Resonance Raman spectra and vibrational assignments of Azulene-d0 and Azulene-d8

Spectrochimica Ads, Vol.33A.pp. 53 IO62.Pergamon

Press

1977.Printed

in Northern

Ireland

Resonance Raman spectra and vibrational assignments*

of Aznlened-

and Amlene-ds

ROBERT S. CHAO and R. K. KHANNA Department of Chemistry, University of Maryland College Park, MD 20742, U.S.A. (Receioed 12 December, 1975) observed resonance effects in the Raman spectra of Azulene (CrcHs) and its completely deuterated analog are utilized to assign the totally symmetric modes of these molecules. In conjunction with the data on the ir. spectra and the normal coordinate analysis a complete assignment of the vibrational modes of these molecules is presented. The experimental excitation profiles are analyzed in the light of some current theoretical approaches. The experimental data strongly suggest that the variation of transition moment with the vibrational coordinate gives a dominant factor in determining the resonance Raman intensity of a mode. Abstract-The

lNTRODUCTION

the excitation frequency within the contour of the electronic absorption bands of Azulene. An analysis of these intensity data in the light of some current theoretical developments [ll-131 is also presented in this report.

The interpretation of the vibrational spectrum of azulene has been a challenging problem to spectroscopists for a long time. A great deal of work has been carried out on the i.r. spectra [l-S] of this compound and several of its deuterated derivatives. These data along with the results of normal coordinate analysis [6-81 have principally formed the basis for the assignments of the vibrational modes of azulene. These assignments remain incomplete and to some extent uncertain because of the lack of Raman data. Azulene has a dark blue color as a result of several long wavelength electronic absorption bands well beyond the visible region which makes it difficult to obtain the Raman spectrum of this compound. The Raman data on azulene investigated by BAILEY and LIPPINCOTT[9] report vibrational frequencies below 1700cm-‘. A recent report [lo] on the high resolution fluorescence spectrum of azulene discusses resonance enhancement of some of the Raman lines with selected laser excitations. After a great deal of experimentation with the sample preparation techniques we found that excellent quality Raman spectra of absorbing materials could be obtained by employing proper sample concentration. We succeeded in obtaining the Raman data on azulene-d, and -dg in the region 3200-300 cm-r, which along with the i.r. and the normal coordinate analysis data are discussed in this report. The radiation from a tunable dye-laser enabled us to obtain the Raman intensity dependence on

EXPERIMENTAL

Azulene powder (J. T. Baker Chemical Company) was purified by sublimation and filteration several times before preparing the sample pellets. The deuterated axulene was prepared by repeated exchange with DZO in a bomb [14,15] and was handled at all times in a dry box. The sample pellets were prepared by mixing the compound with potassium iodine in the molar ratio -1:lOO. The mixture was pressed into the form of a disc under 4000 psi pressure. The Raman spectra were obtained on a spex double monochromator (Model 1401) equipped with an EM1 9658 photomultiplier tube and the associated photon counting unit. Monochromatic light sources were the coherent radiation laboratory Model 52 Argon ion laser (4579, 4880 and 5145 A), a spectra phys& model 125 Helium-Neon laser (6328 A) and a coherent radiation laboratory model 496 tunable dye-laser pumped by an Argon laser. The dye employed was a Rhodamine 6G which rovided continuous radiation in the region 58006100 K A coherent radiation laboratory model 201 power meter was employed to monitor the laser output power at various excitation wavelengths. The spectral slit-width employed in each measurement was -5 cm-‘. All observed relative Raman intensities were converted to the true values by means of the spectral sensitivity response curve for the instrument. The product of the peak height and the half band width of a band was taken as a measure of the Raman intensity of the mode associated with that band. For comparison purposes the i.r. spectra of azulene-d,, and ds were also recorded in the reaion 4000-200 cm’. The spectrograph employed w; a Perkin-Elmer 225 oneratine under a soectral resolution of -2cm-‘. The electronic labsorption spectra of azulene were recorded on a Perkin-Elmer model 350 spectrophotometer.

