The symmetry properties of correlated wave functions

Abstract

The resolution of a correlated wave function Ψ about an orbital approximation Ψ₀ for any state of an N-electron system is discussed with particular reference to the symmetry conditions which the n-electron correlation functions of X_n must satisfy in order that Ψ have the correct symmetry properties for the state in question. It is shown how for a closed-shell state the symmetry properties of the correlation functions are determined by those of the spin-orbital products which they replace in Ψ₀, and how this is not in general true for an open-shell state. It is shown how the symmetry properties of an n-electron correlation function can always be uniquely defined by those of the (N-n)-electron spin-orbital product to which it is coupled in X_n , and the general symmetry conditions which the correlation functions must satisfy are derived.