TUNNELING SPLITTINGS IN VIBRATIONAL-SPECTRA OF NONRIGID MOLECULES - IV - KINEMATIC COUPLINGS

The perturbative instanton approach (PIA) developed previously [Bender skii and co-workers, Chem. Phys. 219 (1997) 119; 219 (1997) 143; 234 ( 1998) 153] is generalized to multidimensional Hamiltonians in which th e potential is non-separable and the kinetic energy operator is tunnel ing coordinate dependent, i.e. both potential and kinematic couplings between the tunneling and transverse coordinates are considered. The p otential couplings uniquely define the symmetry of the kinematic coupl ings. The first-order extreme tunneling trajectory (ETT) and the semi- classical wave functions are determined, without using the Eckart-Sayv etz conditions, from the solutions of classical equations of motion an d the semi-classical Hamilton-Jacobi and transport equations. The seco nd-order effect of kinematic couplings is shown to result in the appea rance of the pseudo-potential terms in the above equations. For active transverse vibrations, kinematic couplings contribute to an action pr oportional to the products of the potential and kinematic coupling con stants. 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 ag ree well with the results of quantum calculation. (C) 1998 Elsevier Sc ience B.V. All rights reserved.