The near-infrared spectra of some simple aldehydes'

Transcription

1 The near-infrared spectra of some simple aldehydes' G. LUCAZEAU~ AND C. SANDORFY De'parternent de Chinlie, U?ziversitt? de Montrtal, Montre'al, Que'bec Received July 13, 1970 The near-infrared spectra of CH3CH0, CD3CH0, CH3CD0, CF3CH0, CHC,CHO, and CC13CH0 were measured from 4000 to 9000 cm-' in solution at room and liquid nitrogen temperatures. Assignments are made and cases of Fermi resonance are examined. A few potential and anharmonicity constants are obtained. Solvent effects affecting fundamentals and overtones are discussed. Canadian Journal of Chemistry, 48,3694 (1970) ntroduction The infrared spectrum of acetaldehyde was thoroughly studied by Pitzer and Weltner (1) and by Evans and Bernstein (2) and some of its deuterated homologues were examined by Cossee and Schachtschneider (3) and by Capwell (4). The spectra of CC1,CHO and CHC1,CHO were studied by Lucazeau and Novak (5,6) and that of CF,CHO by Berney (7). Some interesting cases of Fermi resonance were observed (2-8) and some parts of the near-infrared spectra were measured (9, 10). This and the increasing attention given to anharmonicity in the analysis of vibrations of polyatomic molecules induced us to measure the spectra of acetaldehyde and some of its derivatives in the overtone-region, that is, in the near infrared from 4000 to 9000 cm-l. The following molecules were examined: CH,CHO, CH,CDO, CD,CHO, CF,CHO, CCl,CHO, and CHC1,CHO. Most of the spectra were measured in solution, in a 1:l mixture of CC1,F (freon-l 1) and CF,Br-CF,Br (freon 114-B-2) which gives a good glass at liquid nitrogen temperature. This solvent, first used by Durocher and Sandorfy (11, 12), is highly translucent in the near infrared and makes it possible to work at low temperatures and thereby to obtain better resolved solution spectra than has been hitherto possible. We measured our spectra at 298 and at 83 OK. n certain cases vapor and crystal phase spectra were also taken. Our aim was to assign as many bands as possible in the near-infrared 'Photocopies of a more detailed version of this paper including Tables to V may be obtained free of charge, upon request, from the Depository of Unpublished Data, National Science Library, National Research Council of Canada, Ottawa, Canada. 2Permanent address: Laboratoire de Chimie-Physique du C.N.R.S., 2 rue Henri Dunant, Thiais 94, France. part of the spectra, to study cases of anharmonic resonances which are found, determine the values of anharmonicity and potential constants whenever possible, to make observations on intensity ratios of fundamentals and overtones, and on solvent effects affecting these. Experimental All the spectra were determined on a Cary-14 spectrometer. The purification of the compounds has been described in a recent publication on their far-ultraviolet spectra (14). The solvent and low temperature techniques used were described in earlier publications from this laboratory (11-13). The great vapor pressure of CF3CH0, CH3CH0, CDBCHO, and CH3CD0 allowed us to examine them as gaseous samples at pressures near 600 mm Hg. For the last three compounds, the spectra are not well resolved and we present only the spectrum of CH3CH0 (Fig. ). The resolution is progressively improved in the spectra in solution at 295 "K, at 85 OK, and in the solid state (Figs. 1-9). All solutions were prepared under vacuum by condensing the compounds into a graduated cylinder containing the solvent cooled by liquid nitrogen. The concentrations were M. Solid samples were obtained by condensation of the vapor on a quartz window cooled by liquid nitrogen. The extinction coefficients in the near-infrared region were so low that we were obliged to prepare thick solid samples (a hundred times thicker than in the fundamental region). To circumvent the problem of scattered light, we projected gaseous helium onto the condensed sample. Thus we could observe bands with E values less than For CF3CH0 we observed a phase change, as shown by the 3000 cm-' region: the vo, band which was split into three components becomes unique after this treatment (Fig. 8) while vo2,~~ keeps the same intensity. (The indices 0 and 2 stand for the vibrational quantum numbers. So vo2 is a first overtone.) Generally this treatment favors the formation of a vitreous phase (this was the case for CF3CH0 and CC1,CHO) and it lowers the amount of scattering. No changes due to polymer formation were observed in the spectra.

