Tunneling splittings in vibrational spectra of non-rigid molecules: IV. Kinematic couplings

Abstract

The perturbative instanton approach (PIA) developed previously [Benderskii and co-workers, Chem. Phys. 219 (1997) 119; 219 (1997) 143; 234 (1998) 153] is generalized to multidimensional Hamiltonians in which the potential is non-separable and the kinetic energy operator is tunneling coordinate dependent, i.e. both potential and kinematic couplings between the tunneling and transverse coordinates are considered. The potential couplings uniquely define the symmetry of the kinematic couplings. The first-order extreme tunneling trajectory (ETT) and the semi-classical wave functions are determined, without using the Eckart–Sayvetz conditions, from the solutions of classical equations of motion and the semi-classical Hamilton–Jacobi and transport equations. The second-order effect of kinematic couplings is shown to result in the appearance of the pseudo-potential terms in the above equations. For active transverse vibrations, kinematic couplings contribute to an action proportional to the products of the potential and kinematic coupling constants. Analytical expressions for the ETT, the semi-classical action and the prefactor of the wave function in the vicinity to the ETT are given. For 2D potentials, tunneling splittings evaluated within PIA agree well with the results of quantum calculation.