value for
( 1/R8^ (x 1057 cm8)
9.20
0.274
0.274
6.55
b
Calculated value for
15.57
5.98
5.98
11.1
N (x 10 ^pairs/cm8)
122

TABLE IX (continued)
Collision-induced intensity 97.5C 2.72 0.33 3.AO
cm mmole (from Eq. 6-27
a.
Orientation I is "axial"; III is "resting" and II, IV, and V are different edgewise interactions.
In these figures o—o is the chlorine molecule and -A- is benzene. The line represents the six¬
fold axis.
b. These values have been derived as illustrated in the text for the axial orientation.
c. When we used the value of 11.2 x 10 ^ for (9o//3r„) , the intensity is 237 cm mmole \ and when
1 1 0
we used the value of 3.6 x 10 ^ for (3a^/9r^)^, we found the intensity to be A.16 cm mmole
123

124
solid angle (4ir) in order to obtain the total number of collision
pairs and hence the total induced intensity. This cannot be done
as illustrated above in the example given for the axial chlorine-
benzene pair, since the radial distribution is not the same for all
orientations. However, from our calculations the contribution to the
total collision-induced infrared intensity from any chlorine-benzene
orientation other than the "axial" one is expected to be negligible.
We may take the largest intensity contribution from one of these
alternate orientations (3.40 cm mmole ^ from case IV in Table IX)
and multiply it by 4tt to obtain the upper limit of the total colli¬
sion-induced infrared intensity expected from all chlorine-benzene
orientations except the axial one, then add the contribution from the
axially oriented pair to estimate the overall total intensity from
the collision-induced absorption. When this was done, we found that
the upper limit of the total collision-induced infrared absorption
intensity for chlorine in benzene solution is 140 cm mmole . The
lower limit for this estimated intensity would be 97.5 cm mmole
(assuming that all benzene-chlorine pairs have the axial orientation).
Since these values are much smaller than the observed intensity
(333 cm mmole ", based on total Cl concentration) from Table VII,
we conclude that the neglected charge transfer vibronic effect
probably accounts for the remainder. This conclusion differs from
that reached by Hanna and Williams (31) because of two things: first,
the re-measured intensity (see Chap. V) was found to be greater by
a factor of two than had been previously estimated (21), and second,
the values of (3a'Vsr^) estimated from Lippincott’s model by Hanna and
Williams (31) are believed to be too large by a factor of two (Table VIII).

125
We believe that the refined measurements and calculations presented
here are accurate enough so that we may conclude definitely that
the predicted collision-induced intensity is indeed less than the
experimental value.
Chlorine-Carbon Tetrachloride
Evaluation of
Collision Pairs —
As a test of the reliability of the theory in predicting colli¬
sion-induced infrared intensities, we have repeated the calculations
for chlorine-carbon tetrachloride collision pairs in order to compare
the predicted intensity with the observed result reported in Table VII.
Since the carbon tetrachloride molecule has tetrahedral symmetry,
the electrostatic field it generates is different from that from an
axially symmetric molecule. Therefore, a brief description of the
coordinate system for these two interacting molecules (CC1 and Cl )
4 2
is given below. We expect that the collision-induced infrared
absorption intensity of chlorine should not depend drastically upon
the relative orientation of the carbon tetrachloride molecule with
respect to the chlorine molecule. For this reason, we selected
only two different chlorine-carbon tetrachloride orientations for
study.
For one case, we chose the relative orientation of chlorine
and carbon tetrachloride shown in Fig. 31. (The other orientation
is indicated in Table X.)
The molecule fixed axes for carbon tetrachloride were chosen
to be parallel to the sides of a cube, as was done by Garg, et_ al.
(50). A simple coordinate transformation was carried out from
molecule fixed axes to obtain the expression in the laboratory fixed

126
o
Fig. 31. — Coordinate system used in defining the orientation of
chlorine and carbon tetrachloride, o is a chlorine
atom; ® is a carbon atom.
axes shown in Fig. 31 for the electrostatic field generated by the
carbon tetrachloride molecule at the center of mass of the Cl^
molecule (for details, see Ref. 80). The components of the electro¬
static field transformed from Garg et_ ad. (50) to the coordinate
system defined in Fig. 31 are
(6-28a)
(6-28b)
Here Í2 is defined slightly differently from that defined by Garg
et^ ad. (50) in that Q, of Eq. 6-28b is the total octapole moment.
The expression for the collision-induced infrared absorption
intensity (A) for the chlorine-carbon tetrachloride pairs was derived
by the same method given above for the chlorine-benzene system. The
F„ = F = 0.
2x 2y
F = 0.77 ft/R
2z
calculated results for two different orientations are shown in Table X.

TABLE X
CALCULATED COLLISION-INDUCED INFRARED INTENSITY OF
CHLORINE-CARBON TETRACHLORIDE PAIRS IN TWO DIFFERENT ORIENTATIONS
Chlorine-carbon
tetrachloride orientation
Expression for ((3y/9£^)^)
-o o-
2 • 2 8
{9a (Q ) / 1/R \
2 10' /
O
/
®— o
\
R
Calculated values of:
. a ’
+
4.62
n
a (a )
2
2 ’ 0
2
„ //. '2
+
0.77
ft
(a ) '
2
1 o
L 0
10
R
<1/R8)
<«*’>
(l/R10)
1.96 x IQ57 cm ^
64 -9
3.48 x 10 cm
6.28 x 1071 cm
/
® O
\
(2.25 „* <1/P8)r
- 2.312 v^yvo^9),
+ 0.594 fi2 (aX)’2 (l/R10) }
2 1 0 ' ' R
4.9 x 10 cm ^
64 -9
9.6 x 10 cm
77 -10
1.91 x 10 cm
127

TABLE X (continued)
Value for N
12 o
/ -20 -3.
(x 10 pairs cm )
6.16
7.25
Collision-induced intensity (A)
(cm mmole 'S
c
A.27
5.70b 1.294d
0.1306
3.5
b d
3.12 - 0.4
0.018e
a.
b.
c.
d.
Derived for the particular chlorine-carbon tetrachloride pair indicated.
Total intensity for this orientation. See text for the result averaged over all angles.
8'
<1/R ) R
Contribution from the
Contribution from the ^1/R ^
/ / 10\R
Contribution from the ^1/R
term.
term.
term.
128

129
It is worthwhile to point out that the dominant term in
-*â–  2 2 2 / 8 v
(3u/3£ ) „ is the term in a (30 /3£ ) ( 1/R ) . As we expected,
1° 2 1 10' ' R
the collision-induced infrared intensities for the two different
chlorine-carbon tetrachloride orientations are not much different.
It is believed that the average of these two values multiplied by 4tt
(the total solid angle) as required by Eq. 6-6 will yield an accurate
prediction of the total collision-induced infrared intensity for
chlorine in a carbon tetrachloride solution. The total collision-
induced infrared intensity of chlorine in carbon tetrachloride solu¬
tion calculated in this way is expected to be about 55.5 cm mmole
When we compare this calculated total collision-induced infrared
absorption intensity of chlorine in carbon tetrachloride (55.5 cm
mmole with the observed absolute infrared intensity for this
system (78 cm mmole^from Table VI), the agreement is very good indeed.
Thus, the ordinary electrostatic effect does account for most of the
observed infrared absorption for chlorine in the carbon tetrachloride
solution. We conclude that this theory of collision-induced infrared
intensity is good, and that the parameter values used in the calcula¬
tion (from Table VIII)are probably correct. The success in predict¬
ing the collision-induced intensity of Cl in CC1 reinforces our
2 4
conclusion that the failure of this theory to account for the inten¬
sity observed for Cl^ in benzene must be because some other important
contribution (probably the charge-transfer effect) has been ignored.

