The vibrational Jahn-Teller effect in E⊗e systems

The Jahn-Teller theorem is applied in the vibrational context where degenerate high-frequency vibrational states (E) are considered as adiabatic functions of low-frequency vibrational coordinates (e). For CH₃CN and Cr(C₆H₆)(CO)₃, the global minimum of the non-degenerate electronic potential energy surface occurs at the C_3v geometry, but in CH₃OH, the equilibrium geometry is far from the C_3v reference geometry. In the former cases, the computed spontaneous Jahn-Teller distortion is exceptionally small. In methanol, the vibrational Jahn-Teller interaction results in the splitting of the degenerate E-type CH stretch into what have been traditionally assigned as the distinct ν₂ and ν₉ vibrational bands. The ab initio vibrational frequencies are fit precisely by a two-state high-order Jahn-Teller Hamiltonian (Viel and Eisfeld, 2004). The presence of vibrational conical intersections, including 7 for CH₃OH, has implications for spectroscopy, for geometric phase, and for ultrafast localized non-adiabatic energy transfer.