A Simple Model for Understanding Electron Correlation Methods

Abstract

We describe a simple analytic model for studying electron correlation in the ground state and certain excited states of a helium atom, and use it to exemplify some standard methods for treating correlation effects in electronic structure. The model is based on two bold approximations: the electrons are confined to the surface of a sphere, and they face hard walls when the angle between them approaches 0° or 180°. These two approximations augment each other in providing simplification, but in at least one important physical respect, they counteract each other. Specifically, the combination of the two approximations preserves the basic structure of encounters between the electrons. This renders the model capable of simulating standard methods for treating correlation, including configuration interaction and perturbation expansions, in a realistic and illuminating manner.