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Solvent dependence of the relative Raman trace scattering intensity of the isolated CH stretching bands of cyclohexane-d11
Volume 179, number 5,6
CHEMICAL PHYSICS LETTERS
3 May 1991
Solvent dependence of the relative Raman trace scattering intensity of the isolated CH stretching bands of cyclohexane-d,1 * W.F. Murphy and M.V. Garcia ’ Steacie Institutefor Molecular Sciences, National Research Council of Canada, Ontario, Ottawa, Canada KlA OR6
Received 10 January 1991
The trace scattering Raman spectra of several solutions of cyclohexane-d,, have been measured to observe the solvent dependence of the relative intensities of bands due to the isolated axial and equatorial CH stretching vibrations. The band positions and widths and their relative areas were determined. Significant changes in the relative band intensities were observed, both among the various solution spectra, and between the liquid and vapor phase spectra. These variations are attributed to changes in the relative scattering cross section for the two bands; however, a detailed explanation cannot be-offered at this time.
1. Introduction Recently, our laboratory has measured absolute intensities of CH stretching bands in the gas phase trace Raman scattering spectra of various small alkanes having deuterium isolated CH bonds [ l-31. These bonds are isolated in the sense that all but one hydrogen in the molecule are substituted by deuterium, which results in an effective decoupling of the kinetic interaction between the remaining CH bond and its neighbors. In cases where the single proton can occupy more than one spectroscopically nonequivalent site, the different bands were easily resolved [ 41, but their relative intensities could not be explained on the basis of the existing understanding of relative species abundances or scattering cross sections. In the more recent work [ l-31, the variations in observed intensities have been found to be due to unanticipated differences in the scattering cross sections for the vibrations of the spectroscopically unique CH bonds. Within the assumptions of the Placzek polarizability model, these cross section * Issued as NRCC 328 15. ’ NRCC Guest Worker from Departamento de Quimica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
differences are attributable to differences in the derivative of the mean molecular polarizability with respect to the stretching of the different CH bonds. In the case of cyclohexane-d,,, an intensity ratio of 0.66 was found for the bands due to the stretching of the axial and equatorial CH bonds [ 3 1. In the simultaneous analysis of all trace scattering cross sections for this isotopic species and the normal and perdeuterated ones, it was found that the abundance ratio for the axial and equatorial conformers was 0.898 f 0.079. Since the given error is a single standard deviation, propagated from the error estimates for the measured cross sections, this value was thought to be not inconsistent with the expectation that the two conformers should be essentially equally abundant. For comparison, the axial conformer has been found by NMR to be slightly more stable (6 cal/mol) in a CS2 solution [ 51; this is equivalent to an abundance ratio of 1.OIO. In some preliminary measurements of Raman spectra of solutions containing cyclohexane-d, ,, we had noted that the CH,,/CH,, intensity ratio appeared to be different from the gas phase value. We have investigated this behavior more thoroughly, and, in this paper, we present the results of our study of the solvent influence on this intensity ratio.
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2. Experimental method
The sample of cyclohexane-d,, (98 at% D) and the deuterated solvents cyclohexane-d,, (99 at% D), chloroform-d (99.8 at% D), pyridine-d, (99.5 at% D), acetone-& (99.9 atl D), benzene-d6 (99.6 at% D) and dimethyl sulfoxide-d6 (99.9 at% D) were obtained from MSD isotopes. Acetonitrile-d, (99 at% D) was obtained from Aldrich. Carbon tetrachloride ( Spectranalyzed grade) and carbon disulfide (Reagent grade) were obtained from Fisher Scientific, and perfluorooctane (pure) was obtained from PCR Research. Solutions were prepared at IO- 15 mol% cyclohexane-d,, concentration, except for the perfluorooctane solution for which a 25 mol% solution was required due to the large molar volume of the solvent. The cyclohexane-d,, sample was used as a solution of 11 molOh cyclohexane-d,, in perdeuterocyclohexane. Because of the low solubility of cyclohexane in acetonitrile and dimethyl sulfoxide, spectra of these solutions at saturated concentration were obtained from the solvent phase in the sample capillary. The Raman spectra were excited with about 250 mW of argon-ion laser radiation at 5 14.5 nm. Samples were sealed in melting point capillaries that were mounted transversely to the incident beam and to the observation direction. Spectra were measured using a Spex 14018 double monochromator with a cooled Burle C3 1034 photomultiplier detector, and recorded with a Spex Datamate digital data acquisition system. A spectral slit width of about 2 cm-’ was used, and 25 scans were accumulated to improve the signal-to-noise ratio. Wavenumber shift and spectral sensitivity corrections were applied, and trace and anisotropy scattering spectra were obtained from the polarized components in the usual way [61. The temperature dependence of the acetone-d6 solution spectrum was observed after cooling the sample capillary with a laminar flow cooler [ 71. The trace spectra were analysed by fitting the observed contours with Gauss-Lorentzian sum functions. Estimates of the band-parameter standard deviations were calculated from the variance of the fit [ 8 1. Band areas were then calculated from the fitted band parameters. For comparison, band areas were 504
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determined by a direct integration of the observed spectra, and also by integrating the resolution-enhanced [9] spectra. Satellite bands had been noted in the vapor phase spectrum at 2884 and 2926 cm-‘, and also at 2862 cm- ’ [ 31. This last band is observable in many of the solution spectra, and its solvent frequency shift is consistent with the shift of the principal bands. We conclude that the two other satellite bands behave similarly, and, since they each have a relative intensity of only about 10% of the neighboring main band, the contribution of these satellites to the band fitting results should be negligible. In addition, in the acetonitrile and dimethyl sulfoxide solutions, bands attributed to solvent -h, isotopic impurities were noted. These were far enough from the region of interest not to interfere with the analysis of the cyclohexane-d, 1 bands.
