A multi‐domain weighted residual method for the one‐electron Schrödinger equation: Application to H+2

Abstract

The Schrodinger equation is solved for a single electron moving in the coulombic field of some arbitrary configuration of nuclei. Space is partitioned by centering a sphere on each of the individual nuclei without any overlap or touching of the spheres, i.e., muffin‐tin spheres. All regions are treated by a weighted residual technique, which is a more general approach than the variational method. Outside the spheres, both the wavefunction and its product with the potential energy function are expanded as a linear combination of solutions taken from the modified Helmholtz equation (M.H.E.). A basis set is prepared by solving the M.H.E. repeatedly for a select set of eigenvalues and boundary conditions, using a boundary integral technique. Inside any sphere, the wavefunction is written as a linear combination of terms, each a product of a radial function and a spherical harmonic. The radial factor is written as product of an exponential and a power series. For either region, an alternate basis set is chosen...