A three dimensional quantum mechanical theory to treat tetra-atom reactions: State-to-state cross sections for the H2+OH→H2O+H process

Abstract

A quantum mechanical approach to treat diatom–diatom exchange processes of the type AB+CD→ABC+D is presented. The approach is based on three types of wave functions ψ0ν, ψ0λ, and χ, where the first two are (asymptotic) elastic distorted wave functions for the two arrangement channels ν and λ, and χ is a short range (square integrable) wave function describing the system in the close interaction region. The functions ψ0ν and ψ0λ are presented within the jz approximation, and to calculate χ, a perturbative-type Schrödinger equation which contains negative imaginary potentials (to form absorbing boundary conditions) is solved. The variationally stable solution is obtained employing Gaussians and local adiabatic basis sets. The actual calculation of χ is done employing the quasibreathing sphere model, where the relevant angular coordinates are selected randomly (about 50 sets like that were used) employing a Monte Carlo approach. With this approach, most detailed state-to-state cross sections were calculated for the reaction H2(n1=0, j1=0)+OH(n2=0, j2=0)→H2O(vj̄vKΩK)+H, where (vj̄v) are the usual vibrational-bending states of the water molecule, and K and ΩK are, respectively, the overall rotational quantum number and the corresponding magnetic component. The results were compared with those due to other treatments and with experiment.