Single-Center Wave Function for the Hydrogen Molecule

Abstract

The ground state of the hydrogen molecule is studied using an expansion based on a single center, the molecular midpoint, with basis orbitals constructed from associated Laguerre functions with a single orbital exponent. The convergence of the expansion is studied by systematic addition of terms and is found to be slow. The best wave functions attained have energies of —1.15086 (38 axially symmetric terms), and —1.16141 (44 terms). The results are shown to be very similar to those obtained by using Slater orbitals with nonintegral principal quantum number both from the energy increments observed and from a natural spin orbital occupation number analysis. It is concluded that the slow convergence probably results from failure to represent adequately the singularities at the nuclei, and that further use of single-center expansions in diatomic problems (except at very small internuclear distances) seems unprofitable, irrespective of what set of orbitals is used as a basis.