2 LUCAZEAU AND SANDORFY: THE NEAR-NFR LARED SPECTRA OF SOME SMPLE ALDEHYDES 3695 Assignments Assignments of overtones and combination tones are usually more uncertain than those of the fundamentals. This is because of the great number of possible combinations, and the difficulty of predicting the values of anharmonicity constants. We found the following criteria useful in making assignments. (a) For methyl or aldehydic CH vibrations, deuteration of the respective group was used. (b) CO vibrations shift to lower frequencies in the order gas + solution (295 OK) + pure liquid (295 OK) + glassy solution (85 OK) + vitreous solid (85 OK) + crystal (85 OK). (The shift amounts to about 20 cm-' from the gas to the solid for the fundamental and about 40 cm-' for the first overtone.) The vibrations due to the aldehydic CH bond show the opposite trend. This has been established for the fundamentals by Evans and Bernstein (2) and by Lucazeau and Novak (5). This trend is maintained in the overtones (about 40 and 80 cm-', respectively). Methyl CH, vibrations are much less sensitive to changes in physical state. We made the assumption that bands of a mixed type have an intermediate type of behavior concerning this characteristic shifting. All this is confirmed by the coherent picture which is obtained by the application of the above rules. (c) Characteristic changes in the relative intensities of close lying bands with the change in physical state often reveal the presence of a Fermi resonance and this can be helpful in the identification of certain bands (15). (d) n may cases anharmonicities are approximately preserved in going from one molecule to another and this can also be used in making assignments. (e) ntensities can be helpful in certain cases. (f) n cases of Fermi resonance certain assignments can be eliminated by looking at the terms of the perturbing Hamiltonian (see below). The following symbols are used throughout this paper: vol, vo2, v,,,... fundamental and overtones of stretching vibrations; 601, 602, 603,... the same for bending vibrations. The indices of the anharmonicity constants (X,,, X,,,...) stand for the normal coordinates where 1 represents the (mainly) aldehydic CH stretching motion, 2 the in-plane bending of the aldehydic CH bond (6), 3 the C=O stretching frequency, and 4 the CH, stretching frequencies. The potential constant X,, couples vc, and 26c,,. Anharmonic Resonances The energy levels of anharmonic vibrations are usually computed from perturbation formulas. n polyatomic molecules it often happens that a combination or overtone has nearly the same energy and the same symmetry as a fundamental and that, at the same time, there is a large anharmonic term in the potential which "couples" them. n this case the usual formulas which give the energies to the second order cannot be used and the related part of the perturbational secular determinant must be solved separately. Supposing that the intensity of the combination band can always be taken for zero compared to the fundamental we obtain (17) for AEo, the separation of the unperturbed states where AE is the observed separation of the interacting vibrational states and p is their observed (integrated) intensity ratio. The interaction W,, has the form W,, = Y,"H'Y, dz where Y, is usually a fundamental and Y, a combination band and d~ represents integration for all normal coordinates. Although the best known cases of Fermi resonance are those between the fundamental of one vibration and the first overtone of another, this is by no means the only possibility. n fact Fermi resonance is possible between two overtones or combination tones and more than two vibrations can participate in Fermi resonance. Since, in the case of aldehydes we observed several cases of Fermi resonance where none of the partners are fundamentals we computed the value of W,,, for the cases which are of importance for the interpretation of their near-infrared spectra. (Details are given in a more complete manuscript deposited at the National Science Library along with the tables. See also refs. 18 and 19.) The cases of such superior Fermi resonances which we observed were produced by the three vibrations which can be approximately localized

