Connections between variation principles at the interface of wave-function and density-functional theories

Tom J P Irons; James W Furness; Matthew S Ryley; Jan Zemen; Trygve Helgaker; Andrew M Teale

doi:10.1063/1.4985883

Connections between variation principles at the interface of wave-function and density-functional theories

J Chem Phys. 2017 Oct 7;147(13):134107. doi: 10.1063/1.4985883.

Authors

Tom J P Irons¹, James W Furness¹, Matthew S Ryley¹, Jan Zemen¹, Trygve Helgaker², Andrew M Teale¹

Affiliations

¹ School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
² Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.

PMID: 28987103
DOI: 10.1063/1.4985883

Abstract

A recently proposed variation principle [N. I. Gidopoulos, Phys. Rev. A 83, 040502(R) (2011)] for the determination of Kohn-Sham effective potentials is examined and extended to arbitrary electron-interaction strengths and to mixed states. Comparisons are drawn with Lieb's convex-conjugate functional, which allows for the determination of a potential associated with a given electron density by maximization, yielding the Kohn-Sham potential for a non-interacting system. The mathematical structure of the two functionals is shown to be intrinsically related; the variation principle put forward by Gidopoulos may be expressed in terms of the Lieb functional. The equivalence between the information obtained from the two approaches is illustrated numerically by their implementation in a common framework.