One-Center Perturbation Approach to Molecular Electronic Energies. III. One-Electron Systems

Abstract

A previously formulated one-center perturbation treatment for electronic wavefunctions and energies is applied to the off-center hydrogen atom, the hydrogen-molecule ion, and the HeH++ ion. Two variants of the method are employed to obtain energies up to the second order. In the first, Scheme A, in order to make use of the identity (−12Δ−ζ/r) exp (−ζr)=(−12ζ2) exp (−ζr) for an arbitrary value of ζ, we take exp (—ζr) as the zero-order function with ζ chosen to minimize the expectation value of the total electronic Hamiltonian. In the second, Scheme B, we adopt as zero-order function an accurate analytical approximation to the eigenfunction of the spherical part of the Hamiltonian. Results are tabulated for several one-electron systems. For the electronic energy of H2+ ion at its equilibrium internuclear separation, we obtain −1.07975 and −1.08999 a.u. by Schemes A and B, the exact value being −1.10263 a.u.