3 3696 CANADAN JOURNAL OF CHEMSTRY. VOL. 48, Gos 298.K CH,CHO FG. 1. The near-infrared spectrum of acetaldehyde from 4000 to 6000 cm-'. Dashed curves: the ordinate is to be multiplied by four. Wave numbers against molecular extinction coefficients. /H in the aldehyde group (-C=O): q, the (mainly) C-H stretching mode, q, the (mainly) C-H (in-plane) deformation mode, and q, the (mainly) C==O stretching mode. All cases involve the same potential constant k,,,, (ndex 1 stands for the aldehydic CH stretching vibration and 2 for the bending of the CHO group.) However, because of the approximations which are implied in (1) we do not expect to obtain the same numerical values in all cases. Outside of the approximations proper to the perturbational treatment we had to suppose that one of the partners in all the resonances has zero intensity. This is partly justified by the fact that one of the partners is always a combination of a higher order than the other (binary against ternary etc.). We could not take into account electric anharmonicity. This could affect appreciably the measured intensities and, through eq. 1, it could influence the unperturbed frequencies computed from Fermi doublets. The measured intensities which enter in the calculation of p are, of course, approximate. The band areas were measured with a planimeter assuming an approximate Cauchy (Lorentz) shape, and intensity ratios are believed to be accurate to f 10 p.c. only. For these reasons we shall not attempt to interpret variations in the values of the constants which can be obtained from different bands in the spectra. Anharmonic resonances of higher order are also possible. The one of the next higher order is due to the off-diagonal terms of the quartic part of the potential and is sometimes called Darling- Dennison resonance (20). None of the anharmonic resonances we observed required the inclusion of such higher terms for its interpretation, however. Results () Methyl CH Vibrations Between 6000 and 5600 cm- ' we find a number of peaks and shoulders which are due to CH, vibrations as shown by their complete disappearance in the spectra (Figs. 1 to 4) of CD,CHO, CF,CHO, and CC1,CHO. Supposing the degeneracy due to the C,, symmetry of the methyl group lifted, there are three CH stretching fundamentals which could give three overtones and three other binary combinations between them. Furthermore, the three CH3 bending modes near 1460 and 1380 cm-' could give 18 combinations of the v + 26 type. This means 24 bands in this area and there are, of course, other

4 LUCAZEAU AND SANDORFY: THE NEAR-NFRARED SPECTRA OF SOME SMPLE ALDEHYDES 3697 CD, CHO FG OK. The near-infrared spectra of acetaldehyde and its deuterated homologues in 0.1 A4 solution at 295 and possible combinations. Thus we renounce assigning these bands individually. A relatively clear picture is obtained for the crystalline film spectrum of acetaldehyde (Fig. 1). We have made tentative assignments for this particular case. They are given in Table 1.' The anharmonicity constants which can be obtained from them were computed from simple second order perturbation formulas. For overtones x.. tr = v. t,01 - (~i,02/2) and for combination tones x.. = v LJ comb. - (V~,O + ~j,ol) n making the assignment we supposed that the order of frequencies of the bands at the fundamental level is preserved at the level of the overtones so that if, for example v,,,, > v,,,,, also v,,,, > v,,,,, etc. (a and s stand for antisymmetric and symmetric, respectively). This is tantamount to supposing that the anharmonicities do not change the order of the frequencies of overtones (and combinations) with respect to the fundamentals. We obtained values for the anharmonicity constants ranging from 15 to 30 cm-'. The molecular extinction coefficients of the CH, fundamentals are weak, of the order of E = 10. The respective overtones have about E = 0.2, a factor of about 50. n CHC,CHO, the remaining methyl hydro-