CHAPTER VII
CALCULATIONS OF THE RAMAN INTENSITY ENHANCEMENT
FOR CHLORINE IN BENZENE AND IN CARBON TETRACHLORIDE SOLUTIONS
Introduction
From both the ultraviolet and Raman spectroscopic studies discussed
in Chaps. Ill and IV, we see that the complex of chlorine with benzene
is indeed very weak. On the other hand, we observed a large intensi¬
fication in the relative Raman intensity of chlorine when we changed
the solvent from pure carbon tetrachloride to pure benzene (see
Table V). We have proposed two possible reasons for this drastic
change in intensity; one due to the non-specific solvent effects, the
other due to a charge-transfer vibronic effect from a definite one-
to-one complex. To test which of these two possible mechanisms may
be responsible for our observation, we carried out two theoretical
calculations of possible non-charge-transfer mechanisms; one based
on the collision complex theory of Bernstein (81), the other based
on the pre-resonance Raman effect (82-84). The former theory was
derived by considering the ordinary electrostatic interaction (such
as induced-dipole-induced-dipole interaction) between solute and
solvent; the latter describes the dependence of Raman intensity on
the frequency difference between the Raman exciting line and the
electronic transition of the molecule. However, Bernstein (81)
assumed that the collision complexes were in contact, with only one
130

131
dominant configuration. In our application of his theory given below,
we calculate the contribution to the Raman intensity enhancement for all
the chlorine-benzene pairs (or chlorine-carbon tetrachloride pairs)
that have the same orientation, averaged over all values of R, the
distance between chlorine and benzene (or chlorine and carbon tetra¬
chloride) molecules. Thus, our treatment is parallel to the calcula¬
tion given in Chap. VI for the collision-induced infrared intensity.
As in that chapter, our aim here is to make the best possible
quantitative attempt to explain the observed intensification of the
Raman shift (here; the infrared spectrum in Chap. VI) of chlorine in
benzene without involving any charge-transfer vibronic effects. Any
unexplained intensification may be the result of charge-transfer
vibronic effects, since we believe there are no other possible mechan¬
isms to explain this intensification that do not involve charge-
transfer .
Theory of the Raman Intensity Enhancement Caused by Electrostatic
Interaction (Bernstein's Collision-Complex Theory)
The theory was formulated to estimate the magnitude of Raman
intensity changes from gas phase to liquid phase (or solution) when
a nonpolar solute is condensed (or dissolved). The direct electro¬
static interaction becomes significant in solution, since the inter-
molecular distances between molecules are much smaller there than
they are in the gas phase at low pressure.
Physically, the potential at point B(R, 0, ) due to a real
dipole at origin A can be expressed (74) (for R > 1/2) by:

132
n
V(R, 0,4>) = e/R l [1 - (-1) ] U/2R) P (cos 0)
. n=0 n
2 2 2 \
= y cos 0/R [ 1 + (£ /8R )(5 cos 0 - 3) + ...]
(7-1)
Here e is the point charge, P (cos 0) is the nth Legendre
n —
polynomial and y is the real dipole y = eJl. Although Eq. 7-1 is
derived for a real dipole, it can also be applied for an induced
dipole. The coordinates used for Eq. 7-1 are defined in Fig. 32.
x
Fig. 32. — Coordinate system and symbols used for deriving the
electrostatic potential due to a dipole.
When R >> i,/2 (as is usually true), we retain only the first term
of the expression so that Eq. 7-1 becomes:
2
V(R, 0, ) = y cos 0/R
(7-2)

The components of the field produced by this potential are then given
by:
133
3
F = - 3V/3R = (2y/R ) cos 0
R
3
F = - 3V/R39 = (y/R ) sin 0
0
F = - 3V/(R sin 0) 3 = 0
Thus, the field F is
-* J -> J
F = e (2y/R ) cos 0 + e (y/R ) sin 0
R 6
(7-3a)
(7-3b)
(7-3c)
(7-4)
Here e and e are the polar coordinate unit vectors.
R 0
->z -vx ->y
We denote by P , P , and P the induced dipoles of molecule A
A A A
at point A along the z, x, and y axes, respectively. Let us consider
the special case where the polar coordinate unit vectors e , e , and
R 8
e are parallel to the z, x, and y axes, as shown in Fig. 33.
e
4
(py>
B
-> -*z
e (P )
R B
Fig. 33. — The relative orientation between cartesian coordinates
(x, y, z) and the polar coordinate unit vectors (e^,eg ,<2^) .

134
Then from Eq. 7-4, we see that P will produce a field at B given by:
A
•>z -> /0i-»-Z| 3
F = e (2 P I / R )
A r A
(7-5)
since 8 for this case is 0 . F will then interact with the polari-
A
z
zability a of molecule B at B and produce an induced dipole moment
z ->z B "hz
a F in the same direction as P ; i.e.,
BA A
z z ->
a F = e (2 a
BA R B
z -,->z, 3 z "^z 3
P /R ) = 2 a P /R
A BA
->z
since P and e are in the same direction (see Fig. 33)
->x B R
P and will produce induced dipoles at B given by
A A
x ->x x -*x 3
a F = - a P /R ,
BA BA
x ±y y ^y/D3
a F = - a P /R
BA B A
(7-6a)
Similarly,
(7 —6b)
(7-6c)
x y
Here ot^, are the principal polarizability components of molecule B
because of the way we have chosen the coordinate system (with x, y,
and z axes parallel to the principal axes of the polarizability ten-
->x -»-y ->x -*y
sor of B), F' and F' are the fields produced by P and P ,
A A A A
respectively. The reason for the negative signs in Eqs. 7-6b and
O
7-6c is because in both cases 0 is 270 .
On the other hand, the polarizability a of molecule B will
B
interact with the electric field E of the exciting light and produce
-v z -y x
an induced dipole moment a E, which has 3 components a E, a E,
B B B
y "*â– 
and a E. Therefore, there are two contributions for the induced
B
dipole moment of molecule B, i.e.:

135
->-z z -> z ->z 3
P = a E + 2a P /R
B B B A
"be
x **
X
-be .
P =
a E -
a
P/R
B
B
B
A
-*y
y -»■
y
±y. :
P =
a E -
a
P /R
B
B
B
A
(7-7 a)
(7—7b)
(7-7c)
And similarly,
"'"z Z ->• Z -»Z J
P = a E + 2a P /R
A A A B
->x x -> x -be 3
P = a E - a P/R
A A A B
-*y y y ^y, 3
P = a E - a P/R
A A A B
(7-8a)
(7-8b)
(7-8c)
(We note that Bernstein started his formulation (81) for the collision
->z
complex theory from Eqs. 7-7 and 7-8.) By stustituting P in
B
Eq. 7-8a, we get
->z [ p = —— ——— E
A [1 - (4 a.Z a*/R6)]
A n
(7-9a)
In the same way, we get the expression for the other two quantities:
(7-9b)
r x , x x .3v i
r « laA ~ °A V* )] J
A r . . x x . 6,
[ 1 - (a a /R )]
A B
*y [°I ~ (aI °b/r3)1 J
A [ 1 - (a7 ay/R6)]
A B
(7-9c)

136
And similarly
-yz
z z z 3
[a + (2 a a /R ) ]
p - B B A p
B z z 6
[ 1 - (4 a a /R )]
B A
-*x
P =
B
x x x 3
[a - (a a /R )]
B B A
x x 5
[ 1 - (a a /R )]
B A
-*y
p =
B
[a
B
y y 3
(a_ a /R )]
D A
v y 6
[ 1 - (a a /R )]
B A
E
(7-10a)
(7-10b)
(7-10c)
Now we can express the total induced dipole moment as a function
of the two polarizabilities a and a , the electric field of the
exciting light E, and the intermolecular distance R. Bernstein
defined the principal polarizabilities of a binary collision pair
AB as follows:
**i '*i i â– *
P + P = a " E, where i = x, y or z,
A B AB
or
a1 = (P1+P1)/E . (7-11)
AB A b
From Eqs. 7-9a, 7-10a and 7-11, we obtain
a = a + a + ka a /R + 4aZaZ(aZ + O/R6 + 0 (1/R9) .
abab ab abab
(7-12 a)
9 9
Here 0 (1/R ) refers to terms depending on 1/R .
Similarly,
x
a
AB
x x „ x x 3 xx x x 6 9
a +a -2aa/R +aa (a + a)/R + 0 (1/R )
ab ab abab
and
(7-12b)

137
y y v yy3 yy y v 6 9
a = a + a -2aa/R + a a (o¡ + a)/R + 0 (1/R ). (7-12c)
abab a b abab
Eqs. 7-12a, 7-12b and 7-12c indicate that we can express the polariza¬
bility of the complex AB in terms of the polarizabilities of the
parent molecules A and B.
The average and the anisotropic polarizabilities of the AB pair
can now be obtained from these principal polarizability components.
The average polarizability is given by
a = (1/3) (aX + + a )
AB AB AB AB
(7-13)
and the anisotropic polarizability is given by
xy x y yz y z zx z x
Y = a -a,y =a - a , y =a -a
AB ABABABABABabABAB
(7-14)
Correspondingly, the derivatives of the average and of the anisotropy
polarizability of the complex AB with respect to one of the normal
coordinates (£ ) of molecule A is given by
A
2 'll2
* ) J
AB
and
(a1 )
= 1/9 [(a )’ +
(ay )’ + (
AB
AB
AB
(y' )2
= 1/2 ([(aX j
y • 2
- (a )]
AB
AB
AB
,, z ' „ X
' 2 1/2
+ [(a ) - (a
)] >
xy:
AB
z » 2
i )]
AB
AB
AB
(7-15)
(7-16)
Here the prime denotes the derivative with respect to £ ; e.g.,
A
a' = da /dE, .
AB AB A
In principle, one can take the derivatives of a in Eq. 7-13
xy yz zx _ M
and of y , y , and y in Eq. 7-14 with respect to E , and then
AB AB AB A

138
substitute them into Eqs. 7-15 and 7-16 to obtain a general ex-
2 2
pression for either (af ) or (y’ ) in terms of the derivatives of
AB AB
the principal polarizability components of the parent molecules. For
pairs formed between two axially symmetric molecules or between an
axially symmetric molecule and a tetrahedrally symmetric molecule,
so that the AB pair has at least two equal principal polarizability
2 2
components, the expression for (a' ) and (y1 ) can be very much
AB AB
simplified. Formulae for special cases like those mentioned above have
been derived by Bernstein (81).
Calculation of the Raman Intensity Enhancement for Chlorine-Benzene
and Chlorine-Carbon Tetrachloride Pairs in Different Solute-Solvent
Orientations
In these calculations what we must actually do is to estimate
the magnitude of the intensity enhancement, so that we want to calcu-
2 2
late the differences A(a’ ) and A(y' ) , which are defined as
AB AN
2 2 2
A(a' ) = (o’ ) - (a') , (7-17a)
AB AB A
and
A(y* )2 = (Y' )2 - (y')2 • (7-17b)
AB AB A
2 2
There are at least two ways to evaluate A(ct’ ) and A(y' ) .
AB AB
One is to make the evaluation at only one particular value for R,
the intermolecular distance between a pair of solute and solvent
2 2
molecules in contact; the other is to evaluate A(a' ) and A(y' )
AB AB
as an appropriate statistical average for all pairs of appropriately
oriented molecular pairs over all possible distances as defined in
Eqs. 7-l8a and 7-18b, and then multiply each áverage value by
f
(N /N ) as defined in Chap. VI, and make another statistical average
12 A

139
over all possible angular orientations. For comparison, we have
2 2
evaluated A(a’ ) and A(y' ) for the chlorine-benzene pair at one
AB AB
particular distance (the van der Waals distance) for one particular
orientation (axial model). For the most part we will estimate these
quantities by the second method, since the liquid structure (unlike
a solid) is distorted even though there may be one preferred orienta¬
tion of the solute-solvent pair. To obtain an appropriate statistical
2 2
average of A(a' ) and A(y' ) over all distances for the AB complex
AB AB
at one particular orientation, we define
Oy > r
Ra 2 -*â–  2
2 A(a^) G(R12, u^, a)2) R dR
(7-18a)
and
AB 7 R
^ G(v v yR dE
^ 4(^)2 G(R12' V V ***
R 2
/ a G(R , u , u ) R dR
R0 12 l 2
(7-18b)
Here G(R , m , w ) is the same pair correlation function for chlorine
12 12
in benzene solution or chlorine in carbon tetrachloride solution as
that used in Chap. VI and given also in the Appendix. Before the
integrals in Eqs. 7-18a and 7-18b were evaluated, we inserted all
2 2
the parameters into the expressions for (a' ) and (y* ) (such as
AB A5
the ones given by Eqs. 7-19a and 7-19b) and simplified the expressions
into 4 terms. The first one is a constant, the second one involved
3 6
1/R , and the third and fourth ones involved 1/R . [Note: In our
re-derivation of these expressions we believe that some errors in
6
some of the coefficients of the 1/R terms originally given by
Bernstein (81) have been detected. For this reason we write the