*Work supported by a grant from NSF (GP-31646) and in part by a grant from Center of Materials Research, University of Maryland. 53

ROBERT S. GAO

54

KHANNA

and R. K.

and

phases of azulene-d,, -d, and -da. carried out a normal coordinate analysis of these molecules and computed their vibrational frequencies by transferring force constants from benzene. BAILEY and LIPPINCO~T [9] assigned, on the basis of the depolarization ratio, the Raman lines to totally symmetric and nontotally symmetric species. The resonance effects observed in our study of the Raman spectra of azulene have given additional data on the assignments of the totally symmetric modes. Thus, strong Raman peaks at 406, 680, 825, 971, 1210, 1268, 1396 and 1579cm-’ which clearly exhibit resonance effects (Fig. 1) are assigned to the A, species. Relatively less strong peaks at 1457, 1448, 1160 and 900cm-’ which also exhibit resonance effects are also classified under A, species. The peaks in the region 3100-2800 cm-’ are due to characteristic CH vibrations and among the observed ones, the peaks centered around 3098,3072,3037 (presumably, an unresolved doublet) and 2968 cm-’ are the strongest and, hence, assigned to the Al species. These peaks shift to 2332,2290,2247,2240 and 2188 cm-’ respectively on complete deuteration. Thus, the resonance Raman data provides the assignments for all the 17 totally symmetric modes which are given in Table 2. The i.r. data (Figs.

The tracings of various spectra (Raman, i.r. and electronic) are reproduced in Figs. 1-6.

solid

STEELE [6-81

DISCUSSION

(a) Vibrational anuIysis Azulene is a planar molecule (Fig. 7) possessing a C,, point group symmetry [4,16]. Its 48 fundamental modes are classified among the symmetry species of C,, as follows: r= 17A,+16BI+6A,+9B, The selection rules [17, 181 permit all modes to be Raman active; however, only AI, B, and Bz modes are i.r. active. The crystal structure of azulene [16] indicates disorder with respect to the orientation of the planar molecule. Consequently, the reduced site symmetry (C,) results in a complete relaxation of selection rules. Table 1 gives an approximate description of the normal modes (as bond stretches and bends) and their expected frequency ranges which are based on the interpretation of the vibrational spectrum of naphthalene. HUNT and Ross [l l] made a partial assignment of the vibrational modes of azulene based primarily on the polarized i.r. data on oriented single crystals and vapor phase band contours. VAN TETS and GUNTHARD [2,3] reported the results of an extensive study of the i.r. spectra of the solution

Azulene 45798, (21832 cm-’

I

3100

I

I

2900 '

)

I

1600

I

1400

I

I

1200 Frequency,

1000

I

I

ac0

600

I

400

cm-’

Fig. 1. Raman spectra of C1,,Hs/KI pellet. The laser excitations are: 21832, 20488 and 19429cn-’ from top to bottom (from Ar*+ ion laser). L: emission lines from laser (grating ghosts).

200

55

Resonance Raman spectra and vibrational assignments of Axulene-dc and Azulene-ds

I

Cl0He

I

I 1600

I 1400

Power

I 1203

17294

I 1000

I 800

Frequency,

cm-’

I 600

I 400

cm-’

Fig. 2. Raman spectra of &Hs/KI pellet. The laser excitations are: 17294, 17110, 16844 and 16564 cm-’ from top to bottom (from dye-laser).

CD De in KI pellet

19429 cm

I 2350

I 2150

,I ‘1700

I 1500

I 1300

Frequency,

Fig. 3. Raman spectra of C,,,D&I

I IICXI

I 900

I 700

I

I

500

300

cm-’

pellet. The laser excitations are: 20488 and 19429 cn-’ A?’ ion laser).

(from

56

ROBERTS. CHAOand R. K.

