Correcting the Charge Delocalization Error of Density Functional Theory

The
charge delocalization error, besides nondynamic correlation,
has been a major challenge to density functional theory. Contemporary functionals undershoot the dissociation
of symmetric charged dimers A2+, a simple but
stringent test, predict a spurious barrier, and improperly delocalize
charges for charged molecular clusters. We extend a functional designed
for nondynamic correlation to treat the charge delocalization error
by modifying the nondynamic correlation for parallel spins. The modified
functional eliminates those problems and reduces the multielectron
self-interaction error. Furthermore, its results are the closest to
those of CCSD­(T) in the whole range of the dissociation compared with
contemporary functionals. It correctly localizes the net positive
charge in (CH4)n+ clusters and predicts a nearly constant ionization potential as
a result. Testing of the SIE4x4 set shows that the new functional
outperforms a wide variety of functionals assessed for this set in
the literature. Overall, we show the feasibility of treating charge
delocalization together with nondynamic correlation.

电荷离域误差（charge delocalization error）与非动态相关（nondynamic correlation）一道，长期以来均为密度泛函理论（density functional theory）所面临的核心挑战之一。当前主流泛函会低估对称带电二聚体A₂⁺的解离能——这是一项简单却严苛的测试基准，还会预测出虚假能垒，且对带电分子团簇的电荷进行不合理的离域处理。我们通过修正平行自旋体系下的非动态相关项，将一款专为处理非动态相关而设计的泛函拓展至电荷离域误差的修正场景中。经修正后的泛函可消除上述所有问题，并降低多电子自相互作用误差（multielectron self-interaction error）。此外，相较于现有主流泛函，在全解离区间内，该泛函的计算结果与CCSD(T)的参考值最为接近。其可准确将净正电荷定域在(CH₄)ₙ⁺团簇中，并由此预测出近乎恒定的电离势。对SIE4x4基准测试集的测试结果表明，相较于文献中已针对该集评估的各类泛函，这款新泛函的综合表现更为优异。综上，本研究证实了同时处理电荷离域误差与非动态相关问题的可行性。