Exact expressions for the Kohn–Sham exchange-correlation potential in terms of wave-function-based quantities

Abstract

ABSTRACTSeveral workers have deduced various exact expressions for the Kohn–Sham exchange-correlation potential in terms of quantities computable from the interacting and noninteracting wave functions of the system. We show that all these expressions can be obtained by one general method in which the interacting N-electron wave function is expanded in products of one- and (N − 1)-electron functions. Different expressions correspond to different choices of the latter functions. Our analysis unifies and clarifies the previously proposed exact treatments of the exchange-correlation potential, and suggests new ways of expressing this quantity.