5 3698 CANADAN JOURNAL OF CHEMSTRY. VOL. 48, '.02 boa /L. A A /L CF, CHO FG. 3. The near-infrared spectrum of CF3CH0. Dotted curves: the ordinate is to be multiplied by four. Dashed curves: crystal. C Solul~on 298 "K LA C Solld Solution 85'K 298 'K Solullon 83.K -00s f h i am0, ~cca 5500 LOW Lnquid 298'K Solnd 85.K C 1, lljlta 7 Ju #e..,muar!:...., 0,. Om0 7 5 ~?OOO 6500 SO0 Xa FG. 4. The near-infrared spectrum of CC13CH0. Dotted curves: the ordinate is to be multiplied by four. +5m

6 LUCAZEAU AND SANDORFY: THE NEAR-NFRARED SPECTRA OF SOME SMPLE ALDEHYDES 3699 FG. 5. The near-infrared spectrum of CHC1,CHO in solution. Dotted curve: the ordinate is to be multiplied by three. gen gives a well defined overtone at 5894 cm-' (E = 0.4). The fundamental (6) is at (E = 6) so that X,, = 64 cm- l. At both levels there is a weaker band due to the gauche isomer (5789 and 2963 cm-', respectively) giving X,, = 69 cm-'. The relative values of X,, for the case of CHC1,CHO (one hydrogen) and CH,CHO (three hydrogens) (15 to 30 cm-') are in line with considerations of Siebrand and Williams (21) concerning the division of the anharmonic contribution to the energy between bonds ending at a common atom. The second overtones of the CH, stretching vibrations and the combinations among them yield weak bands in the cm-' region. Most of them are likely to be complex. Their molecular extinction coefficients are about 0.01 or less, about a thousand times weaker than their fundamentals. Between 4300 and 4850 cm- ' we find a number of strong combination bands (E between 1 and 2 for the strongest). By comparing the spectra of CH,CHO with those of CD,CHO, CH,CDO, and the halogenated aldehydes we can identify three groups of bands. Starting at the low frequency end of this range there are about five CH, stretching + CH, bending combination bands (Table 11), followed at higher frequencies by aldehydic CH stretching + CO stretching and by CH, stretching + CO stretching combinations (see below). The coupling constants for the v + 6 type CH, bands are of the order of Xij = cm-' if our assignments made according to the above hypothesis are correct. (2) Aldehydic CH Vibrations The C-H stretching fundamental is affected by a pronounced Fermi resonance which was reported by previous authors (1-8). We remea- sured these bands in our solvent at a concentration of 0.1 M (Figs. 6-9, Table 11). As is seen, the conditions are not simple. For CH,CHO there is a large splitting yielding bands at 2852 and 2761 cm-' at 83 OK. Both bands are at least doublets, however. The advantage of measuring the spectra at low temperature appears clearly on Fig. 6. There is a changeover in the intensities of the overlapping bands at 2761 and 2739 (low temperature values) in going from room to liquid nitrogen temperature, which may be due partly to the solvent affecting the two bands differently and partly to the sharpening of the bands leading to changed overlap conditions. n CD,CHO only the two main bands at 2843 and 2746 cm-' are observed. The other two bands which intervene in the CH, containing molecules are likely to be the first overtone of the 1425 deformation mode (2850 cm-l) and the combination of 1425 and 1342 cm- ' (2728 cm-'). So this is a complicated case of multiple resonance. We computed the unperturbed frequencies form [ ] by taking mean values for the small splittings. The unperturbed frequencies, the W,, and k,,, values are given in Table 111. The average value of W,, is 50 cm-' for the acetaldehydes in solution at 83 OK and that of k,,, is 100 cm-' under the same conditions. CC,CHO has only one strong band which is probably slightly affected by resonance with its two weak neighbors. The E values are diminished by a factor of about three with respect to acetaldehyde. n the gas phase spectrum of CF,CHO the CH band shows some rotational contour with, an apparent Q branch. t is probably in weak resonance with its neighbor at 2734 cm-' which has a similar shape (Fig. 8). This spectrum was first published by Berney (7). We also measured