140
1/R term as a sum of two terms (the third and fourth); we believe
the coefficients of the third term (containing ^Og> ct^y^, °B^A
and y y ) given by Bernstein (81) are correct, but that the, coeffi-
A B 2 2
cients of the fourth term (containing a , a y , and y ) given by
B B B , B
6
Bernstein (81) are not correct. Since both 1/R terms make only a
small contribution to the intensity enhancement, we used Bernstein’s
terms without any correction. (The term in question is the coefficient
2 2
C in Table XI.) Since the first term is exactly (ct^) [or (y^) ],
2 2 3
the expressions for A(a' ) and A(y’ ) contain only the second (1/R )
AB AB
6
and the third and fourth (1/R ) terms. The numerator of Eq. 7-18
was then broken into three separate integrals, which were calculated
numerically as described in Chap. VI. The process will become clear
below where we present a sample calculation in some detail. The
limits of the integral (in Eqs. 7-18a and 7-18b) were chosen to be
* *â– 
from R = 0.84 to R = 5.0, in reduced units. The reason for choosing
0 a
* *
these limits of integration instead of R = 0.84 to R = 2.40 as in
0 a
Chap. VI for the collision-induced infrared intensity calculations
2 2 3
is because the expressions for A(a' ) and A(y' ) involve 1/R terms.
AB AB
^ 8 9 10
which do not fall off as rapidly as does the 1/R (or 1/R , 1/R )
term in the expression for the collision-induced infrared intensity.
2 2
The expressions for (a’ ) and (y* ) which were derived by
M AB
Bernstein (81) for chlorine (label A) and benzene (label B) in the
axial orientation are given below:

141
* 2 ' 2 3 3
(a ) = (a ) {1+ 8y /3R + (1/3R ) [24a a + 8a y + 8a y
AB A B ABABBA
2 2 '2 2,6
+ 8y y + 12a + 8a y + 16y /3] } + (y ) (12a + 4y ) /81R
A B B B B B A B B
• ' 3 6
+ (y a ) { (24a + 8y )/9R + (1/9R ) [24a a + 24a y
A A BB ABAB
2 2
+ 24a y + 40y y /3 + 12a + 56a y + 52y /3] } ,
BA A A B A B B
(7-19a)
2 t 2 3 6
(y ) = (y ) { 1 + 4(a + y )/R + (1/3R ) [36a a + 20a y + 20a y
AB A BB ABABBA
2 2 i 2 2 6
+ 43y y /3 + 30a + 44a y 4- 58y /3] } + (a ) (6a + 2y ) /R
AB B BB B 'A BB
i 3 6
+ (y'a.) { 2(6a + 2y )/R + (1/R ) [12a a + 12a y + 12a y
A A BB AB AB BA
2 2
+ 20y y /3 + 30a + 44a y + 28y /3] }
A B B B B B
(7-19b)
The polarizabilities (a and a , respectively) of chlorine and benzene
A B
and these estimates for the polarizability derivatives of chlorine
* *
[isotropic (a ) and anisotropic (y )] were calculated from Table VIII.
A A
For the calculations in this chapter we will use the experimental
values of the polarizability derivatives [set (2) in Table VIII] . With
these parameters, we obtain from Eqs. 7-19a and 7-19b,
(a ) = [0.1508 + (0.0264/R 3) + (0.0061/R ) + (0.0043/R )]
AB
-30 4
x 10 cm ,
(7-20a)

142
and
*3,
*6.
*6.
(y' ) = [0.389 + (0.2743/R J) + (0.0248/R ) + (0.0569/R )]
AB
-30 4
x 10 cm
(7-20b)
So from Eqs. 7-17a and 7-20a, we have
2 *6 *6 -30 4
A(o' ) = [0.0264/R + 0.0061/R + 0.0043/R ] x 10 cm
AB
*6 *6
= (C /R J + C /R + C /R )
12 3
(7-21a)
And from Eqs. 7-17b and 7-20b, we have
2 *3 *6 *6 -30 4
A(y' ) = [0.2743/R + 0.0248/R + 0.0569/R ] x 10 cm
AB
*3 *6
= (C /R + C2/R + C3/R )
(7-21b)
Substituting Eq. 7-21a into Eq. 7-18a and evaluating the integrals as
described in Chap. VI, we get
/ 2V -30 4
^A(a^) ) R = 0.0031 x 10 cm
From Eqs. 7-18b and 7-2lb, we get
/ 2 v -30 4
\ AB / R
2. , 2,
) and I.
AB / R ' 'AB ' R 12 A
pairs of chlorine and benzene in several other orientations and for
We
calculated ^A(af ) \ , (A(y* ) ^ and N /N for
' aw / v ' AW / R 12 a
pairs of chlorine and carbon tetrachloride at two different orienta¬
tions. The coefficients corresponding to Eqs. 7-21a and 7-21b are
I
presented in Table XI. The calculated values of N /N and the
12 A
resulting intensity enhancement (AP) are shown in Table XII.

143
TABLE XI
COEFFICIENTS OF THE 1/R TERMS IN THE EXPRESSIONS FOR
2 2
A(a’ ) AND A(y’ ) (EQS. 7-21a AND 7-21b)
AB AB
FOR SEVERAL DIFFERENT SOLUTE-SOLVENT (AB) ORIENTATIONS
Case
b
Orientation of
Solute-Solvent
c
C1
c
C2
cc
3
(I)
0 0
d
A.
0.0
0.0
0.0
isolated A
molecule
d
B.
0.0
0.0
0.0
(II)
<+>
o
1
o
A.
0.0264
0.0061
0.0043
B.
0.0740
0.0248
0.0570
(III)
0
1
0
-e-
A.
0.0752
0.0111
0.0154
B.
0.0740
0.0498
0.1425
(IV)
l o
A.
- 0.0450
0.0036
0.0086
B.
- 0.2190
0.0337
(V)
0 0
A.
- 0.0132
0.0030
0.0037
B.
- 0.1213
0.0131
0.1589

144
TABLE XI(continued)
(VI)
0
i
0
o
1
©
oXf\
A.
0.0668
0.0292
B.
0.1910
0.2297
(VII)
T /°
° \o
A.
- 0.0334
0.0111
B.
- 0.2308
0.1336
e
e
e
e
a.The experimental values of the polarizability derivatives for
chlorine [set (2) of Table VIII] in carbon tetrachloride have
been used to obtain the coefficients.
b. See Table IX for a description of these symbols.
-30 4
c. The units are 10 cm .
2 2
d. Lines A and B give the coefficients of A (at' ) and of A(y' ) ,
respectively. ^ ^
*6
e. Both constants (C^ and C^) of 1/R are combined into one term.

