The molecular orbital theory of chemical valency IX. The interaction of paired electrons in chemical bonds

Abstract

In previous parts of this series the molecular orbital theory has been developed in a way which, while dealing satisfactorily with the interaction of electrons in different orbitals, is not adequate to describe the wave theory of two paired electrons in the same orbital. This paper is an attempt to improve this part of the theory. Most of the work is restricted to the problem of two electrons in the bond of a homonuclear diatomic molecule. The method is based on expansions of the wave function and the interelectronic repulsion term of the Hamiltonian over the irreducible representations of the symmetry group. A series of coupled equations are obtained for the terms of the wave-function expansion. These exact equations form a useful background against which to examine some approximate wave functions, including the simple molecular orbital function and the electron-pair function. Some approximate calculations on the hydrogen molecule indicate that inclusion of higher terms in the wave-function expansion substantially reduces the calculated electron repulsion energy.