3. Results As mentioned above, the observed Raman trace spectra were fit by pairs of symmetric bands. The band positions and widths so determined are presented in table 1, and compared to the gas phase values. Keeping in mind the limitations imposed by such a numerical treatment, we may comment briefly on the values found in these computations. As expected, the vibrational frequencies of the two bands are lower in solution than in the gas phase, and depend on the solvent. The frequencies observed here for the cyclohexane-diz solution agree with those reported earlier for the absorption spectrum [ 121, and also agree with the frequencies reported for the disordered, low pressure solid phase [ 13 1, when the latter are extrapolated to ambient pressure. The band separation is usually about 1 cm-i and at most 2 cm-’ smaller than the 32 cm-’ gas phase value, so the solvent influence on the frequency does not differ appreciably for the two bands. Non-specific solute-solvent interactions that influence band frequencies can be ascribed to solvent polarity and/or polarization properties. The frequency shifts observed for the vibrations of polar bonds are related mainly to solvent polarity [ 141, but such influences in the present case are clearly smaller than the influence of solvent polarization. This is seen by the
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Table 1 Solvent dependence of positions, I, and widths, 6 (in cm-‘), of isolated axial and equatorial CH stretching bands in trace Raman spectrum of cyclohexane-d,, solutions, with polarity and polarization functions used in solvent interaction models a) Solvent
V,
&a
%
6,
(G-1)/(2ttl)
(n2-l)/(Zn2+1)
14.5 f0.3 23.2f0.6 21.6t0.3 11.7+0.3 20.3 +0.4 17.3 +0.3 12.850.2 23.9f0.4 19.1 f0.3 27.9f 1.2 12.8f0.2
2923.0 2919.6fO. I 2916.2kO.2 2914.2+0.1 2913.3fO.l 2914.0+0.1 2914.1~0.1 2913.8&0.1 2913.5kO.l 2912.6+0.1 2911.2f0.3 2909.3kO.l
18.9+0.3 27.6kO.5 23.2kO.3 14.0+0.3 26.1 kO.3 21.4kO.3 14.4kO.l 27.9kO.4 23.9kO.3 32.7 & 1.0 14.4kO.l
0.1809” 0.4803 0.3587 0.2024 0.4646 0.226 1 0.2024 0.4414 0.2297 0.4841 0.2612
0.1455 c, 0.1748 0.2114 0.2040 0.1804 0.2150 0.2040 0.2293 0.2266 0.2207 0.2623
I vapor b, Ci,P,s CD,CN CDCl, Csh (CW2CO
CCI, C,HD, I CSDSN GD6 (CD&SO CS2
2891.0 2887.3k0.1 2884.8? 0.2 2883.4kO.l 2883.3kO.l 2883.1+0.1 2882.9i0.1 2882.920.1 2882.3i0.1 2881.7iO.l 2880.1 LO.4 2879.320.1
a1Except as noted, dielectric constant and refractive index values are taken from ref. [ IO]. All values used are for the normal, undeuterated compounds. b, Values from ref. [3]. ‘) Dielectric constant and refractive index values are taken from ref. [ 111.
better (but not quantitative) correlation of the frequency shifts with the polarization function, (n2- l)/(2n2t 1), included in table 1, so that the largest frequency shifts are observed for the solution in the highly polarizable CS2. The function of the dielectric constant, ( E- 1) / (2t t 1)) which appears in models describing reaction field interactions [ 151, is also included in table 1 for reference. The band widths determined in the fit (table 1) are much larger than those observed in the vapor phase spectrum (2.5-3 cm-’ ) [ 3 1. (All band widths discussed here are taken directly from the band titting results; no spectral slit function corrections have been applied.) Also, the width of the CH, band is from 2 to 6 cm-’ greater than that of the CH, band in the different solutions. The band widths correlate better with solvent polarity, in contrast to the frequency shift behavior, but note that the widths are greater in Ccl, and C6D6solutions than in the other non-polar solvents. Finally, the band widths are essentially the same for cyclohexane-d, , liquid and for cyclohexane-d, , in perdeuterated cyclohexane. This indicates that there is no significant resonant transfer effect in this case, similar to the behavior for trace scattering of CH stretching modes of haloforms and acetonitrile [ 161. The widths reported for the absorption bands in the cyclohexane-d,, solution [ 12 ] are somewhat greater than those found here for Ra-
man trace scattering, as expected from the additional contribution of rotational correlation to the absorption band width. Also, in that spectrum [ 121, the band widths differ by an amount similar to that found here fore the trace Raman spectrum. The main interest of this project is the solvent dependence of the relative trace scattering intensity of the CH, and CH, stretching bands. Band intensity ratios, calculated from the areas of the fitted bands, varied from 0.55 to 0.73 for the various solutions, compared to the ratio 0.66 found for the vapor phase spectrum [ 31. However, these values are not plausible measures of the relative band areas, as seen by making a detailed inspection of the observed spectra. The problem with the fitting procedure is that the best-fit results are nearly pure Lorentzian functions; for such functions there is significant integrated area contribution from outside of the spectral range being considered, in the far wings of the bands. The minimum relative CH,, intensity was for the acetone and dimethyl sulfoxide solutions, for which the fitted bands have the largest difference in width, and thus the greatest difference in area contributions from the far wings. So, even though the band fitting results are considered to give a reasonable indication of the frequency shift and band width variation within the limitations imposed by constraining the functional form for the two bands, we concluded that 505
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the relative area estimates obtained from the band fitting results did not accurately indicate the relative intensity variations in the observed spectra. However, it is easily demonstrated that there is indeed a significant variation in the relative intensities of these two bands. In fig. 1, the relative intensities are compared for the liquid phase and vapor phase cyclohexane-d, , spectra. Here, the vapor phase spectrum has been broadened by a convolution procedure to match the CH, band contour on the high frequency side in the liquid spectrum, and then shifted and scaled to match its peak position. Thus, the converted spectrum consists of two bands that are separated by the same frequency difference and have the same relative intensity as in the observed vapor phase spectrum, but that both have symmetric band contours matching the high frequency side of the CH,, band. The significant increase in the relative intensity of the CH,, band in the condensed phase is clearly seen, as is the increased intensity of the low frequency satellite band. Note that the two liquid spectra bands are not quite symmetric (as assumed in the fitting procedure), and the differences
