Tunneling splitting in vibrational spectra of non-rigid molecules. II. Excited states Original Research Article

The perturbative instanton approach (PIA), developed previously [1], is used to evaluate tunneling splittings of excited vibrational levels in multidimensional double well potential surfaces. Solutions of the two-dimensional semi-classical equations of motion are expanded into a perturbative series of the parameter C/ω (< 1), where C is the coupling constant between the tunneling coordinate and the coordinate of a transverse mode with frequency ω. Semi-classical action, found from the Hamilton-Jacobi equation, is shown to have a minimum on the zero energy extreme tunneling trajectory, defined by the classical equations of motion in the inverted potential. Prefactors of semi-classical wave functions of excited vibrational states are derived from the first order solution of the transport equation. Coupling between longitudinal and transverse vibrations leads to a mixing of their excited states. Even if the coupling parameter is as small as ≈10−2, resonant mixing increassesthe tunneling splitting in the transverse ladder by several orders of magnitude as compared to the ground state. The generalized Lifshitz-Herring formula, taking into account this mixing, is presented. At Fermi resonances, the tunneling splittings become equal for both states. Possibilites of experimental observations of these resonances in Raman spectra of matrix isolated non-rigid molecules are discussed briefly.