Volume 224, 2020

Improving the exchange and correlation potential in density-functional approximations through constraints

Abstract

We review and expand on our work to impose constraints on the effective Kohn–Sham (KS) potential of local and semi-local density-functional approximations. Constraining the minimisation of the approximate total energy density-functional invariably leads to an optimised effective potential (OEP) equation, the solution of which yields the KS potential. We review briefly our previous work on this and demonstrate with numerous examples that despite the well-known mathematical issues of the OEP with finite basis sets, our OEP equations are numerically robust. We demonstrate that appropriately constraining the ‘screening charge’ which corresponds to the Hartree, exchange and correlation potential not only corrects its asymptotic behaviour but also allows the exchange and correlation potential to exhibit a non-zero derivative discontinuity, a feature of the exact KS potential that is necessary for the accurate prediction of band-gaps in solids but very hard to capture with semi-local approximations.

Graphical abstract: Improving the exchange and correlation potential in density-functional approximations through constraints

Associated articles

Article information

Article type
Paper
Submitted
21 May 2020
Accepted
06 Jul 2020
First published
06 Jul 2020
This article is Open Access
Creative Commons BY license

Faraday Discuss., 2020,224, 126-144

Improving the exchange and correlation potential in density-functional approximations through constraints

T. J. Callow, B. J. Pearce, T. Pitts, Nektarios N. Lathiotakis, M. J. P. Hodgson and N. I. Gidopoulos, Faraday Discuss., 2020, 224, 126 DOI: 10.1039/D0FD00069H

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