A Study of the atom diatom reactive scattering problems by a quantum wave packet method in three dimensions

VI ABSTRACT Ph.D. THESIS INVESTIGATION OF THE ATOM DIATOM REACTIVE SCATTERING PROBLEM BY A QUANTUM WAVE PACKET METHOD IN THREE DIMENSIONS Niyazi BULUT Firat University Graduate School of Natural and Applied Sciences Department of Physics 2002, Page: 104 In this study, we have applied the time dependent quantum wave packet method to three dimensional reactive scattering oîO+HCl reaction including two heavy atoms. The time dependent quantum wave packet method is based on solution of the time-dependent Schrodinger equation which is an initial value problem. The time- dependent Schrodinger equation is solved by using an expansion in terms of modified complex Chebychev polinomials. The method involves the propagation of a predefined initial wave function on a potential energy surface. The initial wave function is set up in the asymptotic region in terms of reactant Jacobi coordinates. Then, it is propagated along the reactant channel towards the strong interaction region. After the wave packet is fully located into the interaction region it is then transformed to product Jacobi coordinates by Fourier interpolation technique. Thus the propagation is carried out in term of product Jacobi coordinates along the exit channel. The propagation requires repeatedly operation of the wave function with the Hamiltonian operator. The operation of the Hamiltonian operator is carried out by means of Fast Fourier Transformation (FFT) and Discrate Variable Represantation (DVR) techniques.VII As the wave function evolves some portions of it (high energy portion) cross the exit channel and reach to the asymptotic region of the product channel. These portions of the wave packet contain the quantum mechanical information which one seeks. In order to extract the quantum mechanical quantites an analysis line is set up across the exit valley. At each time step, the wave packet was analysed on this line giving a time- dependent coefficient for each quantum state. The Fourier transformation of these time dependent coefficients give the energy dependent amplitudes. The reactive scattering probabilities from an initial quantum state of HCl to final quantum states of OCl are proportional with the square modules of the ratio of the scattered amplitude to the incoming amplitude. The reaction probabilities for a broad range of collision energy are extracted from a single solution of the time dependent Schrödinger equation. Keywords: Reactive scattering, Wave packet method, Jacobi coordinates, Reaction probabilities, Potential energy surface, O+HCl