A MULTIDOMAIN WEIGHTED RESIDUAL METHOD FOR THE ONE-ELECTRON SCHRODINGER-EQUATION - APPLICATION TO H-2(+)

The Schrodinger equation is solved for a single electron moving in the coulombic field of some arbitrary configuration of nuclei. Space is p artitioned by centering a sphere on each of the individual nuclei with out any overlap or touching of the spheres, i.e., muffin-tin spheres. All regions are treated by a weighted residual technique, which is a m ore general approach than the variational method. Outside the spheres, both the wavefunction and its product with the potential energy funct ion are expanded as a linear combination of solutions taken from the m odified Helmholtz equation (M.H.E.). A basis set is prepared by solvin g the M.H.E. repeatedly for a select set of eigenvalues and boundary c onditions, using a boundary integral technique. Inside any sphere, the wavefunction is written as a linear combination of terms, each a prod uct of a radial function and a spherical harmonic. The radial factor i s written as product of an exponential and a power series. For either region, an alternate basis set is chosen to supply the weight function s required by the weighted residual approach. Weight functions are cho sen according to their ability to provide increased efficiency and acc uracy. Only simple integrals over the sphere surfaces are involved in calculating matrix coefficients. In order to demonstrate the method, t he H-2(+) molecule is considered as a test case, with the potential en ergy function treated in full. (C) 1996 American Institute of Physics.