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

Callow, Timothy J.; Pearce, Benjamin J.; Pitts, Tom; Lathiotakis, Nektarios N.; Hodgson, Matthew J.P.; Gidopoulos, Nikitas I.

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 bandgaps in solids but very hard to capture with semi-local approximations.

Citation

Callow, T. J., Pearce, B. J., Pitts, T., Lathiotakis, N., Hodgson, M. J., & Gidopoulos, N. I. (2020). Improving the exchange and correlation potential in density-functional approximations through constraints. Faraday Discussions, 224, 126-144. https://doi.org/10.1039/d0fd00069h

• Journal Article Type: Article
• Acceptance Date: Jul 6, 2020
• Online Publication Date: Jul 6, 2020
• Publication Date: 2020
• Deposit Date: Dec 3, 2020
• Publicly Available Date: Jan 13, 2021
• Journal: Faraday Discussions
• Print ISSN: 1359-6640
• Electronic ISSN: 1364-5498
• Publisher: Royal Society of Chemistry
• Peer Reviewed: Peer Reviewed
• Volume: 224
• Pages: 126-144
• DOI: https://doi.org/10.1039/d0fd00069h
• Public URL: https://durham-repository.worktribe.com/output/1256059