The calculation of transition probabilities and cross sections for three-dimensional nonreactive scattering of C(1D1)+H2

In this study, quantum wave packet method based on the solution of the time-dependentSchrödinger equation was applied to three dimensional C (1D ) + H 2 (ν , j ) → C (1D ) + H 2 (ν ı , j ı )inelastic scattering.In section 1, quantum reaction dynamics has been discussed in general and recent worksdone have been summarized. In section 2, some basic concepts related to reaction kinetics have beendiscussed. In section 3, quantum time-independent and time-dependent equations of motion have beenderived and the methods for the solution of the time-dependent Schrödinger equation have beenexplained in details. In section 4, three dimensional quantum mechanical equations of motion forA+BC(v,j) inelastic scattering have been derived and from the solutions of these equations, theexpressions for the state-to-state inelastic transition probabilities have been obtained. In sections 5 and6, the time-dependent quantum wave packet method has been applied to C+H2(v,j) inelastic scatteringproblem and the results obtained have been discussed.In this study, the Schrödinger equation has been solved in terms of complex Chebychevpolynomials as proposed by Kosloff. The operation of the Hamiltonian operator on the wave functionhas been performed by Fourier Transformation and Discrete Variable Representation techniques. TheFourier Grid analysis method has been used to analyze the final wave function and extract thetransition probabilities from it. The partial cross sections for J>0 have been estimated by J-Shiftingmethod. The integral cross sections have been calculated by summing the partial cross sections overall J states and the thermal rate constants were calculated by Boltzmann averaging of the integral crosssections over all energies.Keywords: Inelastic Scattering, Hamiltonian Operation, Cross Sections.