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in the band shifts and band widths for the two bands, as found in the fit, are confirmed. A similar comparison in fig. 2 shows the variation in relative intensities between two of the liquid phase spectra. Here, the spectrum for liquid cyclohexaned, 1 has been broadened to match the contour of the CH, band in the acetone solution spectrum+ The decrease in relative intensity of the CH,, band in the acetone solution is again obvious. To quantify this behavior, we integrated the spectra directly, with one of the integration limits taken to be the minimum intensity point between the CH,, and CH,, bands. Since the low frequency satellite band was often not easily resolved, its contribution was included with the area of the CH,, band. The resulting intensity ratios are given in table 2; they are not correlated with either the solvent polarity or polarization functions of table 1. Spectral integration of partially resolved bands can be strongly affected by the choice of baseline. In an attempt to minimize this uncertainty, we narrowed the observed spectral band widths by up to a factor of two using the Fourier self-deconvolution resolution-enhancement tech-
Wave number shift, cm-’ Fig. 1. Observed spectrum of isolated CH stretching region in liquid cyclohexane-d,, (solid line), and the comparison with relative intensities of corresponding bands in the vapor phase spectrum. The observed vapor phase spectrum has been broadened, shifted and scaled (dotted line) to match the high frequency side of the CH, stretching band at 29 I4 cm- ’ in the liquid spectrum.
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CHEMICAL PHYSICS LElTERS
-I 2850
2900
2950
3000
Wave number shift, cm” Fig. 2. Observed spectrum of isolated CH stretching bands from cyclohexane-d, , in an acetone-d6 solution (solid line), and the comparison with relative intensities of corresponding bands in the pure liquid spectrum. The observed pure liquid spectrum has been broadened and scaled (dotted line) to match the CH,, stretching band at 29 14 cm-’ in the solution spectrum,
Table 2 Solvent dependence of relative intensities of isolated CH stretching bands in trace Raman spectra of cyclohexane-d,, solutions, from band area ratios, Am/A,, for observed and resolution-enhanced spectra Solvent
Observed spectrum
Resolution-enhanced spectrum
vapor *) (CD&SO (CD,)zCO CSDJN CsF,s CCI,
0.66 0.69 0.69 0.71 0.72 0.72 0.75 0.77 0.77 0.77 0.77 0.79
0.68 0.70 0.72 0.71 0.71 0.74 0.76 0.72 0.76 0.76 0.78
C6D6
CDCI, CD,CN CsHD,, GD,, (32
‘) Ref. [3].
nique [ 9 1. These narrowed spectra were then integrated in the same way as for the original ones; the resulting ratios are also included in table 2. The two sets of results correspond quite well; the differences
give some indication of the errors to be expected for these ratios. Any explanation for the observed intensity behavior must involve one of the three factors governing the intensity of Raman scattering: the power of the incident radiation (which is constant during our experiment and thus not a factor in the present case), the abundance of the scattering species, and the scattering cross section for the observed transition for that species. If we assume that the relative cross sections for the two transitions are unchanged from the vapor phase value, the observed behavior would be due to changes in the relative abundance of the ax and eq species in the various solutions. Then, from the vapor phase cross sections, the intensity ratio found for the CS2 solution corresponds to a preference for the axial conformer (AG=40 cal/mol), which agrees, to within the accuracy of our measurements, with the somewhat smaller NMR result for this value [ 5 1. On the other hand, if we take the relative abundance in the CS2 solution from the NMR results [ 5 1, and compare the intensity ratio for the CS2 solution with that for the acetone solution, we expect the eq 507
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species to be more strongly favored in acetone, if the relative cross sections are the same. Then, the more stable eq species should increase in abundance in the acetone solution at lower temperature. We attempted to observe such a temperature variation, but, on cooling to - 50°C we could detect no change in the observed spectrum of the acetone-d, solution #I. This implies that the observed intensity behavior is not due to changes in relative species abundance in the various solutions. However, the expected temperature variation is just larger than our detection limit, and it would be good to confirm this point with a direct measurement of the solvent dependence of the relative abundance by, for example, the more sensitive NMR method [ 5 1. At this point, we are compelled to conclude that the observed behavior is due to a variation in the relative scattering cross sections of the two bands in the various solutions. The local field effect on the scattering cross section of a gas phase molecule when it is placed in a (uniform) condensed phase system has been summarized [ 171; the resulting effect is the same for all spectral bands, and it cannot explain the changes in relative intensity observed here. Since the scattering cross section is proportional to the square of the polarizability derivative under the Placzek polarizability model for Raman scattering [ 171, the solvent dependence observed here would correspond to changes in the relative polarizability derivatives of up to about lOohfrom the gas phase value. It is well established [ 181 that, in the absence of specific interactions such as hydrogen bonding, the detailed structure of a liquid is governed by local packing or steric effects that depend on the repulsive core of the intermolecular potential. The local environment of the scattering molecule in the solution is thus very sensitive to the detailed shapes of the solvent and solute molecules. For this reason, the in111
If the relative cross sections are invariant, and the mole ratio for the CS, solution is that found in the NMR experiment [5], the mole ratio X.,/X, in the acetone solution would be 0.88 at room temperature. This would mean that, in acetone, the eq species is z 75 cal/mol more stable than the ax species, so the mole ratio at -50°C would be x0.85: the relative band intensities should decrease 3% from the room temperature value. However, the spectrum at this temperature was identical to that at room temperature, to within the combined noise level of less than 1%.