7 3700 CANADAN JOURNAL OF CHEMSTRY. VOL. 48, 1970 FG. 6. The region of the vcl,, and vch fundamentals of CH3CH0 in solution. FG. 7. The region of the vch fundamental of CD3CH0 in solution. the spectrum of the solid at 77 O K. There is a spectacular difference between the spectrum of the glass3 (solid curve on Fig. 8) and that of the crystalline solid. The relative intensities of two weak bands at 2765 and 2724 cm-' probably in weak resonance with the fundamental, are 3We found the same frequency, 2918 cm-', as Berney for this molecule in a CO, matrix. also affected. A similar observation can be made in the corresponding overtone region. n spite of the weakness of 6,,,,,, (2685 cm-') and the presence of a third combination band in the fundamental region for halogenated aldehydes, k,,, was computed and found equal to 72 and 105 cm-', respectively, for CC1,CHO and CHC1,CHO in solution at 295 O K. These values are very similar to those obtained in the same

8 LUCAZEAU AND SANDORFY: THE NEAR-NFRARED SPECTRA OF SOME SMPLE ALDEHYDES 3701 FG. 8. The region of the VCH fundamental of CF3CH0. Dotted curve: crystal; solid curve: glass. physical state at the first overtone level. The agreement is less good for CF,CHO (105 cm-' at the fundamental level). The first overtone region of the CH vibration, seems to "inherit" the Fermi resonance found at the fundamental level. We find two bands in the spectra of CH,CHO and CD,CHO separated by about 100 cm-', respectively, at 5385, 5502 cm- ' (E = 0.1 1) and 5386, 5487 cm-' in solution at 85 OK (E = 0.08). For CH,CHO the band at 5502 seems to be broadened by the neighboring CH, absorptions4 while this is not the case for CD,CHO. This, with the effect of temperature on the intensity of this band (see below) can be closely related to the observations made at the fundamental level. We computed W,, = 53, k,,, = 75 cm-' for both compounds at 85 OK, that is 25% less than the value computed at the fundamental level and this may be due to the approximations already mentioned. Other data are compiled in Tables 11 and V. When the bands do not have an equal intensity (CF,CHO, CD,CHO in solution at 295 OK, CH,CHO in the gaseous and crystalline phases), the stronger one is always at the lower frequency and therefore must have strong CH stretching character. This implies that the ternary v n fact, smaller bands (E 2: 0.01) at this frequency can be observed in the spectrum of CH3CD0 and can be attributed to combinations of ZicH3 modes. combination is the one borrowing intensity from the binary 2vc,, and not the opposite. The contrary was true at the fundamental level, v, having a higher frequency than 2Fc,. To explain this reversal, we computed the anharmonic coupling constant from the unperturbed frequency v + 26 for CD,CHO in solution at 295 OK and obtained At the same time, the unperturbed frequencies of v,, and 6,, yield and X, = v,, - (vo,/2) = -95 cm-' X,, = F,, - (6,,/2) = -1 cm- The larger value of X, compared to X, explains the observed reversal of frequencies in going from the fundamental level to the first overtone level. (For related formulas see ref. 16, p. 206.) A similar situation is encountered with fluoral (gas) (Fig. 3). From v + 6 we obtain X, = (v,, + 6,') - v,, - F,, = 6 cm-' and from v + 26, X,, = - 66 and X,, = - 6 cm- '. The large value of X, suffices to reverse the order of the bands. For CHC1,CHO X,, = +20 oi 19 cm-', X, = -68 cm-', and X,, = +3 cm-'. t is seen that the X, coupling constant has widely different values for the different molecules.