145
TABLE XII
a / 2 y . 2 \ »
THE CALCULATED VALUES OF , N /N ,
' AB 'R ' AB 12 A
AND THE ENHANCEMENT OF INTENSITY (AP)
c
Case
(I)
(II)
(III)
(IV)
(V)
(VI)
(VII)
0.0
0.003105
0.00143
- 0.0008881
- 0.00066
0.00276
- 0.00140
0.0
0.0308
0.00634
- 0.00415
- 0.00262
0.00895
- 0.00885
N /N
12 A
35.9
31.0
31.2
33.9
26.3
26.9
b
AP
0.0
1.34
0.356
- 0.225
- 0.158
0.517
- 0.353
a. As defined in the text in Eqs. 7-18a, 7-18b, and in Chap. VI (see
text).
b. AP is defined in Eq. 7-22.
c. As defined in Table XIt
d. The units are 10-^^ cm"4.

146
Here AP is the ratio of the calculated Raman intensity enhancement
(averaged over R) for the AB pair compared to the Raman intensity
(7-22)
[45 (a')2 + 7 (y!)2]
A A
Discussion
It is difficult to say just what the total Raman intensity
enhancement will be when AP from Table XII is averaged over all
possible orientations for chlorine in benzene (or in carbon tetra¬
chloride) . As Bernstein (81) points out, if we evaluate the un¬
weighted average of the intensity enhancement over all possible
orientations, it will be almost zero. On the other hand, if we
expect that the chlorine-benzene pairs in an axial orientation are
favored and form the predominant configuration, we predict a maximum
enhancement of the Raman intensity of chlorine of 134% of the value
for the isolated molecule. This value is still only a small enhance¬
ment, compared to our observation (Table V) that the intensification
is by a factor of 4 (400%), based on total chlorine concentration.
We have also repeated this calculation, using the polarizability
derivative for chlorine calculated from Lippincott's model [set (1)
of Table VIII]. The predicted Raman intensity enhancement (AP values)
is not much different from the values shown in Table XII. We have
also calculated the intensity enhancement of the chlorine predicted
from Eq. 7-19a and 7-19b for the case of axially oriented chlorine-
benzene pairs at only one fixed value of R. At the van der Waals

147
distance (R = 4.535 A), we predicted a 73% increase in intensity for
a single one-to-one contact axial benzene-chlorine pair instead of
the value of 134% predicted on averaging over all pairs with that
orientation (see Table XII). However, we may have overestimated the
number of pairs (N /N ) because the volume of the interacting
12 A
sphere may possibly be too large, due to the choice of integration
* *
limits of the integral from = 0.84 to R =5.0. Furthermore,
U a
it may not be true that there is simple additive contribution to the
total Raman intensity enhancement for the chlorine molecule from all
I
collision pairs (N /N ), since the electrostatic field of a benzene
12 A
molecule far from the chlorine molecule could be shielded by an
intervening benzene molecule. If this should happen to an important
extent, we believe that predicted enhancement (Table XU) could be
overestimated.
A similar dilemma occurs when we try to predict the magnitude
of the intensity enhancement for chlorine from the gas phase to the
solution in carbon tetrachloride, using the results in Table XII.
Since there is no predominant orientation expected for chlorine in
carbon tetrachloride solution, we may estimate an upper limit of
100% for the predicted enhancement of intensity. This value is
obtained by noting that the enhancement predicted for the case VI
oriented pair is greater than the decrease predicted for the case
VII pair so that we estimate the total contribution to AP by multi¬
plying the sum (AP,tt + AP = 15%) by 2 tt (one half of the total
solid angle). Unfortunately, there is no measured gas phase value
for the absolute Raman intensity of chlorine for comparison with the

148
solution phase value (Table V) so that a definite conclusion about
the ability of the Bernstein theory (81) to predict accurately the
change in Raman intensity from gas phase to solution in an "inert"
solvent is difficult to reach. However, this theory is similar to
that for collision-induced infrared intensity (Chap. VI), and so it
may be expected to predict this change for chlorine in carbon tetra¬
chloride solution fairly well. It is quite clear from the comparison
of results given above for the chlorine-benzene solutions that the
observed intensification of the CI2 Raman shift in benzene solutions
is much greater than can be explained by the Bernstein theory.
Theory of the Pre-resonance Raman Effect
It has been shown (for example see Ref. 83) that the total in¬
tensity of light with a frequency v = \j + v = v + v , scattered
£ 0 — 0 mn
on the average by one freely orientable molecule undergoing a
transition from state m to state n (all in the electronic ground
state for the vibrational Raman effect) can be expressed as
I
mn
5.-2 4, 4
(2 TT /3 C ) I V
0 e
I I
p,o
a
Ptf ,mn
2
(7-23)
Here is the frequency of the plane-polarized incident light, the
vibrational frequency v = |v |> 0, with v = - v =(E -E )/hc;
mn mn nm m n
c is the velocity of light and the sum goes over p = x, y, z and
a - x, y, z which independently refer to the molecule fixed coordi¬
nate system, and I is the intensity of the incident light. Accord¬
ing to the dispersion theory of Kramers and Heisenberg (85) , the
path matrix element a of the scattering tensor for the transi-
— pa,mn
-*â–  n is given by:
tion m

149
a = (1/h) l
pa ,mn
(M ) (M )
p rn a mr
- +
v - V. + i<5
rm 0 r
(M ) (M )
p mr 0 rn
v + v„ + i<5
rn 0 r
(7-24)
Here h is Planck's constant and the sum goes over the intermediate
states r of the molecule. Here (M ) , (M ) , etc.,refer to the
p rn a mr
values of the corresponding transition moments. However, there are
several ways (82-84) to estimate how a and hence I can best
pa,mn mn
be approximated as the incident light frequency approaches one of
the vibronic transition frequencies v
rm
(Note: v is an electronic
rm
transition frequency far removed from the vibrational frequency v .)
mn
The behavior observed as this happens, and before actually
becomes equal to v is called the pre-resonance Raman effect. The
rm
first attempt to estimate the vibration behavior of a in this
pa ,mn
region was made by Shorygin and associates (see the review in Ref.82).
The theory was reformulated later by Behringer with a quantum mechanical
approach involving the Franck-Condon principle (82) . There ^
was approximated by considering that only the first excited vibronic
state (with an allowed transition from the ground state) in the sum¬
mation given in Eq. 7-24 is important. The result for the Raman
scattering involving a fundamental vibrational transition (v = 0 -* 1)
is given by:
(a ) o i = 1/h { [(2v )/(v2 - v )]
Pa u’ £,V2 1 eg eg 0
X [31(M ) (M ) )|/3? ]
p eg o ge i o
- [2(v2 + vj/(v2 - vJ] [ | (M ) (M ) | (3v /3£.)_} ?f
eg 0 eg 0 1 p eg a ge1 eg i 0 (
(7-25)