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termolecular dispersion interactions, which affect the molecular polarizabilities [ 191 and their derivatives, depend not only on the polarizability components of the isolated molecules and their separation, but also on the details of their relative orientation. On this basis, it is quite plausible that the different principal polarizability components for the cyclohexane could be affected differently in different solution environments, to modify the different polarizability derivatives and, thereby, the relative cross sections observed here. A prediction of the expected intensity variation due to intermolecular interactions can be sketched through consideration of the expression for the scattering cross section given by a summation of terms due to excited electronic states. We can assume that a major contribution to this summation for a CH stretching vibration will be from the electronic orbital located on the vibrating CH bond. In the condensed phase, the energy level of this orbital will be perturbed from that of the isolated molecule, and this will affect the denominator of the term in the cross section expression. The case most easily visualized is that of liquid cyclohexane. Since the axial and equatorial CH bond properties are so different in the ground state, we can assume that the energies of the electronic orbitals centered on these bonds differ significantly as well. In such a case, the strongest intermolecular interactions affecting the CH bond orbitals will be resonance interactions between like bonds - CH,,-CH,, and CH,-CH,,. Only the symmetric perturbed level contributes to the cross section expression; its position relative to the unperturbed level depends on the relative orientation of the interacting bonds: when the bonds are anti-parallel, the symmetric combination shifts to higher energy, and the contribution to the cross section is reduced for the visible excitation case considered here. On steric grounds, the more exposed equatorial CH bond is more likely to be near to a similar bond on an adjacent molecule than is the axial bond. This is indeed found in the low-temperature crystal structure, where the distances between nearest equatorial bond pairs on adjacent molecules are for the most part shorter than for axial bond pairs (see table 3 of ref. [ 201). On this basis, we expect the stronger interactions between antiparallel equatorial bond pairs to shift the symmetric perturbed level to higher en-
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ergy to a greater extent than for axial bond pairs, and thus the cross section for the CH,, stretching mode will be reduced compared to that for the CH,, mode. Indeed, this is the observed behavior. The fact that both the liquid cyclohexane-d,, spectrum and that for the solution of cyclohexane-d,, in cyclohexaned,, behave similarly is understandable in that the electronic levels should not be strongly dependent on isotopic substitution. It is clear that this type of interaction could serve to explain the intensity behavior of all of the solutions measured in this work, but the effects of non-resonant interactions cannot be dealt with as easily. In summary, we have observed the changes in frequencies, band widths and relative intensities of the bands attributed to the isolated CH,, and CH,, stretching modes in the trace Raman spectrum of cyclohexane-d,, on going from the vapor to the condensed phase. Of special interest to us is the change in relative intensities between the vapor phase and the various solutions, which varies from 5Ohto 20%, and the changes of up to 15Ohfor the different solutions. The relative intensity observations reported here cannot be explained by the usual models for condensed phase intensity behavior. Clearly, further study of these intriguing results is needed.
Acknowledgement MVG thanks the DGICYT of Spain for financial support. We also thank Dr. J.M. Fernindez-Sgnchez and Dr. W. Siebrand for their thoughtful suggestions
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for improving an earlier version of this paper. References [ 1] KM. Gough and W.F. Murphy, J. Chem. Phys. 85 ( 1986) 4290. [Z] K.M. Gougb, W.F. Murphy, T. Stroyer-Hansen and EN. Svendsen, 3. Chem. Phys. 87 ( 1987) 3341. (31 K.M. Cough and W.F. Murphy, J. Chem. Phys. 87 ( 1987) 1509. 1,41 R.G. Snyder, A.L. Aljibury, H.L. Strauss, H.L. Casal, K.M. Cough and W.F. Murphy, J. Chem. Phys. 81 (1984) 5352. 151 F.A.L. Anet and M. Kopelevich, J. Am. Chem. Sot. 108 (1986) 1355. 61 J.R. Scherer, S. Kint and G.F. Bailey, J. Mol. Spectry. 39 (1971) 146. 7) J.R. Scherer and R.G. Snyder, J. Chem. Phys. 72 (1980) 5798. 81 A.A. Clifford, Multivariate error analysis (Applied Science Publishers, Barking, I975 ) , 91 H.H. Mantsch, D.J. Moffatt and H.L. Casal, J. Mol. Struct. 173 (1988) 285. [lo] J.A. Dean, ed., Lange’s handbook of chemistry, 13th Ed. (McGraw-Hill, New York, 1985). [ 1 I] J.E. BradyandP.W. Carr, J. Phys. Chem. 86 (1982) 3053. [ 121J.S. Wong, R.A. MacPhail, C.B. Moore and H.L. Strauss, J. Phys. Chem. 86 ( 1982) 1478. [ 131 J. Haines and D.F.R. Gilson, J. Phys. Chem. 94 (1990) 4712. [ 141D. Scheibe, J. Raman Spectry. 13 (1982) 103. [ 151L. Onsager, J. Am. Chem. Sot. 58 (1936) 1486. [ 161D.W. Oxtoby, in: Advan. Chem. Phys., Vol. 40, eds. I. Prigogine and S.A. Rice (Wiley, New York, 1979) p. 1. [ 171 H.W. Schriitter and H.W. Klijckner, in: Raman spectroscopy ofgases and liquids, ed. A. Weber (Springer, Berlin, 1979) p. 123. [ 181 D. Chandler, Ann. Rev. Phys. Chem. 29 ( 1980) 44 I. [ 191A.D. Buckingham and K.L. Clarke, Chem. Phys. Letters 57 (1978) 321. [ 201 R Kahn, R. Fourme, D. Andre and M. Renaud, Acta Cryst. B29 (1973) 131.