9 3702 CANADAN JOURNAL OF CHEMSTRY. VOL Solution 295" K Solution 83" K -10 A FG. 9. The region of the vcn fundamental of CC,CHO in solution. n the cases where the coincidence of 2v and v + 26 is quasi-perfect we must have the same mixture of v and 6, in the two bands resulting from Fermi resonance. The respective anharmonicity constants are given in Table V. X,, = -71 cm-' for CH,CHO in solution at 85 OK, X, = - 92,. X,, = +6 very close to those for CD,CHO where the two bands were of unequal intensity. This confirms our interpretation of the reversal of the order of the two bands in the latter case. For CC1,CHO X, = +4 or + 10, X, = -72, X,, = -4 cm-' in solution at 85 OK. At the level of the second overtone of CH,CHO and CD,CHO we find a weak band. There is a possibility of a Fermi resonance between v,, and v,, + Zo2 so that there should be two bands in this area. Actually we find two bands for CCl,- CHO and CF,CHO with the one at higher frequency stronger. This was so at the level of v,, but not at the level of v,,. Whether there is a switch back in the order of the frequencies, or only the relative intensities change we cannot tell. and (vo3/3) - (vo,/4) are, X,, = - 8, - 14, and - 11, respectively, showing the validity of the second order perturbation approach. Only the intensity of the third overtone seems to be relatively high. For gaseous CF,CHO we obtain the anharmonicity constants - 11, - 10, and - 10 in the same order. For acetaldehyde in solution at 295 OK we obtain -4 and - 10 for the first two levels. This is a case of low anharmonicity with no apparent complications. (4) Combination between CH,, CH, and CO Vibrations These combinations are the most intense in the spectra. There is Fermi resonance between Vo1,co + V01,~" and v01,co + 602,~~ as well as between vo2,co + vo,,c, and vo2,co + 602,~~. These bands are in the 4500 and 6200 cm-' areas (Table 1). We obtain again k,,, (about 90 cm-' for acetaldehyde, Table 111). For X, the unperturbed frequencies give - 32 in the case of acetaldehyde at 295 OK. t is +4 for chloral and - 1 for fluoral. Combination between CO and CH, stretching (3) The C=O Stretching Bands bands are numerous because of the degenerate The were measured previous CH3 bands. The average value of X,, is about 6 authors (1-7). We measured the first, second, cm-~. and third overtones. Other data are given in Table V. A typical case is that of chloral. The respective molecular extinction coefficients are E = 550, (5) Environmental Efects 10, 0.1, and The anharmonicity constants n Buckingham's theory (18) (23, 24) it is computed from v,, - (vo2/2),(vo2/2)- (vo3/3), predicted that the gas to solution shifts of the

10 LUCAZEAU AND SANDORFY: THE NEAR-NFR ARED SPECTRA OF SOME SMPLE ALDEHYDES 3703 fundamental, first, and second overtones..- of a diatomic vibrator are in a proportion 1 :2:3 : This relation does not depend on the actual potential between solute and solvent molecules but only on the validity of the second order perturbation calculation. Since some of the vibrations we encounter in the aldehydes can be considered as localized in a CH or CO bond we thought it interesting to check upon the validity of Buckingham's relation. We have gas to solution (or glass) values in two cases only but we measured the shift from room to liquid nitrogen temperature in all possible cases, in the same solvent. Since a change in temperature may be supposed to have a similar effect on the solute as going from one solvent to the other it is reasonable to study Buckingham's relation in this case too. Table V contains a few typical results. t is seen that the 1 :2:3 relation is fairly well kept for both the gas to