Molecular Schrödinger Equation. I. One-Electron Solutions

Abstract

A general form for the wavefunction of a single bound electron moving in the field of arbitrary fixed nuclei is proposed. The use of this wavefunction in the molecular Schrödinger equation results in the exact cancellation of singularities due to the electron—nuclear attractive potential. Illustrations of its application to the first few states of the hydrogen molecule—ion (H₂⁺) as well as information about accuracy and convergence rate are presented.