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Solvent dependence of the relative Raman trace scattering intensity of the isolated CH stretching bands of cyclohexane-d,1 * W.F. Murphy and M.V. Garcia ’ Steacie Institutefor Molecular Sciences, National Research Council of Canada, Ontario, Ottawa, Canada KlA OR6
Received 10 January 1991
The trace scattering Raman spectra of several solutions of cyclohexane-d,, have been measured to observe the solvent dependence of the relative intensities of bands due to the isolated axial and equatorial CH stretching vibrations. The band positions and widths and their relative areas were determined. Significant changes in the relative band intensities were observed, both among the various solution spectra, and between the liquid and vapor phase spectra. These variations are attributed to changes in the relative scattering cross section for the two bands; however, a detailed explanation cannot be-offered at this time.
1. Introduction Recently, our laboratory has measured absolute intensities of CH stretching bands in the gas phase trace Raman scattering spectra of various small alkanes having deuterium isolated CH bonds [ l-31. These bonds are isolated in the sense that all but one hydrogen in the molecule are substituted by deuterium, which results in an effective decoupling of the kinetic interaction between the remaining CH bond and its neighbors. In cases where the single proton can occupy more than one spectroscopically nonequivalent site, the different bands were easily resolved [ 41, but their relative intensities could not be explained on the basis of the existing understanding of relative species abundances or scattering cross sections. In the more recent work [ l-31, the variations in observed intensities have been found to be due to unanticipated differences in the scattering cross sections for the vibrations of the spectroscopically unique CH bonds. Within the assumptions of the Placzek polarizability model, these cross section * Issued as NRCC 328 15. ’ NRCC Guest Worker from Departamento de Quimica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
differences are attributable to differences in the derivative of the mean molecular polarizability with respect to the stretching of the different CH bonds. In the case of cyclohexane-d,,, an intensity ratio of 0.66 was found for the bands due to the stretching of the axial and equatorial CH bonds [ 3 1. In the simultaneous analysis of all trace scattering cross sections for this isotopic species and the normal and perdeuterated ones, it was found that the abundance ratio for the axial and equatorial conformers was 0.898 f 0.079. Since the given error is a single standard deviation, propagated from the error estimates for the measured cross sections, this value was thought to be not inconsistent with the expectation that the two conformers should be essentially equally abundant. For comparison, the axial conformer has been found by NMR to be slightly more stable (6 cal/mol) in a CS2 solution [ 51; this is equivalent to an abundance ratio of 1.OIO. In some preliminary measurements of Raman spectra of solutions containing cyclohexane-d, ,, we had noted that the CH,,/CH,, intensity ratio appeared to be different from the gas phase value. We have investigated this behavior more thoroughly, and, in this paper, we present the results of our study of the solvent influence on this intensity ratio.
0009-2614/9 I /$ 03.50 0 199I - Elsevier Science Publishers B.V. ( North-Holland )
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2. Experimental method
The sample of cyclohexane-d,, (98 at% D) and the deuterated solvents cyclohexane-d,, (99 at% D), chloroform-d (99.8 at% D), pyridine-d, (99.5 at% D), acetone-& (99.9 atl D), benzene-d6 (99.6 at% D) and dimethyl sulfoxide-d6 (99.9 at% D) were obtained from MSD isotopes. Acetonitrile-d, (99 at% D) was obtained from Aldrich. Carbon tetrachloride ( Spectranalyzed grade) and carbon disulfide (Reagent grade) were obtained from Fisher Scientific, and perfluorooctane (pure) was obtained from PCR Research. Solutions were prepared at IO- 15 mol% cyclohexane-d,, concentration, except for the perfluorooctane solution for which a 25 mol% solution was required due to the large molar volume of the solvent. The cyclohexane-d,, sample was used as a solution of 11 molOh cyclohexane-d,, in perdeuterocyclohexane. Because of the low solubility of cyclohexane in acetonitrile and dimethyl sulfoxide, spectra of these solutions at saturated concentration were obtained from the solvent phase in the sample capillary. The Raman spectra were excited with about 250 mW of argon-ion laser radiation at 5 14.5 nm. Samples were sealed in melting point capillaries that were mounted transversely to the incident beam and to the observation direction. Spectra were measured using a Spex 14018 double monochromator with a cooled Burle C3 1034 photomultiplier detector, and recorded with a Spex Datamate digital data acquisition system. A spectral slit width of about 2 cm-’ was used, and 25 scans were accumulated to improve the signal-to-noise ratio. Wavenumber shift and spectral sensitivity corrections were applied, and trace and anisotropy scattering spectra were obtained from the polarized components in the usual way [61. The temperature dependence of the acetone-d6 solution spectrum was observed after cooling the sample capillary with a laminar flow cooler [ 71. The trace spectra were analysed by fitting the observed contours with Gauss-Lorentzian sum functions. Estimates of the band-parameter standard deviations were calculated from the variance of the fit [ 8 1. Band areas were then calculated from the fitted band parameters. For comparison, band areas were 504
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determined by a direct integration of the observed spectra, and also by integrating the resolution-enhanced [9] spectra. Satellite bands had been noted in the vapor phase spectrum at 2884 and 2926 cm-‘, and also at 2862 cm- ’ [ 31. This last band is observable in many of the solution spectra, and its solvent frequency shift is consistent with the shift of the principal bands. We conclude that the two other satellite bands behave similarly, and, since they each have a relative intensity of only about 10% of the neighboring main band, the contribution of these satellites to the band fitting results should be negligible. In addition, in the acetonitrile and dimethyl sulfoxide solutions, bands attributed to solvent -h, isotopic impurities were noted. These were far enough from the region of interest not to interfere with the analysis of the cyclohexane-d, 1 bands.