solution and 295, 85 "K shifts for the CO and CH stretching vibrations but less well for the CH than for the CO. This is in keeping with the larger anharmonicity of the CH stretching motion. t seems that we are at the limit of the second order approach in the latter case. As mentioned above vco undergoes a red shift whereas vch undergoes a blue shift. This is not due to the anharmonicities which have the same sign and comparable magnitudes. The 6, bands show much smaller shifts. Also their anharmonicities are small. The combinations vco + VCH, vco + 6CH and vch + 6, exhibit a somewhat irregular behavior. However, with a few exceptions, the shifts of the combinations are fairly close to the sum of the shifts of the respective fundamentals. This is closer to being true for CH + CH than for CH +.CO combinations. n view of the errors inherent in the method of computing the unperturbed frequencies we cannot hope to draw more precise information from our data. Anharmonicity constants should be environment-independent to the second order (24, 25). This is approximately verified in the cases we have studied (Table V). Conclusions The near-infrared spectra of aldehydes are dominated by the overtones of CH,, aldehydic CH and CO stretching vibrations, and combinations between these and with 6,,, and 6, deformation vibrations. Several cases of Fermi resonance are found. The most pronounced are of the type v-26, 2v-(v + 26), 3v-(2v + 26). n all these cases first order anharmonic resonance seems to suffice to interpret the phenomenon. We found no cases of higher order anharmonic resonances although these might make slight contributions to the observed ones. The value of the potential constant k,,, was computed from observed Fermi doublets. Six anharmonicity constants were also computed. Buckingham's 1 :2:3 relation concerning solvent shifts is approximately valid and the shifting of combination bands is seen to have a connection with that of the corresponding fundamentals. We are indebted to the National Research Council of Canada for financial help. 1. K. S. PTZER and W. WELTNER. J. Amer. Chem. SOC (1949). 2. J. C. E;ANS and H. J. BERNSTEN. Can. J. Chem. 34, 1083 (1956). 3. P. COSSEE and J. H. SCHACHTSCHNEDER. J. Chem. Phys. 44, 97 (1966). 4. R. J. CAPWELL. JR. J. Chem. Phvs (1968). 5. G. LUCAZEAU and A. NOVAK. Svectrochim.' Acta. 25A, 1615 (1969). 6. G. LUCAZEAU and A. NOVAK. J. Mol. Struct. 5, 85 (1970). 7. C. V. BERNEY. Spectrochim. Acta, 25A, 793 (1969). 8. E. L. SAER, L. R. COUSNS, and M. R. BASLA. J. Phys. Chem. 66,232 (1962). 9. E. TALLANDER et M. TALLANDER. C. R. Acad. Sci. Paris, 257, 1522 (1963). 10. M. P. GROENEWEGE and H. A. VAN VUCHT. Mikrochim. Acta, 2, 471 (1955). 11. G. DUROCHER and C. SANDORFY. J. Mol. Spectry. 20, 410 (1966). 12. C. SANDORFY. Can. Spectry. 10 (4), 85 (1965). 13. M. ASSELN, G. BELANGER, and C. SANDORFY. J. Mol. Spectry. 30, 96 (1969). 14. G. LUCAZEAU and C. SANDORFY. J. Mol. Spectry. 35, 214 (1970). 15. J. FERNANDEZ BERTRAN, L. BALLESTER, L. DOBR- HAMVA, N. SANCHEZ, and R. ARRETA. Spectrochim. Acta, 25A, 1765 (1968). 16. G. HERZBERG. nfrared and Raman spectra. Vol. 11. Van Nostrand, Princeton, New Jersey J. OVEREND. nfrared suectroscoov and molecular structure. Edited by ~ansel ~avis:~lsevier- ond don p A. D. BUCKNGHAM. Proc. Roy. Soc. A248, 169 (1958). 19. P. BARCHEWTZ. Spectroscopic infrarouge.. Gauthier-Villars, Paris p B. T. DARLNG and D. M. DENNSON. Phys. Rev (1940). 21. W: SEBRAND'~~~ D. F. WLLAMS. J. Chem. Phys. 49, 1860 (1968). 22. A. D. BUCKNGHAM. Proc. Roy. Soc. A255, 32 (1 960) 23. A: D'BUCKNGHAM. Trans. Faraday Soc. 56, 753 (1960). 24. G. DUROCHER and C. SANDORFY. J. Mol. Spectry. 22, 347 (1967).