Csonka Gábor I, Vydrov Oleg A, Scuseria Gustavo E, Ruzsinszky Adrienn, Perdew John P
Department of Chemistry, Budapest University of Technology and Economics, H-1521 Budapest, Hungary.
J Chem Phys. 2007 Jun 28;126(24):244107. doi: 10.1063/1.2743985.
The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for the exchange-correlation energy functional has two nonempirical constructions, based on satisfaction of universal exact constraints on the hole density or on the energy. We show here that, by identifying one possible free parameter in exchange and a second in correlation, we can continue to satisfy these constraints while diminishing the gradient dependence almost to zero (i.e., almost recovering the local spin density approximation or LSDA). This points out the important role played by the Perdew-Wang 1991 nonempirical hole construction in shaping PBE and later constructions. Only the undiminished PBE is good for atoms and molecules, for reasons we present, but a somewhat diminished PBE could be useful for solids; in particular, the surface energies of solids could be improved. Even for atoms and molecules, a strongly diminished PBE works well when combined with a scaled-down self-interaction correction (although perhaps not significantly better than LSDA). This shows that the undiminished gradient dependence of PBE and related functionals works somewhat like a scaled-down self-interaction correction to LSDA.
用于交换关联能泛函的佩德韦-伯克-恩泽尔霍夫（PBE）广义梯度近似有两种非经验构造，分别基于对空穴密度或能量的普遍精确约束的满足情况。我们在此表明，通过确定交换项中的一个可能的自由参数和关联项中的另一个自由参数，我们可以在几乎将梯度依赖性降至零（即几乎恢复局域自旋密度近似或LSDA）的同时继续满足这些约束。这指出了佩德韦-王1991年的非经验空穴构造在塑造PBE及后续构造中所起的重要作用。如我们所阐述的原因，只有未减弱的PBE对原子和分子是适用的，但某种程度上减弱的PBE对固体可能有用；特别是，固体的表面能可能会得到改善。即使对于原子和分子，当与按比例缩小的自相互作用校正相结合时，大幅减弱后的PBE也能很好地发挥作用（尽管可能并不比LSDA明显更好）。这表明PBE及相关泛函未减弱的梯度依赖性在某种程度上类似于对LSDA的按比例缩小的自相互作用校正。
