Perdew John P, Yang Weitao, Burke Kieron, Yang Zenghui, Gross Eberhard K U, Scheffler Matthias, Scuseria Gustavo E, Henderson Thomas M, Zhang Igor Ying, Ruzsinszky Adrienn, Peng Haowei, Sun Jianwei, Trushin Egor, Görling Andreas
Department of Physics, Temple University, Philadelphia, PA 19122;
Department of Chemistry, Temple University, Philadelphia, PA 19122.
Proc Natl Acad Sci U S A. 2017 Mar 14;114(11):2801-2806. doi: 10.1073/pnas.1621352114. Epub 2017 Mar 6.
The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density-functional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.
周期性固体的基本能隙将绝缘体与金属区分开来，并表征低能单电子激发。然而，精确乘法科恩-沙姆（KS）势的能带结构中的能隙大大低估了基本能隙，这是KS密度泛函理论的一个主要局限。在此，我们给出一个定理的简单证明：在广义KS理论（GKS）中，如果GKS势算子连续且添加一个电子或空穴时密度变化是离域的，那么扩展系统的带隙等于近似泛函的基本能隙。我们的定理解释了元广义梯度近似（meta-GGA）和杂化泛函给出的GKS带隙如何比广义梯度近似（GGA）甚至精确KS势给出的带隙更符合实际。该定理也源于早期工作。GKS单电子谱中的带边也与可测量的能量相关。氢分子线性链、固体砷化铝和固体氩给出了数值示例。