3. Results As mentioned above, the observed Raman trace spectra were fit by pairs of symmetric bands. The band positions and widths so determined are presented in table 1, and compared to the gas phase values. Keeping in mind the limitations imposed by such a numerical treatment, we may comment briefly on the values found in these computations. As expected, the vibrational frequencies of the two bands are lower in solution than in the gas phase, and depend on the solvent. The frequencies observed here for the cyclohexane-diz solution agree with those reported earlier for the absorption spectrum [ 121, and also agree with the frequencies reported for the disordered, low pressure solid phase [ 13 1, when the latter are extrapolated to ambient pressure. The band separation is usually about 1 cm-i and at most 2 cm-’ smaller than the 32 cm-’ gas phase value, so the solvent influence on the frequency does not differ appreciably for the two bands. Non-specific solute-solvent interactions that influence band frequencies can be ascribed to solvent polarity and/or polarization properties. The frequency shifts observed for the vibrations of polar bonds are related mainly to solvent polarity [ 141, but such influences in the present case are clearly smaller than the influence of solvent polarization. This is seen by the
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Table 1 Solvent dependence of positions, I, and widths, 6 (in cm-‘), of isolated axial and equatorial CH stretching bands in trace Raman spectrum of cyclohexane-d,, solutions, with polarity and polarization functions used in solvent interaction models a) Solvent
V,
&a
%
6,
(G-1)/(2ttl)
(n2-l)/(Zn2+1)
14.5 f0.3 23.2f0.6 21.6t0.3 11.7+0.3 20.3 +0.4 17.3 +0.3 12.850.2 23.9f0.4 19.1 f0.3 27.9f 1.2 12.8f0.2
2923.0 2919.6fO. I 2916.2kO.2 2914.2+0.1 2913.3fO.l 2914.0+0.1 2914.1~0.1 2913.8&0.1 2913.5kO.l 2912.6+0.1 2911.2f0.3 2909.3kO.l
18.9+0.3 27.6kO.5 23.2kO.3 14.0+0.3 26.1 kO.3 21.4kO.3 14.4kO.l 27.9kO.4 23.9kO.3 32.7 & 1.0 14.4kO.l
0.1809” 0.4803 0.3587 0.2024 0.4646 0.226 1 0.2024 0.4414 0.2297 0.4841 0.2612
0.1455 c, 0.1748 0.2114 0.2040 0.1804 0.2150 0.2040 0.2293 0.2266 0.2207 0.2623
I vapor b, Ci,P,s CD,CN CDCl, Csh (CW2CO
CCI, C,HD, I CSDSN GD6 (CD&SO CS2
2891.0 2887.3k0.1 2884.8? 0.2 2883.4kO.l 2883.3kO.l 2883.1+0.1 2882.9i0.1 2882.920.1 2882.3i0.1 2881.7iO.l 2880.1 LO.4 2879.320.1
a1Except as noted, dielectric constant and refractive index values are taken from ref. [ IO]. All values used are for the normal, undeuterated compounds. b, Values from ref. [3]. ‘) Dielectric constant and refractive index values are taken from ref. [ 111.
better (but not quantitative) correlation of the frequency shifts with the polarization function, (n2- l)/(2n2t 1), included in table 1, so that the largest frequency shifts are observed for the solution in the highly polarizable CS2. The function of the dielectric constant, ( E- 1) / (2t t 1)) which appears in models describing reaction field interactions [ 151, is also included in table 1 for reference. The band widths determined in the fit (table 1) are much larger than those observed in the vapor phase spectrum (2.5-3 cm-’ ) [ 3 1. (All band widths discussed here are taken directly from the band titting results; no spectral slit function corrections have been applied.) Also, the width of the CH, band is from 2 to 6 cm-’ greater than that of the CH, band in the different solutions. The band widths correlate better with solvent polarity, in contrast to the frequency shift behavior, but note that the widths are greater in Ccl, and C6D6solutions than in the other non-polar solvents. Finally, the band widths are essentially the same for cyclohexane-d, , liquid and for cyclohexane-d, , in perdeuterated cyclohexane. This indicates that there is no significant resonant transfer effect in this case, similar to the behavior for trace scattering of CH stretching modes of haloforms and acetonitrile [ 161. The widths reported for the absorption bands in the cyclohexane-d,, solution [ 12 ] are somewhat greater than those found here for Ra-
man trace scattering, as expected from the additional contribution of rotational correlation to the absorption band width. Also, in that spectrum [ 121, the band widths differ by an amount similar to that found here fore the trace Raman spectrum. The main interest of this project is the solvent dependence of the relative trace scattering intensity of the CH, and CH, stretching bands. Band intensity ratios, calculated from the areas of the fitted bands, varied from 0.55 to 0.73 for the various solutions, compared to the ratio 0.66 found for the vapor phase spectrum [ 31. However, these values are not plausible measures of the relative band areas, as seen by making a detailed inspection of the observed spectra. The problem with the fitting procedure is that the best-fit results are nearly pure Lorentzian functions; for such functions there is significant integrated area contribution from outside of the spectral range being considered, in the far wings of the bands. The minimum relative CH,, intensity was for the acetone and dimethyl sulfoxide solutions, for which the fitted bands have the largest difference in width, and thus the greatest difference in area contributions from the far wings. So, even though the band fitting results are considered to give a reasonable indication of the frequency shift and band width variation within the limitations imposed by constraining the functional form for the two bands, we concluded that 505
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the relative area estimates obtained from the band fitting results did not accurately indicate the relative intensity variations in the observed spectra. However, it is easily demonstrated that there is indeed a significant variation in the relative intensities of these two bands. In fig. 1, the relative intensities are compared for the liquid phase and vapor phase cyclohexane-d, , spectra. Here, the vapor phase spectrum has been broadened by a convolution procedure to match the CH, band contour on the high frequency side in the liquid spectrum, and then shifted and scaled to match its peak position. Thus, the converted spectrum consists of two bands that are separated by the same frequency difference and have the same relative intensity as in the observed vapor phase spectrum, but that both have symmetric band contours matching the high frequency side of the CH,, band. The significant increase in the relative intensity of the CH,, band in the condensed phase is clearly seen, as is the increased intensity of the low frequency satellite band. Note that the two liquid spectra bands are not quite symmetric (as assumed in the fitting procedure), and the differences
