QUANTUM MECHANICAL AND SEMICLASSICAL APPROACH TO MOLECULAR DYNAMICS

Several new quantum and semiclassical mechanical methods are proposed and tested by applying to a variety of problems in molecular dynamics.; A new multichannel exchange kernel formalism for reactive scattering is introduced. The central feature of the method is the expansion of the reactive scattering wavefunction in terms of the non-reactive coupled-channel scattering waves in all of the arrangements. The exact S matrix is found from the non-reactive coupled-channel scattering calculations in each arrangements. A approximate version of formula is obtained by virtue of the distorted wave Born approximation (DWBA) where the non-reactive coupled-channel scattering wavefunction is utilized for distorted waves. Application to a standard test problem (collinear H + H(,2)) shows that multichannel DWBA is extremely accurate if the reaction probability is no larger than 0.1 and if (TURN) 3 to 4 vibrational states are included in the non-reactive coupled-channel expansion, and that the full exact calculation is stable, accurate and easy to implement.; Semiclassical perturbation theory combined with two approximate models for polyatomic Hamiltonian--the reaction path model and the kinetic coupling model--leads to extremely simple, analytical formulae for S-matrix and the spectra of overtone. The numerical tests indicate that these simple approximate methods are of useful accuracy.; A new semiclassical approach is proposed. In this approach the evolution of the states of a system, which are parameterized by label variables, is determined by calculating the time development of the label variables classically. The formalism for calculating the S-matrix within this framework is developed. Sample calculations show that this method is very simple and describes quantum phenomena very well.