Vibrational spectra of phenol are calculated with ab initio Hartree-Fock and MP2 methods as well as with density functional theory (DFT) using the 6-31G(d,p) basis set. A clear-cut assignment of the vibrational frequencies is reported on the basis of the potential energy distribution (PED) calculated at the three theory levels. These results are compared with the previously reported ab initio data and with the experiment. Several reassignments are suggested for the phenol modes: OH bend, 9b, 17a, 8a, and 8b. It is demonstrated that the MP2/6-31G(d,p) level fails in predicting the frequencies for two modes, labeled 14 and 4 in phenol. The calculated frequency of the former is about 140 cm -1 too high, and that of the latter is 220 cm -1 too low. Very similar results at the MP2 level have been reported earlier for the corresponding ω 14 and ω 4 in benzene. The HF/6-31G(d,p) method provides incorrect results for the modes related to the OH bend in phenol. It is remarkable that DFT with the BLYP functional gives excellent agreement between the calculated and observed frequencies for phenol. In particular, the modes 4 and 14 are predicted to within 11 and 6 cm -1 , respectively, which confirms the reliability of DFT (BLYP) in reproducing vibrational frequencies.

The 13C spectra of cyclohexene oxide (1) show decoalescence of the peak at lowest frequency, with slow exchange at −187.7 °C and a coalescence temperature slightly above −178.2 °C. The low-temperature NMR results are interpreted in terms of two enantiomeric half-chair conformations, 1a and 1b, which could interconvert by way of either the endo-boat (1c) or exo-boat (1d) conformation. Ab initio calculations indicate that the endo-boat is significantly lower in energy than the exo-boat. Both boat conformations are shallow energy minima, as evidenced by the absence of imaginary frequencies. Relative free energies for the three conformations at −187.7 °C obtained from Allinger's MM3 program are in reasonable agreement with the ab initio results for 25 °C. A possible explanation for the greater stability of the endo-boat in terms of less eclipsing for the CH hydrogens of the three-membered ring with the CH2 hydrogens on the adjacent carbons is supported by calculated geometries. The experimental rate constant and free-energy barrier for interconversion of 1a and 1b were 227 s-1 and 4.3 ± 0.2 kcal/mol at −178.2 °C, and the corresponding parameters for the conversion of the half-chair to the endo-boat were 454 s-1 and 4.2 kcal/mol at this temperature. Estimates of the free energy at 25 °C of the transition state leading to the ring inversion were obtained at the HF/6-311G* and MP2/6-311G* levels by using the STQN method and were found to be 1.09 and 0.88 kcal/mol, respectively, above the local endo-boat minima. The corresponding calculated half-chair to endo-boat free-energy barriers at 25 °C were 4.87 and 4.96 kcal/mol, in reasonable agreement with the experimental value at −178.2 °C. Chemical shifts for the carbons of 1a were calculated at the HF/6-311G* and HF/6-311+G(2d,p) levels, using the GIAO method, to assign peaks to specific carbons.