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. In this work, we relax a previously imposed positivity constraint, which increased the computational cost and we find that it is safe to do so, except in systems with very few electrons. The constrained minimisation leads invariably to the solution of an optimised effective potential (OEP) equation in order to determine the KS potential. We review briefly our previous work on this problem and demonstrate with numerous examples that despite well-known mathematical issues of the OEP with finite basis sets, our OEP equations are well behaved. We demonstrate that constraining the screening charge of the Hartree, exchange and correlation potential not only corrects its asymptotic behaviour but also allows the exchange and correlation potential to exhibit nonzero 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.
Cite
@article{arxiv.2005.10562,
title = {Improving the exchange and correlation potential in density functional approximations through constraints},
author = {Timothy J. Callow and Benjamin J. Pearce and Tom Pitts and Nektarios N. Lathiotakis and Matthew J. P. Hodgson and Nikitas I. Gidopoulos},
journal= {arXiv preprint arXiv:2005.10562},
year = {2021}
}
Comments
26 pages, 11 figures. Accepted to Faraday Discussions 06 July 2020; open access. The article is part of the themed collection: New horizons in density functional theory. V3 is the accepted manuscript (after 12 month embargo period)