’

’

’

’

1500

’

’

CM-’

’

KHANNA

’

’

1000

’

/ , 500

y&J-J 400

200

Fig. 4. Infrared spectrum of ClOHs/KI pellet. 4,5) are also consistent with these assignments except that the 825,680 and 406 cm-’ modes do not appear strongly in the i.r. spectrum. However, in view of their strong Raman intensity and the accompanying resonance effects their assignments to Al species are certain. A few remarks on a comparison of our assignments with those of earlier workers are in order. First, Hunt and Ross, Van Tets and Gunthard and Steel have assigned the highest ring mode a frequency of 1640cm-‘. The i.r. spectra of nujol mulled samples of azulene-d, and ds do not show

this band. The Raman spectrum exhibits a band at 1644 cm-’ only when excited by the radiation in the center of the electronic absorption peak. We believe that the 1644 cm-’ Raman peak is due to the first overtone of the 825 cm-r which is one of the most intense Raman active fundamentals. Second, Van Tets and Gunthard suggest two peaks around 1580 cm-‘. Our i.r. spectra recorded under -1.5 cm-’ spectral slit width give no such indication, instead one strong peak at 1579 cm-’ which shifts to 1563 cm-’ on complete deuteration is observed. Third, the peak at 1268 cm-’ in the Raman

C M-

Fig. 5. Infrared spectrum of &D,/KI

pellet.

Resonance Ramau spectra and vibrational assignments of Azulene_do and Azulene-d,,

SOcm-’17240

cml

Fig. 6. Electronic absorption spectrum of CloHB solution in cyclohexane in the visible region.

Fig. 7. Resonance structure of azulene. spectrum

of azulene-d

plete deuteration indicates that this is to be associated with C,C, stretching. Even though this is a single bond we believe that this mode is highly coupled to the stretching modes of the adjacent Cr;;C bonds. Our assignments of 1268 and 825 cm-’ agree with those of Hunt and Ross. Table 1. Approximate frequency range for vibrational modes of azulene Mode description

Spectral region(cm-‘)

Al

Species AZ B1 Bz

Total allowed

2950-3100 1250-1700 850-1400 350-900

5 6 3 3

3 5 4 4

8 11 7 7

In plane

CH stretch CC stretch CCH bend CCC bend Out of Plane CCH bend CCC bend

750-1000 150-600

3 3

5 4

The assignments of the modes of the AZ species should be straightforward, in principle. Modes which appear in the Raman spectrum but with no counterpart in the i.r. should be classified under this category for an isolated molecule of azulene. However, these modes may develop significant intensity in the i.r. spectrum as well. This basis along with the results of normal coordinate analysis has been utilized to assign the AZ modes (Table 2). The modes of the B, and Bz species appear strongly in the i.r. spectra. Since Bz species contains all out of plane vibrations their frequencies are expected below 1100 cm-‘. The C z C stretches of the B, species are, however, expected in the range 16001100 cm-‘. This basis, along with comparison of the spectra of azulene-d, and -d, as well as the results of normal coordinate analysis has been utilized to give assignments of the modes of B1 and B2 species. These are also presented in Table 2. Table 3 gives a comparison of the Teller-Redlich product rule ratios obtained from the mass factors (theoretical) and the observed frequencies (calculated). It is seen that the agreement for AZ and B2 species is almost perfect. Perhaps, a 5% difference between the theoretical and calculated values of the product rule ratio for the A, and B, species is insignificant because both of these species contain a large number of vibrations. Even as little as a 0.3% correction to each vibrational frequency due to anharmonicity or crystal field effects could result in accounting for the difference. (b) Resonance

shifts to 1270 cm-’ on com-

8 7

57

effects

Experimental excitation profile. The electronic absorption spectrum of azulene (Fig. 6) exhibits four peaks in the region 15,000-20,000 cm-’ which are close to the excitation frequencies employed in this work (He-Ne laser: 15802cm-‘, A$+ ion laser: 20488 and 19429cm-‘, dye laser: 1635017350 cm-‘). The tracings of the Raman spectra in Figs. 3 and 4 clearly show that the intensities of several Raman lines (in particular, 825, 971 and 1396 cm-‘) are enhanced remarkably when the excitation frequency is tuned in the absorption region. A quantitative analysis of this intensity enhancement is complicated because of our inability to incorporate an internal standard which does not interfere with the Raman lines of the sample. To overcome this difficulty we employed the 680 cm-’ Raman line of azulene itself for standardization purposes. It was established in the previous section that the 680 cm-’ mode belongs to the A, species and exhibits resonance effects. We found from the

