Exact one-electron method tested by means of H+2 eigenvalue problem

Abstract

A method assigned to solve exactly the Schrodinger equation with a non-muffin-tin molecular potential is numerically tested. The general equations derived recently by Gegusin (1991) are adapted for diatomic molecules with symmetries Cinfinity v and Dinfinity h. Owing to cylindrical symmetry all the integrations needed are reduced to one-dimensional quadratures. The method is verified by computations of H+2 eigenenergies. The bound states with symmetries sigma g, sigma u, pi g and pi u are studied. Two values of internuclear separation, R=1 au and R=2 au, are tried. The calculated energy eigenvalues are numerically shown to approach the exact ones.