150
Rere g and e designate the ground and the first (nondegenerate)
electronic excited states, is what Behringer calls the zero-point
amplitude and is just l^lgg^ > and the subscript indicates
that the derivative is evaluated when the ith normal coordinate E,, = 0.
— i
In obtaining the above equation the states m and n are described by
vibronic state quantum numbers; i.e., m = gv^, n = gv^, etc., with
the first quantum number giving the electronic state, and the second
the vibrational level in that state. The first term in Eq. 7-25
corresponds to the term appearing in Placzek's polarizability theory
(86), while the second term accounts for the additional larger in¬
crease in a associated with the pre-resonance Raman effect,
pa^nn
In the review of this effect by Koningstein (84), Albrecht's
vibronic coupling model (83) has been cited as being a more flexible
expression for (a )g,vi;g,v„. In principle, the total wavefunction
pa. 1 2
of the molecule (excluding the rotational part) can be written as
Â¥ = t|i (r, O ip (O
total g - i v x
(7-26)
Rere t(t (r,£ ) is the ground state electronic wavefunction,

g “ i V X
the vibrational wavefunction, r is the electronic coordinate and £
~ i
is the ith normal coordinate. Retaining the first order term in
-)â– 
the vibronic coupling model, i[i (r, £ ) can be expressed (85) as
g ~ i
. 0 r* £"i O
(r, O = 4- + I h^1 • K. • r
g x g t^g tg i t
(7-27)
where
|(3H/3C.)Sl=ol *g)
tg
0 0
E - E
g t

151
Here the superscript "0" denotes values at the point £. = 0; e.g.,
t|< = £ = 0) , H is the electronic Hamiltonian. With Eqs. 7-26
g i
and 7-27, the pamn element of the scattering tensor can now be
written as:
(a ) = (1/h) l
pa g»v ;g,v2 r,v
(M°) (M°)
v py rg v o’gr
V - V + id
rjVjg^ o r, v
-
( (£.) | * (£.) ) ( (5.) | (£ ) )
1 V i / \ V i V2 i 7 J
I h (M°) (M°) (ip (£ ) U (£.)\
r tr L p rg a gt ' v i v2 i /
r,t,v,
(t/r)
+
((£ ) | a ) )
' 1 V 1 /
X v - v + id
r,v;g,v1 0 r,v
;0) ( K (?.} I * ^â– ))

    a gr P tg \ vx i v i / \ v i i v i7J
    â– > - v + id
    r,v;g,v1 o r,v
    + I
    r,t,v,
    (t^g)
    5i
    0. . 0
    htg |_(Vtr (Vrg {\ (5i> >*v (V>
    (i> (5 ) I €.| 4» (£.) >
    \ v i 1 1 /
    vr>v;g,v1 - "0 + 16r,v
    (lf!>r.(*v <5)1* «>)(* (C.) | 5,1* (5))
    ptr orgNv-j^ i v i/vv i i v2 ± / m
    v - v + id
    r »v;g»v^ 0 r»v
    + terms containing [ p •<->- a]/(u + v + id ) . (7-28)
    g»vi;g>v2 0 r,v

    152
    This expression was obtained under the assumption that all wave-
    0 , 0 *%i *£.
    functions are real so that (1L) = (Ik) and also h = h 1
    P tr P rt tr tr
    (see Ref. 84). Retaining only the zero-order terms in Eq. 7-28,
    we get
    (a )
    p° g>vi;g,v2
    l/h
    I
    r,v
    r ,v.
    g»v2
    V
    0
    + ÍÓ )
    r ,v
    +
    !/('
    r>vi;g,v.
    + v + id
    0 r =
    (M°) (M°) (if; U ) U ) )
    P rg ° gr \ vx ± y i '
    x ( (C.) | * U.)>
    \ V 1 V2 1 '
    . (7-29)
    Eq. 7-29 is the starting point used by Behringer to obtain Eq. 7-25,
    under the conditions that v ->v ,v = v + 1; i.e., to predict
    0 r, g 2 1
    the pre-resonance Raman effect for a fundamental vibrational transi¬
    tion. The second and third terms of Eq. 7-28 give the first order
    correction due to vibronic perturbation.
    Application of the Pre-resonance Raman Effect Theory to the Interpre¬
    tation of the Raman Intensity Data of Chlorine in Benzene Solutions
    Since the visible and near ultraviolet absorption by chlorine
    in carbon tetrachloride solution is very weak, we assume that any
    strong pre-resonance Raman effect for that system must come from
    the first allowed electronic transition (around 60,000 cm ) (87).
    There is, however, a new strong absorption band (presumably the
    charge-transfer band) observed at about 36,000 cm (or about 278 nm)
    when chlorine is dissolved in benzene solution (see Ref. 6 or

    153
    Chap. IV). In our studies, the experimental plane-polarized exciting
    incident light was from the Ne-He laser, so that the exciting frequency
    is about 16,000 cm ^ (632.8 nm) . The frequency dependent factors
    were calculated for the terms in Eq. 7-25 corresponding to Placzek's
    normal Raman effect and corresponding to the pre-resonance Raman
    effect. The ratios of the squares of these two frequency dependent
    factors for chlorine in benzene to the squares of their values for
    chlorine in carbon tetrachloride solution were estimated to be 3.8
    2,2 22 2 22.2 24
    and 17.0 for v /(v - v,.) and for (v + v ) / (v -v ) ,
    eg eg 0 eg 0 eg 0
    respectively.
    One must be careful how the comparison is made between the
    theoretical predictions obtained above and the experimental Raman
    results given in Chap. IV. The observed change in the Raman intensity
    (in Table V) from that for a solution of chlorine in carbon tetra¬
    chloride to that for a solution of chlorine in benzene should be
    compared with the intensity calculated from Eq. 7-25, and not just
    with one of the ratios of the squared frequency factors given above.
    In order to make a direct comparison between theoretical and experi¬
    mental values, we must know the absolute values of [31(M ) (M^) I
    P eg n ge1
    ,0 0 .
    /3£ ] and of (M ) (M ) (3v /3£ ) for both free and complexed
    i 0 P eg ° ge eg ± q
    chlorine. Unfortunately, these quantities are not easily obtainable.
    If we assume that both quantities have the same values for free
    chlorine and for complexed chlorine, and also assume that the second
    term is much more important than the first one in Eq. 7-25, then
    the observed intensification (by a factor of 20 — see Chap. IV) of
    the chlorine Raman shift when the benzene is added is in good agree-