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in the band shifts and band widths for the two bands, as found in the fit, are confirmed. A similar comparison in fig. 2 shows the variation in relative intensities between two of the liquid phase spectra. Here, the spectrum for liquid cyclohexaned, 1 has been broadened to match the contour of the CH, band in the acetone solution spectrum+ The decrease in relative intensity of the CH,, band in the acetone solution is again obvious. To quantify this behavior, we integrated the spectra directly, with one of the integration limits taken to be the minimum intensity point between the CH,, and CH,, bands. Since the low frequency satellite band was often not easily resolved, its contribution was included with the area of the CH,, band. The resulting intensity ratios are given in table 2; they are not correlated with either the solvent polarity or polarization functions of table 1. Spectral integration of partially resolved bands can be strongly affected by the choice of baseline. In an attempt to minimize this uncertainty, we narrowed the observed spectral band widths by up to a factor of two using the Fourier self-deconvolution resolution-enhancement tech-
Wave number shift, cm-’ Fig. 1. Observed spectrum of isolated CH stretching region in liquid cyclohexane-d,, (solid line), and the comparison with relative intensities of corresponding bands in the vapor phase spectrum. The observed vapor phase spectrum has been broadened, shifted and scaled (dotted line) to match the high frequency side of the CH, stretching band at 29 I4 cm- ’ in the liquid spectrum.
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-I 2850
2900
2950
3000
Wave number shift, cm” Fig. 2. Observed spectrum of isolated CH stretching bands from cyclohexane-d, , in an acetone-d6 solution (solid line), and the comparison with relative intensities of corresponding bands in the pure liquid spectrum. The observed pure liquid spectrum has been broadened and scaled (dotted line) to match the CH,, stretching band at 29 14 cm-’ in the solution spectrum,
Table 2 Solvent dependence of relative intensities of isolated CH stretching bands in trace Raman spectra of cyclohexane-d,, solutions, from band area ratios, Am/A,, for observed and resolution-enhanced spectra Solvent
Observed spectrum
Resolution-enhanced spectrum
vapor *) (CD&SO (CD,)zCO CSDJN CsF,s CCI,
0.66 0.69 0.69 0.71 0.72 0.72 0.75 0.77 0.77 0.77 0.77 0.79
0.68 0.70 0.72 0.71 0.71 0.74 0.76 0.72 0.76 0.76 0.78
C6D6
CDCI, CD,CN CsHD,, GD,, (32
‘) Ref. [3].
nique [ 9 1. These narrowed spectra were then integrated in the same way as for the original ones; the resulting ratios are also included in table 2. The two sets of results correspond quite well; the differences
give some indication of the errors to be expected for these ratios. Any explanation for the observed intensity behavior must involve one of the three factors governing the intensity of Raman scattering: the power of the incident radiation (which is constant during our experiment and thus not a factor in the present case), the abundance of the scattering species, and the scattering cross section for the observed transition for that species. If we assume that the relative cross sections for the two transitions are unchanged from the vapor phase value, the observed behavior would be due to changes in the relative abundance of the ax and eq species in the various solutions. Then, from the vapor phase cross sections, the intensity ratio found for the CS2 solution corresponds to a preference for the axial conformer (AG=40 cal/mol), which agrees, to within the accuracy of our measurements, with the somewhat smaller NMR result for this value [ 5 1. On the other hand, if we take the relative abundance in the CS2 solution from the NMR results [ 5 1, and compare the intensity ratio for the CS2 solution with that for the acetone solution, we expect the eq 507
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species to be more strongly favored in acetone, if the relative cross sections are the same. Then, the more stable eq species should increase in abundance in the acetone solution at lower temperature. We attempted to observe such a temperature variation, but, on cooling to - 50°C we could detect no change in the observed spectrum of the acetone-d, solution #I. This implies that the observed intensity behavior is not due to changes in relative species abundance in the various solutions. However, the expected temperature variation is just larger than our detection limit, and it would be good to confirm this point with a direct measurement of the solvent dependence of the relative abundance by, for example, the more sensitive NMR method [ 5 1. At this point, we are compelled to conclude that the observed behavior is due to a variation in the relative scattering cross sections of the two bands in the various solutions. The local field effect on the scattering cross section of a gas phase molecule when it is placed in a (uniform) condensed phase system has been summarized [ 171; the resulting effect is the same for all spectral bands, and it cannot explain the changes in relative intensity observed here. Since the scattering cross section is proportional to the square of the polarizability derivative under the Placzek polarizability model for Raman scattering [ 171, the solvent dependence observed here would correspond to changes in the relative polarizability derivatives of up to about lOohfrom the gas phase value. It is well established [ 181 that, in the absence of specific interactions such as hydrogen bonding, the detailed structure of a liquid is governed by local packing or steric effects that depend on the repulsive core of the intermolecular potential. The local environment of the scattering molecule in the solution is thus very sensitive to the detailed shapes of the solvent and solute molecules. For this reason, the in111
If the relative cross sections are invariant, and the mole ratio for the CS, solution is that found in the NMR experiment [5], the mole ratio X.,/X, in the acetone solution would be 0.88 at room temperature. This would mean that, in acetone, the eq species is z 75 cal/mol more stable than the ax species, so the mole ratio at -50°C would be x0.85: the relative band intensities should decrease 3% from the room temperature value. However, the spectrum at this temperature was identical to that at room temperature, to within the combined noise level of less than 1%.
