Gedanken densities and exact constraints in density functional theory.
Gedanken densities and exact constraints in density functional theory.
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密度泛函理论中的格丹肯密度和精确约束。
DOI：
10.1063/1.4870763
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
K. Burke
中科院分区：
文献类型：
--
作者：
J. Perdew;A. Ruzsinszky;Jianwei Sun;K. Burke
对多电子基态交换相关能的精确密度泛函的近似可以通过满足普遍的约束来构造，即对所有电子密度都有效。Gedanken密度是为这种建筑的目的而设计的，但不一定是现实的。均匀的电子气体是一种古老的密度。在这里，我们提出了一个球形的双电子格丹肯密度，其中无量纲密度梯度可以是任意的正常数，只要密度不为零。在广义梯度近似（GGA）中，交换能的Lieb-Oxford下界可以通过限定其增强因子或最简单的GGA交换能密度来满足。众所周知，这个增强因子界是充分的，但我们的根丹肯密度表明它也是必要的。传统的精确交换能量密度不满足这样的局部边界，但能量密度不是唯一的，最简单的GGA交换能量密度也不是它的近似。我们进一步推导了双电子密度交换增强因子的一个强和最优收紧约束，该约束由局部密度近似满足，但被所有已发表的GGA或元GGA所违背。最后，给出了GGA或元GGA交换增强因子渐近性的非均匀密度标度性的一些结果。
Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a two-electron density, which is satisfied by the local density approximation but is violated by all published GGA's or meta-GGA's. Finally, some consequences of the non-uniform density-scaling behavior for the asymptotics of the exchange enhancement factor of a GGA or meta-GGA are given.