Large-Scale Benchmark of Exchange–Correlation Functionals for the Determination of Electronic Band Gaps of Solids

We compile a large data set designed for the efficient benchmarking of exchange–correlation functionals for the calculation of electronic band gaps. The data set comprises information on the experimental structure and band gap of 472 nonmagnetic materials and includes a diverse group of covalent-, ionic-, and van der Waals-bonded solids. We used it to benchmark 12 functionals, ranging from standard local and semilocal functionals, passing through meta-generalized-gradient approximations, and several hybrids. We included both general purpose functionals, like the Perdew–Burke–Ernzerhof approximation, and functionals specifically crafted for the determination of band gaps. The comparison of experimental and theoretical band gaps shows that the modified Becke–Johnson is at the moment the best available density functional, closely followed by the Heyd–Scuseria–Ernzerhof screened hybrid from 2006 and the high-local-exchange generalized-gradient approximation.本研究构建了一套大型数据集，专为电子能带隙（electronic band gaps）计算所用的交换-关联泛函（exchange–correlation functionals）的高效基准测试而开发。该数据集涵盖472种非磁性材料的实验晶体结构与能带隙信息，包含共价键合、离子键合以及范德华键合的多种类型固体材料。我们利用该数据集对12种泛函开展基准测试，测试范围覆盖标准局域泛函、半局域泛函，直至meta广义梯度近似（meta-generalized-gradient approximations）以及多款杂化泛函。测试所用的泛函既包含通用型泛函（如Perdew–Burke–Ernzerhof近似），也包含专为能带隙计算专门设计的专用泛函。通过对比实验与理论能带隙结果可知，修正Becke–Johnson泛函是当前性能最优的密度泛函（density functional），紧随其后的是2006年提出的Heyd–Scuseria–Ernzerhof屏蔽型杂化泛函，以及高局域交换广义梯度近似泛函。