    154
    ment with that expected (a factor of 17.0, with these assumptions)
    from the pre-resonance Raman effect. The idea of a possible pre¬
    resonance Raman effect due to the charge-transfer complex formation
    has also been suggested by Rosen, Shen and Stenman (32) for iodine
    in benzene solution. A pre-resonance Raman effect has been reported
    (88) in tetracyanoethylene charge-transfer complexes with benzene,
    but this observation is contrary to the conclusion reached in another
    study (89) of that system. Nevertheless, as Behringer has pointed
    out (82), better evidence that a pre-resonance Raman effect is
    responsible for intensity effects such as these would be the observa¬
    tion of soma dependence of the Raman intensity on the frequency of
    the exciting light. We tried several experiments in the Chemistry
    Department at Old Dominion University, Norfolk, Va. (courtesy of
    Prof. A. Bandy) to observe the Raman spectrum of chlorine in benzene
    solutions using a tunable argon-ion laser with a Spex double mono¬
    chromator (in a 1 ml liquid cell and with three different exciting
    lines at 514.5 nm, 488.0 nm and 457.9 nm) . Unfortunately, the photo¬
    chemical reaction occurred in the Raman cell so rapidly with these
    higher frequency exciting lines that we could not obtain any spectrum
    to test the possible frequency dependence.
    If, indeed, the pre-resonance Raman effect is the main factor
    responsible for the large intensification of chlorine in benzene, an
    interesting feature appears from the theory (83, 84). The point
    group of an axial model for the chlorine-benzene complex state is C^.
    It is found to have this geometry in the solid [from a crystallograph¬
    ic study (90)], but the structure of the complex in solution is not
    known. However, from our statistical calculation (Chap. VI), the

    155
    axial structure is predicted to be dominant in the mixture because
    of the stabilization by quadrupole-induced dipole force (see also
    R.ef. 31). The wavefunction for the ground state of the chlorine-
    benzene complex with C symmetry belongs to the ^A, representation.
    According to the charge-transfer theory (37) , there are two possible
    excited charge-transfer states: ^A^ and E^. If the excited charge-
    transfer state that is coupled vibronically to the ground state is
    A , then we will expect the intensity enhancement from pre-resonance
    Raman effect to appear as an increase in the value of ctzz for the
    complexed chlorine. If the excited charge-transfer state that
    1
    couples vibronically is E^, then we will expect the intensity en¬
    hancement to appear in a and a for the complexed chlorine. Thus,
    xx yy
    an accurate measurement of the depolarization ratio as a function of
    the percent of chlorine that is complexed might allow us to decide
    on the symmetry of vibronically coupled charge-transfer state.
    Since the charge-transfer state that couples vibronically is expected
    to be the one that also stabilized the ground state, ve might hope
    to be able to decide the important question of which of these two
    states does indeed mix with the ground state. (See Ref. 37, sections
    10.3, 11.2, 14.1, and elsewhere.) Unfortunately, the accuracy of
    our measurment for p (Chap. IV) that is possible with our spectro¬
    meter (PE LR-1; see Chap. IV) is not sufficient to determine this
    potentially interesting result.
    One last point is worth mentioning. A further test of the
    question of whether pre-resonance Raman effect does really occur for
    the chlorine-benzene system can possibly be made by studying the

    156
    overtones of the complexed chlorine. The ratio of overtone intensity
    to fundamental intensity of a Raman band is usually less than 1% for
    vibrations when the spectra are observed outside the resonance region
    in liquids (see Ref. 60 and the references cited). However, in the
    resonance region, the ratio is expected to increase drastically (60,
    91). The overtone of the chlorine vibration is expected near
    1060 cm , in a region which is overlapped by the Raman shift from
    benzene at 991.6 cm and 1030 cm (92). Possibly the improved
    characteristics of a good modern laser Raman spectrometer would
    allow observation of this overtone.
    In summary, we have found in the first part of this chapter
    that the observed intensification of the chlorine Raman shift in
    benzene solution (compared to carbon tetrachloride) cannot be
    explained solely by Bernstein's theory of the electrostatic inter¬
    action effect. It is possible that a pre-resonance Raman effect
    acting in a benzene-chlorine complex as a result of the new, strong,
    and relatively low frequency charge transfer absorption band may
    explain the observed intensification of the Cl^ Raman shift in
    benzene, without involving any vibronic charge-transfer effect.
    Attempts to verify such a pre-resonance Raman effect and attempts to
    obtain potentially important information about the symmetry of the
    charge-transfer state that is vibronically coupled to the ground
    state must await better instrumentation.

    APPENDIX
    THE ANGULARLY DEPENDENT PAIR
    CORRELATION FUNCTION
    We will summarize below the pair correlation functions G(R ,co ,uk
    v 12 1 2
    for mixtures of chlorine in benzene and of chlorine in carbon tetra¬
    chloride, obtained from calculations based on the perturbation theory
    for the angular pair correlation function in molecular- fluids developed
    by Gubbins and Gray (51) and on related methods (50, 52, 73, 93, 94).
    Pair Correlation Function G(R ,w ,m ) for Chlorine-Benzene Pairs
    12 1 1
    From the perturbation theory (51) the pair correlation function
    G(R ,o) ,u ) for the interaction of the axially symmetric chlorine
    12 1 2
    molecule with the axially symmetric benzene molecule (about the six¬
    fold symmetry axis) can be approximated by
    + 0
    G(R ,0) ,w ) = G (R ) [1 - u (R ,u), ,w )/kT] . (A-l)
    12 1 2 12 12 a 12 1 1
    0
    Here G (R^) t*ie Lennard-Jones radial distribution function at
    separation R for the chlorine-benzene pair; k is the Boltzmann
    o
    constant; T is the temperature in K; and u (R ,u ,m ) is the
    a 12 1 T
    anisotropic intermolecular potential.
    If we assume u arises from the quadrupole-quadrupole force,
    3.
    then (77)

    158
    * * * 1/2
    Here r = R /a , r = R /a , T = kT/e , e = (e e ) ,
    1 I2 1 2 12 2 12 12 12
    * 5 1/2 * 5 1/2
    Q = Ci-L/(c1a1) » Q2 = Q2/(£2a2) ’ 311,1
    2 2 2 2 2 2 2
    F =1-5 cos .0-5 cos 0 +17 cos 0 cos -0O + 2 sin 0 sin 0 cos é
    QQ 1 2 1 2 1 2 12
    + 16 sin0 sin 0 cos0 cos0 cosd>
    1 2 1 2 12
    The constants a , e and a , e are Lennard-Jones potential parameters
    1 1 2 2
    for chlorine and benzene molecules, respectively, from gas phase
    studies; and Q are quadrupole moments of chlorine and benzene,
    respectively. The coordinate system is defined in Fig. 30. From
    values given in Table A-l, we estimated u (R , w, ,u> )/kT for
    a 12 1 ¿
    different chlorine-benzene pairs, with results shown in Table A-2.
    0
    G (R ) of Eq. A-l was obtained by assuming (52)
    12 12
    G12 (R12/012; P’ T’ £12} = G°(R12/ai2; ^5 kT/£12) ' (A'3)
    0
    -3
    Here G (R /a ; pa ; kT/e ) is the Lennard-Jones pair correlation
    12 12 12
    * _3 * -3
    function for pure benzene at p = pa , T = kT/e , where a is
    defined as
    -3 v v 3
    a = l l X X a
    S 3 « 6
    (A-4)
    Here X and X are the mole fractions of chlorine and benzene,
    a 0
    respectively; aag = (a + a^)/2. Since the concentration of
    chlorine is so low, X >> X , so that
    2 1
    2 3 3
    '1 2 12 + 5'2 2 2
    -3 2 3 3
    aJ = X a + 2 X X a +Xa - a
    1 1
    (A-5)

