Effects of vibrational excitation on multidimensional tunneling: General study and proton tunneling in tropolone

Tunneling energy splittings of vibrationally excited states are calculated quantum mechanically using several models of two‐dimensional symmetric double well potentials. Various effects of vibrational excitation on tunneling are found to appear, depending on the topography of potential energy surface; the symmetry of the mode coupling plays an essential role. Especially, oscillation of tunneling splitting with respect to vibrational quantum number can occur and is interpreted by a clear physical picture based on the semiclassical theory formulated recently [Takada and Nakamura, J. Chem. Phys. 100, 98 (1994)]. The mixed tunneling in the C region found there allows the wave functions to have nodal lines in classically inaccessible region and can cause the suppression of the tunneling. The above analysis is followed by the interpretation of recent experiments of proton tunneling in tropolone. Ab initio molecular orbital calculations are carried out for the electronically ground state. A simple three‐dimensional model potential is constructed and employed to analyze the proton tunneling dynamics. Some of the experimentally observed intriguing features can be explained by the typical mechanisms discussed above.