Improving the exchange and correlation potential in density-functional approximations through constraints.,Faraday Discussions

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Improving the exchange and correlation potential in density-functional approximations through constraints.
Faraday Discussions ( IF 3.3 ) Pub Date : 2020-07-06 , DOI: 10.1039/d0fd00069h
Timothy J Callow ₁ , Benjamin J Pearce , Tom Pitts , Nektarios N Lathiotakis , Matthew J P Hodgson , Nikitas I Gidopoulos

Affiliation

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.

中文翻译：

通过约束来提高密度泛函近似中的交换和相关势。

我们回顾并扩展我们的工作，以限制局部和半局部密度泛函近似的有效Kohn-Sham（KS）潜力。限制近似总能量密度函数的最小化始终会导致优化的有效电势（OEP）方程，该方程的解产生KS势。我们简要回顾一下我们以前在此方面的工作，并通过大量示例证明尽管存在有限基集的OEP众所周知的数学问题，但我们的OEP方程在数值上却很健壮。我们证明，适当限制与Hartree相对应的“筛选电荷”，交换和相关势不仅可以纠正其渐近行为，而且还可以使交换和相关势表现出非零的导数间断，

更新日期：2020-07-06

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