ROBERT S. Cmo and R. K. KHANNA

58

Table 2. Vibrational

Species

AI

GODS Ratio vCr,Ds

description

of azulene modes

Observed*

Approximate description of the mode

2332 2290 2247 2240 2188 1563 1375 1218 1392 1270 1122 890 867 699 756 632 394

0.753 0.745 0.739 0.738 0.737 0.989 0.944 0.841 0.997 1.000 0.926 0.771 0.893 0.778 0.916 0.929 0.970

R

941 911 813 542 331 189

836 705 686 474 306 160

0.888 0.773 0.795 0.874 0.924 0.846

R i.r. i.r. R i.r. i.r.

CCH CCH CCH CCC CCC CCC

2284 2252 2232 1470 1453 1360 1267 1042 948 911 1042 921 792 551 389 279 962 782 750 634 610 595 465 280 226

0.742 0.740 0.739 0.958 0.980 0.942 0.919 0.802 0.779 0.815 0.993 0.910 0.802 0.774 0.800 0.864 0.909 0.810 0.788 0.797 0.800 0.814 0.827 0.921 0.942

R R R i.r. i.r. i.r. i.r. i.r. i.r. i.r. i.r. i.r. i.r. R R ix. i.r. i.r. i.r.

V4S

3077 3042 3018 1536 1480 1443 1378 1300 1216 1117 1049 1012 987 712 486 323 1058 965 952 795 762 731 562 304 240

C-H stretch C-H stretch C-H stretch CC stretch CC stretch CC stretch CC stretch CCH bend CCH bend CCH bend CC stretch CCC bend CCC bend CCH bend CCC bend CCC bend CCH bend CCH bend CCH bend CCH bend CCH bend CCC bend CCC bend CCC bend CCC bend

* R = Raman

i.r. = Infrared

v3 V4 V5 v6 v7 V8 v9 VlO V11 v1t v13 v14 v15 h6 v17 V18 v19 v20 V21 v22 v23 BI

vCroDs

and approximate

3098 3072 3037 3037 2968 1579 1457 1448 1396 1268 1210 1160 971 900 825 680 406

VI v2

A2

GoHs

assignments

v24 v25 v26 v27 v28 v29 v30 v31 v32 v33 34 v35 v36 v37 V38 49 v40 V41 v42 v-%3 V44 v45 v46 v47

:: :: R, R, R, R, R R, R R, R, R R R

i.r. ix. i.r. i.r. i.r. i.r. i.r.

g:i.r. ;;‘,’i.r. i.r. i.r.

C-H stretch C-H stretch C-H stretch C-H stretch C-H stretch CC stretch CC stretch CC stretch CC stretch C-C stretch CC stretch CCH bend CCH bend CCH bend CCC bend CCC bend CCC bend bend bend bend bend bend bend

Resonance Raman spectra and vibrational assignments of Andene_do and Azulene-ds Table 3. Calculated and experimental ratio of product rule for azulene-dc and -68

Symmetry Type

Calculated

Observed

0.0687 0.3745 0.0644 0.1986

0.0723 0.3741 0.0654 0.2164

Al AZ RI &

intensity dependence on exciting frequency, v,,, however, that the effective electronic absorption frequency for this mode is the U.V. region. In the limited region of excitation employed in this work this mode shows no appreciable resonance intensity enhancement and, hence, can be used as an internal standard. This choice is further strengthened by the fact that for different excitations in the visible region, the ratios of the Raman intensities of the 680 and 406 cm-’ remains practically constant. Thus, with the 680 cm-’ Raman line as the internal standard we have constructed the experimental excitation profiles (plots of IRamanvs vO) for the 825,1396 and 1579 cm-’ modes of

observed

azulene.

