Publication: Energy expressions for Kohn–Sham potentials and their relation to the Slater–Janak theorem

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Title	Energy expressions for Kohn–Sham potentials and their relation to the Slater–Janak theorem
Authors/Editors*	P. D. Elkind and V. N. Staroverov
Where published*	J. Chem. Phys.
How published*	Journal
Year*	2012
Volume	136
Number
Pages	124115
Publisher
Keywords
Link	http://dx.doi.org/10.1063/1.3695372
Abstract	Direct approximation of exchange-correlation potentials is a promising approach to accurate prediction of molecular response properties. However, little is known about ways of obtaining total energies from model potentials other than by using the Levy–Perdew virial relation. We introduce and explore several alternative formulas which arise as line integrals of potentials taken along density scaling and aufbau-filling paths, and which are not limited to the exchange term. The relaxed-orbital variant of the aufbau-path energy expression is shown to be closely related to the Slater–Janak theorem. Although the Levy–Perdew relation generally yields reasonable energies for all model exchange potentials, the relaxed-orbital aufbau path gives better results for those potentials that predict accurate highest-occupied orbital eigenvalues, such as the potential of Räsänen, Pittalis, and Proetto [J. Chem. Phys. 132, 044112 (2010)]. The ideas presented in this work may guide the development of new types of density-functional approximations for exchange and correlation.

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