Mean-Field Approach to Vibrational Energy Levels and Tunneling Dynamics in Polyatomic Systems

Abstract

Tunneling processes in the vibrational motions of polyatomic molecules, which are affected by the coupling between different modes, are studied by a mean field approximation. The method used is based on a self-consistent field (SCF) approximation in which framework each mode experiences an effective potential produced by the averaged motions of the other modes. Also, a variational principle is used to select coordinates that are optimal for the SCF approach. The method is applied to the calculation of the bending-stretching energy levels of HCN, and of the related HCN → HNC tunneling isomerization rates. An interesting feature of the results is strong decrease of the tunneling rate with increasing excitation of the HC stretching mode. Coupling between modes in HCN is essentially static, with no energy transfer occurring on the timescale of tunneling. A generalized version of the above approximation, the time-dependent self-consistent field (TDSCF) approximation is proposed for cases where energy transfer affects the tunneling process. This method is illustrated for a model problem, it is concluded that the mean- field methods are powerful quantitative tools for calculations of tunneling in systems of several interacting modes.