These

are represented

in Figs. 8, 9 and 10

0

i I6

I5

I 17

I 18

Frequency,

I

I9

I 21

2

103Cm-

Fig. 9. Theoretical and experimental excitation profiles for the 1396cm-’ Raman line of C,,Hs.-Theoretical: using equation (5) with v, = 17150 cm-r, s, = 300 cm-‘, v, = 16350 cm-’ and 8, = 260 cm’. . . . Experimental data points.

1

C,o’-‘e

CIOHe

f

1

x)

t

I .

I

I

I6

17

I 18 Frequency,

I 19

I 2u

I

a

u

103cm“

Fig. 8. Theoretical and experimental excitation profiles for the 825 cm-t Raman line of Ct,Hs.-Theoretical: using equation (5) with v, = 17300 cm-‘, 8, = 300 cm’, v, = 16570 cm-’ and 6,=125cn-‘. . . . Experimental data points.

01 15

I I6

I 17

I I8

I 19

I 20

I 21

I 03cm-’

Fig. 10. Theoretical and experimental excitation profiles for the 1579cm-’ Raman line of C,,H,.-Theoretical: using equation (5) with v, = 17310 cm-‘, 8, = 230 cm-‘, v, = 16520 cm’ and 8, = 180 cm-‘. . . Experimental data points.

60

ROBERTS. CHAO and R. K.

respectively. A clear resemblence between the experimental excitation profiles and the electronic absorption spectrum of azulene (Fig. 6) is seen except that the peaks in the former are somewhat shifted from the corresponding peaks in the latter. As has been suggested earlier [12], the frequencies of the maxima in the experimental excitation profile (also called the effective absorption frequency) should be employed in the theoretical analysis of the experimental intensity data. Theoretical excitation profile. The resonance enhancement of the Raman intensity of a mode is due to the frequency dependence of the molecular polarizability derivative as is seen from the Krgmer-Heisenberg dispersion relation [20]:

which describes the contribution to the matrix element of the polarizability between initial (m) and final (n) states from all possible vibronic levels r. In Equation 1 v0 is the excitation frequency, hv, is the energy difference between initial state m and the intermediate state r which has an associated damping constant S, and M’s are the electronic transition moments. Employing Equation 1 as the basis, several explicit relationships between lRaman and v, have been derived. Among these the one state theory of SHORYGIN [21] and BEHRINGER and BRANDM~LLER [22] and the two state theory of Albrecht are most widely accepted. In the former the contribution to cy,,,, from one electronic level (frequency v,) is taken into account whereas in the latter two electronic levels (frequencies v, and v,) are considered. For totally symmetric modes (Stokes line)

IRaman(one state) o( (%- vmn)4(vez+ Vo2)’ (2) (v,2-v$)4

I Raman

(two

stat4

a

cl%-tv;

_

%“Y(%V3 v;,2tv,”

+ _

vo2)2 v;J2

@)

KOBINATA[~~],PETICOLAS etal.[25]and

COLLINS et al. [26] have given somewhat modified forms of Equation 2. In both cases the damping terms are neglected; consequently Equations 2 and 3 must be considered to be valid only under pre-resonance conditions. Further, in the derivation of these equations it is assumed that the first term in the expansion of polarizability derivative gives a au, aQ

dominant

contribution.

aM, aQ >

(4)

KHANNA

We have derived equivalent relationships by considering only the second term in (4). The results of such derivations for six different cases were given in an earlier publication from our laboratory [ll]. Here we analyze the experimental Raman intensity data in the light of the above mentioned theoretical results, the objective being to decide as to which of the two terms in (4) gives dominant contribution to the Raman intensity. This information, as we shall see later, is of important consequence in correlating the Raman intensity and the electronic absorption data. It needs to be emphasized again that the experimental intensity data obtained with 21832,20488 and 19429 cm-’ excitations are relevent to pre-resonance conditions (case 3 and 6 of reference [ll]) whereas the data obtained with tunable dye laser excitation in the range 1635017350 cm-’ are relevent to rigorous resonance (case 1 of reference ill]). I Raman(case 1, ref. [ll]) a

