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

ABSTRACT

Several 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.

GRAPHICAL ABSTRACT

Keywords:

• Density-functional theory
• exchange-correlation potential
• reduced density matrices
• generalised Fock operator
• Dyson orbitals

Acknowledgments

This article is dedicated to Andreas Savin on the occasion of his 65th birthday.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Postdoctoral Fellowship Program and the Discovery Grants Program [Application No. RGPIN-2015-04814].