J. Phys. Chem. 1984, 88, 363-368 so that the calculated result still does not agree with our predictiori. A further confirmation of any vibrational force field is its ability to predict isotopic frequency shifts. As described above, two features have been observed which are attributed to the isotopomer having a I3Cas the central carbon atom. The calculated frequency shifts for the two bands concerned, zq and q6, are 42.9 and 20.4 cm-', respectively, compared to observed values of 41.5 and 17.7 cm-'. An additional feature identified as the v16 band for the species having a noncentral 13Cwas observed shifted 4.7 cm-' from the main band, compared to a calculated shift of 2.0 cm-l. Here the assignment is consistent with the IRMPD result3 that irradiation at frequencies below 944 ern-,, >27 cm-, below the V I 6 band, resulted predominantly in enrichment of 13C in the CO rather than in the C2F6 product. This is expected only if the substitution of the central carbon atom by I3C results in an appreciably larger isotopic shift than substitution of a noncentral atom. The structural and vibrational frequency data from the present study was used to repeat the literature statistical mechanical entropy calculation.@ It is found that, when a value of 6.2 kJ/mol is used for the potential barrier to internal rotation of the CF3 groups, the calculated entropy matches the experimental value. This potential barrier agrees with the result of the original determination,@in spite of minor differences in the frequencies and moments of inertia used in the two calculations. The value of the barrier, which is assumed to be the same for the two torsional vibrations, may be compared with the energy difference of 4.9 kJ/mol between the C2, and the minimum-energy C2 structure found in our ab initio calculation. Also, a comparable value of 5.8 kJ/mol has been given for the CF3 barrier in l,l,l-trifluoropropanone:' It is clear that the actual potential to internal rotation for HFA is much more complicated than the simple threefold potential assumed in these calculations: the frequencies of the two torsional vibrations should not be equal, and the minimum of the potential function must occur at nonzero torsional angles to be consistent with the accepted equilibrium structure. However, the present data are not adequate for carrying out a more detailed analysis of the torsional motion; 45 such as study (44) Plaush, A. C.; Pace, E. L. J . Chem. Phys. 1967, 47, 44-8.
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must await further experimental results.
Conclusion The detailed reexamination of the vibrational spectrum of HFA in light of the improved Raman spectrum measured in this work leads us to revise the identification of several of the observed bands, especially those at lower frequencies. The intensity properties of the vibrational spectrum are consistent with a C2, molecular point group symmetry, as found earlier,6 but in apparent contradiction to the C, symmetry determined by electron diffraction.I0 The structure determined from an ab initio calculation in this work is also C,, although there are unexpected differences in the theoretical and experimental structural parameters. When an ab initio estimate of the vibrational force field of the C, molecule is used in a normal-coordinate calculation, it is found that coordinates which transform according to different symmetry species under C,, do not couple appreciably in the lower symmetry structure. These results can be understood on the basis of the molecular symmetry group classification of the nontorsional vibrational modes of the molecule," which predicts that the symmetry properties of nontorsional modes may be classified on the basis of the C,, point group. Using the results of the normal-coordinate calculation, one can generate a complete assignment of the vibrational spectrum. The predictions of the isotopic frequency shift of the 971-cm-' band is consistent with isotopically selective IRMPD ~ t u d i e s .Apart ~ from uncertainties associated with two bands which are not directly observable, the assignment provides a self-consistent model for understanding the observed spectrum. Further minor improvements may be expected if the inconsistencies in the structural parameters, described above, can be resolved. Registry No. Hexafluoroacetone, 684-16-2. Supplementary Material Available: Tables of the ab initio force constant matrix (Table VII) and the normal-coordinate matrix (Table VIII) (4 pages). Ordering information is found on any current masthead page. (45) Groner, P.; Sullivan, J. F.; Durig, J. R. In "Vibrational Spectra and Structure"; Durig, J. R., Ed.; Elsevier: New York, 1981; Vol. 9, pp 405-96.
Spectroscopically Evaluated Rates and Energies for Proton Transfer and Bjerrum Defect Migration in Cubic I c e William B. Collier, Gary Ritzhaupt, and J. Paul Devlin* Department of Chemistry, Oklahoma State Uniuersity, Stillwater, Oklahoma 74078 (Received: May 16, 1983) Though historically conductivity and dielectric relaxation measurements on ice have been plagued with interference from surface states and other extrensic factors, experimentation, combined with the elegant theory of Jaccard, has led to a detailed description of charge transport. This description has been tested by spectroscopic methods based on the ability to isolate intact DzO molecules in HzOcrystalline cubic ice and to follow the stepwise conversion of the isolated D 2 0 to coupled (HOD)2 units and, ultimately, to indiviudal isolated HOD. These two steps require primarily ion defect migration and Bjerrum orientational defect migration, respectively, and, therefore, provide a molecular-level view of the activity of the majority and minority charge carriers invoked to explain the conductivity data. The spectroscopic results are basically consistent with the views developed from the conductivity methods, but differ from or extend those views in some important aspects: (a) at 135 K the overall isotopic exchange rate for pure ice is influenced nearly equally by the ion defect and the Bjerrum defect rates, Le., there is no majority carrier, (b) the OH- ion does not participate as a proton transfer agent even in base-doped ice. Consequently,a base impurity strongly suppresses proton migration, (c) aromatic amine dopants accelerate the migration of Bjerrum defects, and (d) the minor difference found between the activation energies for proton transfer and Bjerrum defect migration (9.5 Z+ 0.7 and 12.0f 0.4 kcal/mol, respectively) suggests that there is no clear-cut majority carrier for temperatures which extend from
