LIII. The spatial correlation of electrons in atoms and molecules: I helium and similar two electron systems in their ground states

Abstract

An attempt is made hi this paper to improve the theory of two electrons of opposite spin in a field of spherical symmetry such as exists in some atoms. The method follows closely the theory of paired electrons in a chemical bond, given recently by the authors. In order to take fully into account the spatial correlation of the electrons due to their electrostatic repulsion, the wave function is expressed as a series. Each member of the series contains a function of the radial distances of the electrons multiplied by a Legendre function of the angle which the electrons subtend at the nucleus. It is then found possible to obtain a series of coupled equations for the radial functions in which the angular coordinate does not appear. The exact theory is used to examine some approximate expressions which have been used for the wave functions of the helium atom. Spatial correlation may occur in two ways. It may be of the ‘in-out’ type, one electron tending to be outside the other, or it may be of the angular type, the two electrons tending to be on opposite sides of the nucleus. The spatial correlation of the electrons in helitml in its ground state is examined from this point of view.