Evaluation of two-center, two-electron integrals

Abstract

We present a new analytic treatment of two-electron integrals over two-center integrals including correlation (interelectronic distance) explicitly in the wave function. All the integrals needed for the evaluation of the matrix elements of any diatomic two-electron molecule are obtained as analytic recursion expressions. As an application of this method in molecular physics, we calculate the value of the ground-state energy and equilibrium internuclear distance of the hydrogen molecule in the Born-Oppenheimer approximation.