    159
    Thus, we have finally
    0 0 3
    G (R /a ) - G (R /a ; pa ; kT/e ) . (A-6)
    12 12 12 i2 12 2 12
    0
    From Table A-l, we obtained G (R /a ) for chlorine-benzene pairs
    12 12 12
    to be
    0 0 * *
    G (R /a ) = G (R /a ; p = 0.9916; T = 0.886). (A-7)
    12 12 12 12 12
    The value of the right hand side of Eq. A-7 was taken from Table
    IV of Ref. 94, interpolating or extrapolating as needed to obtain
    0
    the desired G values at each value of R /a
    12 12
    "V
    Pair Correlation Function G(R ,to ,u.'?) for Chlorine-Carbon Tetra-
    chloride Pairs i—2.
    By analogy with Eq. A-l, we obtained G(R^^,m , w^) for chlorine-
    carbon tetrachloride pairs in two different orientations. The
    potential u^ of a chlorine-carbon tetrachloride pair is assumed to
    be due only to the quadrupole-octapole force. The detailed
    procedures in obtaining the expression for u are shown elsewhere (80).
    3.
    Using the values from Table A-l we obtained u /kT for the two differ-
    a
    ent orientations. The results are shown in Table A-3. The value
    0
    of G,„(R /a ) for chlorine-carbon tetrachloride pairs was estimated
    12 12 12
    in the same way as that for chlorine-benzene pairs and was found
    to be
    0 0 * *
    G (R /a ) = G (R /a ; p = 0.75; T = 1.2365).
    12 12 12 12 12
    (A-8)

    160
    TABLE A-l
    PARAMETERS USED FOR THE CALCULATIONS OF THE PAIR-CORRELATION
    FUNCTIONS OF CHLORINE-BENZENE AND CHLORINE-CARBON TETRACHLORIDE PAIRS
    Parameter
    Chlorine
    Benzene
    Carbon Tetrachloride
    a (A)
    A.40
    5.27‘
    4.93
    e/k ( K)
    257
    440
    226
    262 a
    Q (xlO esu cm ) 6.14
    - 15.6
    34 3
    0 (xlO esu cm )
    26.1
    a.
    From
    Ref.
    74
    b.
    From
    Ref.
    93
    c.
    From
    Ref.
    30

    161
    TABLE A-!
    —y
    THE POTENTIAL FUNCTION u (R ,u ,w)/kT FOR CHLORINE-BENZENE PAIRS AS A
    a 12 1 2
    FUNCTION OF RELATIVE ORIENTATION (AT T = 298 °K)
    a
    Configuration
    Chiorine-Benz ene
    b
    6
    1
    b
    0
    2
    b
    ♦
    12
    F
    QQ
    c
    u /kT
    a
    0
    o
    -G-
    0
    tt/2
    0
    - 4
    * 5
    2.65/(R )
    0
    O
    4=
    0
    0
    0
    8
    * 5
    - 5.30/(R )
    ! -oâ– 
    tt/2
    0
    0
    - 4
    * 5
    2.65/CR )
    1 ^
    tt/2
    tt/2
    0
    3
    * 5
    - 1.99/(R )
    s
    0—o
    tt/2
    tt/2
    tt/2
    1
    * 5
    - 0.661/(R )
    It It
    a. 0 is a
    chlorine
    atom; see
    Table VIII
    for definition of symbols
    b. See Fig. 30
    *
    c. R is defined as R /a , a = (c + a )/2; see text.
    12 12 12 12

    TABLE A-3
    THE POTENTIAL FUNCTION u (R ,u ,u) )/kT
    a 12 i 2
    0
    FOR CHLORINE-CARBON TETRACHLORIDE PAIRS (T = 298 K)
    a
    Configuration
    , b
    u /kT
    o o
    0.879/(R*)6
    b
    o
    I
    o
    - 0.176/(R*)6
    b
    a. Symbols were defined in Fig. 31.
    * *
    b. R is defined as R = R /a , a = (a + a„)/2.
    12 12 12 1 1

    REFERENCES
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    BIOGRAPHICAL SKETCH
    Tze Chi Jao was born in Taitung, Taiwan on April 3, 1940. He
    attended high school there and obtained his B.S. degree in entomology
    in 1963 from the National Chung-Hsing University. In 1967 he obtained
    his M.S. degree in chemistry from the University of Puerto Rico at
    Mayaguez. He has been an instructor in physical chemistry at the
    University of Puerto Rico since 1967. He entered the Graduate School
    at the University of Florida in 1970 with a special financial assis-
    tantship provided by a grant from the University of Puerto Rico at
    Mayaguez.
    168

    I certify that I have read this study and that in my
    opinion it conforms to acceptable standards of scholarly
    presentation and is fully adequate, in scope and quality,
    as a dissertation for the degree of Docto?-- of Fhilosophy.
    C í) tisis, 6-
    VJillis £. Person, Chairman
    Professor of Chemistry
    I certify that I have read this study and that in my
    opinion it conforms to acceptable, standards of scholarly
    presentation and is fully adequate, in scope and quality,
    I certify that X have read this study and that in my
    opinion it conforms to acceptable standards of scholarly
    presentatior and is fully adequate, in scope and quality,
    as a dissertation for the degree of Doctor of Philosophy.
    ..LrL-Zjii
    James D. Winefordne
    Professor of Chemis

    I certify that I have read this study and that in ray
    opinion it conforms to acceptable standards of scholarly
    presentation and is fully adequate, in scope and quality,
    as a dissertation for the degree of Doctor of Philosophy.
    I certify that I have read this study and that in my
    opinion it conforms to acceptable standards of scholarly
    presentation and is fully adequate, in scope and quality,
    as a dissertation for the degree of Doctor of Philosophy.
    Thomas M. Reed III
    Associate Professor of
    Chemical Engineering
    This dissertation was submitted to the Graduate Faculty of the
    Department of Chemistry in the College of Arts and Sciences
    and to the Graduate Council, and was accepted as partial
    fulfillment of the requirements for the degree of Doctor of
    Philosophy. •"
    March, 1974
    Dean, Graduate School

    UNIVERSITY OF FLORIDA
    3 1262 08553 8030



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