I Rnman(case 3, ref. [ll]) a I kilnan

(v0- vJ4

(v0-v,)Zi-s2

(vo-

%“)4vo

(vgz - v,2)2

(case 6, ref. [ 1 I]) a (%-- &J4[v,2(2v,2v,“- V,‘)*] (vo2- v,2)2(v$- v,2)2

(5)

(6)

(7)

Comparison between theory and the experimental data. The position and half widths of the peaks in

the experimental excitation profiles (Figs. 8, 9 and 10) give the effective absorption frequencies and the damping constants of the associated electronic states. Thus for the 825 cm-’ Raman line the parameters are: v, = 16,570, S, = 125, v, = 17300, %3~300, vc = 18,600 and S,= 1500 cm-‘. In the theoretical analysis the contribution from vc is ignored because of the large damping constant associated with this level and also because of the fact that this peak is far removed from the excitation frequencies employed in this work. Equation 5 is used to evaluate the contribution to Raman intensity from each v, and v, and the total intensity is plotted against vO.This theoretical curve is given on the same figure (solid lines) which gives the experimental points. For the 825 cm-’ Raman line a comparison between the experimental and theoretical intensities (relative to the intensity at l7,312cm-’ taken as 100 units) is given in Table 4. For the 1396 and 1579 cm-’ modes similar theoretical plots as given in Figs. 9 and 10

Resonance Raman spectra and vibrational assignments of AzuIene_do and AzuIene-ds

Equations 6 and 7 based on our approach utilizing contributions from one and two electronic states respectively. Both Equations 6 as well as 7 give better agreement with the experimental data than Equations 3 and 4. The present experimental work, thus, demon-

Table 4. Calculated and experimental intensities variation for 825cm-’ Mode of azulene-potassium iodide pellet. (Ail the intensities are relative to the intensity at 17312 cm’ as 100) v&m-‘)

Exp.*

Cal.*

21832 20488 19429 17356 17312 17294 17228 17225 17144 17110 17050 16946 16887 16844 16832 16763 16667 16566 16564 16485

27.7 39.5 56.5 98.6 100.0 94.0 88.5 85.8 77.0 69.8 57.8 40.7 19.1 30.3 30.0 33.2 33.0 59.7 58.4 41.8

28.3 41.3 54.3 98.7 100.0 99.3 91.5 91.0 74.9 67.8 56.6 42.8 38.2 37.5 37.2 38.0 47.3 58.1 58.0 45.2

* All the intensities are relaat tive to the intensity 17312cm’ as 100 (arbitrary units). respectively. Thus, the agreement between our theoretical formulae and our experimental data in the rigorous resonance region may be considered extremely good. We also present in Table 5 a comparison between the experimental data in the pre-resonance region (excitations by 21832, 20488 and 19429 cm-‘) and the predictions based on SHORYGIN’S [21] one state theory (Equation 2), ALBRECHT’S[23] two state theory (Equation 3) and Table 5. Calculated and experimental 825 cm-’ mode of CloHs (pre-resonance

intensities for Raman cases)

vc(cm-‘)

Eq. 2

Eq. 3

Eq. 6

Eq. 7

Iexp

21832 20488 19429

0.323 1.000 3.999

0.362 1.000 3.345

0.683 1.000 1.711

0.715 1.000 1.582

0.701 1.000 1.431

* Calculations based v, = 16570 cm’) Equation 2 = Shorygin’s Equation 3 = Albrecht’s Equation 6 = Case 3 in Equation 7 = Case 6 in

on = (v, = 17300 cm-’ one two Ref. Ref.

state state [l l] [ll]

