Institute of Materials Chemistry, Vienna University of Technology, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria.
J Phys Condens Matter. 2013 Oct 30;25(43):435503. doi: 10.1088/0953-8984/25/43/435503. Epub 2013 Oct 9.
(Screened) hybrid functionals are being used more and more for solid-state calculations. Usually the fraction α of Hartree-Fock exchange is kept fixed during the calculation; however, there is no single (universal) value for α which systematically leads to satisfying accuracy. Instead, one could use a property of the system under consideration to determine α, and in this way the functional would be more flexible and potentially more accurate. Recently, it was proposed to use the static dielectric constant ε for the calculation of α (Shimazaki and Asai 2008 Chem. Phys. Lett. 466 91 and Marques et al 2011 Phys. Rev. B 83 035119). We explore this idea further and propose a scheme where the connection between ε and α is optimized based on experimental band gaps. ε, and thus α, is recalculated at each iteration of the self-consistent procedure. We present results for the bandgap and lattice constant of various semiconductors and insulators with this procedure. In addition, we show that this approach can also be combined with a non-self-consistent hybrid approximation to speed up the calculations considerably, while retaining an excellent accuracy in most cases.
（筛选后）混合泛函在固态计算中被越来越多地使用。通常在计算过程中保持 Hartree-Fock 交换的分数α固定；然而，没有一个单一的（通用）α值可以系统地导致令人满意的准确性。相反，可以使用所考虑系统的特性来确定α，这样泛函将更加灵活，并且潜在地更加准确。最近，有人提议使用静态介电常数ε来计算α（Shimazaki 和 Asai，2008 年，Chem. Phys. Lett. 466, 91 和 Marques 等人，2011 年，Phys. Rev. B 83, 035119）。我们进一步探讨了这个想法，并提出了一种方案，根据实验能带隙优化ε和α之间的关系。在自洽过程的每次迭代中，都会重新计算ε，从而也会重新计算α。我们用这种方法给出了各种半导体和绝缘体的能带隙和晶格常数的结果。此外，我们还表明，这种方法也可以与非自洽混合近似相结合，大大加快计算速度，而在大多数情况下保持极高的准确性。
