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We review and expand on our work to impose constraints on the effective KohnSham (KS) potential of local and semi-local density functional approximations.In this work, we relax a previously imposed positivity constraint, whichincreased the computational cost and we find that it is safe to do so, exceptin systems with very few electrons. The constrained minimisation leadsinvariably to the solution of an optimised effective potential (OEP) equationin order to determine the KS potential. We review briefly our previous work onthis problem and demonstrate with numerous examples that despite well-knownmathematical issues of the OEP with finite basis sets, our OEP equations arewell behaved. We demonstrate that constraining the screening charge of theHartree, exchange and correlation potential not only corrects its asymptoticbehaviour but also allows the exchange and correlation potential to exhibitnonzero derivative discontinuity, a feature of the exact KS potential that isnecessary for the accurate prediction of band-gaps in solids but very hard tocapture with semi-local approximations.

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