Heyd Jochen, Peralta Juan E, Scuseria Gustavo E, Martin Richard L
Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA.
J Chem Phys. 2005 Nov 1;123(17):174101. doi: 10.1063/1.2085170.
This work assesses the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional for the prediction of lattice constants and band gaps using a set of 40 simple and binary semiconductors. An extensive analysis of both basis set and relativistic effects is given. Results are compared with established pure density functionals. For lattice constants, HSE outperforms local spin-density approximation (LSDA) with a mean absolute error (MAE) of 0.037 A for HSE vs 0.047 A for LSDA. For this specific test set, all pure functionals tested produce MAEs for band gaps of 1.0-1.3 eV, consistent with the very well-known fact that pure functionals severely underestimate this property. On the other hand, HSE yields a MAE smaller than 0.3 eV. Importantly, HSE correctly predicts semiconducting behavior in systems where pure functionals erroneously predict a metal, such as, for instance, Ge. The short-range nature of the exchange integrals involved in HSE calculations makes their computation notably faster than regular hybrid functionals. The current results, paired with earlier work, suggest that HSE is a fast and accurate alternative to established density functionals, especially for solid state calculations.
本工作使用一组40种简单和二元半导体评估了Heyd-Scuseria-Ernzerhof（HSE）筛选的库仑混合密度泛函对晶格常数和带隙的预测能力。给出了对基组和相对论效应的广泛分析。将结果与已有的纯密度泛函进行了比较。对于晶格常数，HSE的表现优于局域自旋密度近似（LSDA），HSE的平均绝对误差（MAE）为0.037 Å，而LSDA为0.047 Å。对于这个特定的测试集，所有测试的纯泛函对带隙的MAE为1.0 - 1.3 eV，这与众所周知的事实一致，即纯泛函会严重低估这一性质。另一方面，HSE的MAE小于0.3 eV。重要的是，HSE能正确预测纯泛函错误预测为金属的系统中的半导体行为，例如锗。HSE计算中涉及的交换积分的短程性质使得其计算速度明显快于常规混合泛函。当前结果与早期工作相结合，表明HSE是已有的密度泛函的一种快速且准确的替代方法，特别是对于固态计算。