61

and

theory with v, theory with v. and V, with v, with v, and v,

strates that the second term in Equation 4 gives a dominant contribution to the Raman intensity in the resonance region. This signifies that the variation of the transition moment with the vibrational coordinate is more important than the variation of the electronic frequency with the vibrational coordinates. Intuitively, we expect that during vibration the electronic frequency does not vary appreciably; on the other hand the nuclear rearrangement may result in significant change in the transition moment. In a recent report MORTENSEN[27] has predicted on the basis of Albrecht’s theory that the Raman intensity is proportional to the square of the extinction coefficient. If, however, the variation of M with Q is considered more significant the Raman intensity is found to be directly proportional to the extinction coefficient. This indeed is the case as is seen from a comparison of the experimental excitation profiles and the absorption spectrum of azulene reported here. More experimental work is desirable to test if, indeed, the variation of the transition moment with the vibrational coordinate gives a dominant contribution to the resonance Raman intensity. If so, the Placzek’s treatment of the Raman intensity using ground state polarizability may be considered to be generally applicable.

REFERENCES [l] G. HUNT and I. Ross, J. Mol. Specny, 3,604 (1959). [2] A. VAN TETS and H. GUARD, Specnochim. Acta 19, 1495 (1963). [3] A. VAN TETS and H. G~NTHARD,Spectrochim. Acta 28A. 1759 (1972). [4] E. &UBRO~NER~ Non-Benzenoid Aromatic Compounds, (Ed., D. GAINSBURG),Chapters V and VI. Interscience, New York, 1959. [5] G. HUNT and I. Ross, J. Mol. Spectry 9,50 (1962). [6] D. STEELE,J. Mol. Spectry 15,333 (1965). [7] D. STEELE, Spectrochim Acta 22,1275 (1966). [S] D. STEELE, Spectrochim. Acfa 23A, 1599 (1967). [9] R. BAILEY and E. LIPPINCOTT,J. Chem. Phys. 42, 1121 (1965). [lo] J. FRIEDMANand R. HOCHSTRASSER, Chem. Phys. 6, 145 (1974). [ll] R. S. CHAO, R. KHANNA and E. LIPPINCOT~,J. Raman Spectry 3, 121 (1975). [12] H. A. SZYMANSKI,(Editor) Adoances in Raman Spectroscopy, Vol. I., Plenum Press, New York, 1964.

62

ROBERT S. Cmo

[13] H. A. SZYMANSKI, (Editor) Adoances in Raman Spectroscope, Vol. II. Plenum Press, New York, 1570. -.. [14] A. BAIJDER and H. G~~NTHARD,Helu. China. Acta 41, 889 (1958). [15] A. VAN TETS and H. GUNTHARD, Helu. Chim. Acta 45, 457 (1961). [16] J. ROBERTSON, H. SHEARER, G. 0. SIM and D. WATSON, Acta Crysr. 15, 1 (1962). [17] E. WILSON, J. DECIUSand P. CROSS, Molecular Vibrations, McGraw-Hill, New York, 1955. [18] G. HERZBERG, Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand, New York, 1945.

and R. K.

KHANNA

[19] 0. REDLICH, Z. Phys. Chem. (B) 28, 371 (1935). r201 _ _ H. KRAMER and W. HJXSENBERG,Z. Physik 31,681 (1925). [21] P. SHORYGIN,Pure and Apple Chem. 4, 87 (1962). [22] J. BEHRINGER and J. BRANDMULLER, Z. E&ktrochem. 60, 643 (1956). [23] A. ALBRECHT,J. Chem. Phys. 34, 1476 (1961). r241_ S. KOBINATA, Bull. Chem Sot. Japan 46. 3636 _ (1973). [25] W. PETICOLAS, L. NAFIE, P. STEIN and B. FANCONI, J. Chem. Phys. 52, 1576 (1970). [26] D. COLLINS, D. FITCHEN and A. LEWIS, J. Chem. Phys. 59, 5714 (1973). [27] 0. MORTENSEN,J. Mol. Spectry. 39, 48 (1971).