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termolecular dispersion interactions, which affect the molecular polarizabilities [ 191 and their derivatives, depend not only on the polarizability components of the isolated molecules and their separation, but also on the details of their relative orientation. On this basis, it is quite plausible that the different principal polarizability components for the cyclohexane could be affected differently in different solution environments, to modify the different polarizability derivatives and, thereby, the relative cross sections observed here. A prediction of the expected intensity variation due to intermolecular interactions can be sketched through consideration of the expression for the scattering cross section given by a summation of terms due to excited electronic states. We can assume that a major contribution to this summation for a CH stretching vibration will be from the electronic orbital located on the vibrating CH bond. In the condensed phase, the energy level of this orbital will be perturbed from that of the isolated molecule, and this will affect the denominator of the term in the cross section expression. The case most easily visualized is that of liquid cyclohexane. Since the axial and equatorial CH bond properties are so different in the ground state, we can assume that the energies of the electronic orbitals centered on these bonds differ significantly as well. In such a case, the strongest intermolecular interactions affecting the CH bond orbitals will be resonance interactions between like bonds - CH,,-CH,, and CH,-CH,,. Only the symmetric perturbed level contributes to the cross section expression; its position relative to the unperturbed level depends on the relative orientation of the interacting bonds: when the bonds are anti-parallel, the symmetric combination shifts to higher energy, and the contribution to the cross section is reduced for the visible excitation case considered here. On steric grounds, the more exposed equatorial CH bond is more likely to be near to a similar bond on an adjacent molecule than is the axial bond. This is indeed found in the low-temperature crystal structure, where the distances between nearest equatorial bond pairs on adjacent molecules are for the most part shorter than for axial bond pairs (see table 3 of ref. [ 201). On this basis, we expect the stronger interactions between antiparallel equatorial bond pairs to shift the symmetric perturbed level to higher en-
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ergy to a greater extent than for axial bond pairs, and thus the cross section for the CH,, stretching mode will be reduced compared to that for the CH,, mode. Indeed, this is the observed behavior. The fact that both the liquid cyclohexane-d,, spectrum and that for the solution of cyclohexane-d,, in cyclohexaned,, behave similarly is understandable in that the electronic levels should not be strongly dependent on isotopic substitution. It is clear that this type of interaction could serve to explain the intensity behavior of all of the solutions measured in this work, but the effects of non-resonant interactions cannot be dealt with as easily. In summary, we have observed the changes in frequencies, band widths and relative intensities of the bands attributed to the isolated CH,, and CH,, stretching modes in the trace Raman spectrum of cyclohexane-d,, on going from the vapor to the condensed phase. Of special interest to us is the change in relative intensities between the vapor phase and the various solutions, which varies from 5Ohto 20%, and the changes of up to 15Ohfor the different solutions. The relative intensity observations reported here cannot be explained by the usual models for condensed phase intensity behavior. Clearly, further study of these intriguing results is needed.
Acknowledgement MVG thanks the DGICYT of Spain for financial support. We also thank Dr. J.M. Fernindez-Sgnchez and Dr. W. Siebrand for their thoughtful suggestions
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for improving an earlier version of this paper. References [ 1] KM. Gough and W.F. Murphy, J. Chem. Phys. 85 ( 1986) 4290. [Z] K.M. Gougb, W.F. Murphy, T. Stroyer-Hansen and EN. Svendsen, 3. Chem. Phys. 87 ( 1987) 3341. (31 K.M. Cough and W.F. Murphy, J. Chem. Phys. 87 ( 1987) 1509. 1,41 R.G. Snyder, A.L. Aljibury, H.L. Strauss, H.L. Casal, K.M. Cough and W.F. Murphy, J. Chem. Phys. 81 (1984) 5352. 151 F.A.L. Anet and M. Kopelevich, J. Am. Chem. Sot. 108 (1986) 1355. 61 J.R. Scherer, S. Kint and G.F. Bailey, J. Mol. Spectry. 39 (1971) 146. 7) J.R. Scherer and R.G. Snyder, J. Chem. Phys. 72 (1980) 5798. 81 A.A. Clifford, Multivariate error analysis (Applied Science Publishers, Barking, I975 ) , 91 H.H. Mantsch, D.J. Moffatt and H.L. Casal, J. Mol. Struct. 173 (1988) 285. [lo] J.A. Dean, ed., Lange’s handbook of chemistry, 13th Ed. (McGraw-Hill, New York, 1985). [ 1 I] J.E. BradyandP.W. Carr, J. Phys. Chem. 86 (1982) 3053. [ 121J.S. Wong, R.A. MacPhail, C.B. Moore and H.L. Strauss, J. Phys. Chem. 86 ( 1982) 1478. [ 131 J. Haines and D.F.R. Gilson, J. Phys. Chem. 94 (1990) 4712. [ 141D. Scheibe, J. Raman Spectry. 13 (1982) 103. [ 151L. Onsager, J. Am. Chem. Sot. 58 (1936) 1486. [ 161D.W. Oxtoby, in: Advan. Chem. Phys., Vol. 40, eds. I. Prigogine and S.A. Rice (Wiley, New York, 1979) p. 1. [ 171 H.W. Schriitter and H.W. Klijckner, in: Raman spectroscopy ofgases and liquids, ed. A. Weber (Springer, Berlin, 1979) p. 123. [ 181 D. Chandler, Ann. Rev. Phys. Chem. 29 ( 1980) 44 I. [ 191A.D. Buckingham and K.L. Clarke, Chem. Phys. Letters 57 (1978) 321. [ 201 R Kahn, R. Fourme, D. Andre and M. Renaud, Acta Cryst. B29 (1973) 131.
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