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.

arXiv comment26 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)

References in corpus (14)

• Optimized Effective Potentials in Finite Basis Sets
• Quantifying Density Errors in DFT
• The Importance of being consistent
• Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations
• Prediction of the derivative discontinuity in density functional theory from an electrostatic description of the exchange and correlation potential
• Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles
• How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?
• Constraining density functional approximations to yield self-interaction free potentials
• Nonanalyticity of the optimized effective potential with finite basis sets
• N-centered ensemble density-functional theory for open systems
• Density-inversion method for the Kohn-Sham potential: role of the screening density
• Performance of the Constrained Minimization of the Total Energy in Density Functional Approximations: the Electron Repulsion Density and Potential
• Optimal power series expansions of the Kohn-Sham potential
• Fundamental gaps of quantum dots on the cheap

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• Density functionals with spin-density accuracy for open shells
• Effective local potentials for density and density-matrix functional approximations with non-negative screening density
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory