APPLICATIONS OF A PARTIAL CLASSICAL LIMIT OF HEISENBERG'S EQUATIONS TO CHEMICAL DYNAMICS (VIBRATIONAL, PREDISSOCIATION, RELAXATION)

LAWRENCE LEE HALCOMB, Purdue University

Abstract

The principal focus of this work is applications of "hemiquantal" equations (HQE) resulting from a partial classical limit of Heisenberg's equations of motion. The HQE are intended primarily for systems for which a completely classical description is inadequate, yet a fully quantal treatment is unnecessary, and, in many cases, infeasible. The HQE are applied to: (1) vibrational predissociation of a triatomic van der Waals molecule, and (2) vibrational relaxation of a substitutional diatomic impurity in a one-dimensional lattice. The dissociation of the complex HeI(,2)(B('3)(pi)) is treated using a collinear model. The vibration of the iodine is treated classically while the relative motion of the helium is treated quantally. For this problem, the HQE consist of a partial differential equation (PDE) coupled to two ordinary differential equations (ODE's). Using the CYBER 205 supercomputer, the PDE is stepped forward using a fast Fourier transform scheme in conjunction with second-order time differencing, while the ODE's are advanced using a predictor-corrector algorithm. Excellent agreement with experiment and with previous theoretical calculations is obtained.(') In the second problem, non-Markovian relaxation is explored in an ideal prototype: a single diatomic molecule embedded in a cold, one dimensional, classically-behaving lattice. The motion of the lattice atoms is treated classically and the vibration of the diatomic is treated quantally. Here, the HQE comprise a large number (10('3)-10('4)) of coupled first-order non-linear ODE's. These ODE's are solved using a fourth-order Runge-Kutta algorithm designed specifically for the CYBER 205. The resulting population relaxation curves are examined. The first Chapter of the dissertation consists of a pedogogical treatment of a one-dimensional quantum scattering. The problem of a Gaussian wavepacket impinging on a square barrier is solved numerically using momentum eigendifferentials, which are normalized superpositions of momentum eigenkets.

Degree

Ph.D.

Subject Area

Chemistry

COinS