Paier J, Marsman M, Hummer K, Kresse G, Gerber I C, Angyán J G
Institut für Materialphysik, Universität Wien and Center for Computational Material Science, Sensengasse 8, A-1090, Wien, Austria.
J Chem Phys. 2006 Apr 21;124(15):154709. doi: 10.1063/1.2187006.
Hybrid Fock exchange/density functional theory functionals have shown to be very successful in describing a wide range of molecular properties. For periodic systems, however, the long-range nature of the Fock exchange interaction and the resultant large computational requirements present a major drawback. This is especially true for metallic systems, which require a dense Brillouin zone sampling. Recently, a new hybrid functional [HSE03, J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)] that addresses this problem within the context of methods that evaluate the Fock exchange in real space was introduced. We discuss the advantages the HSE03 functional brings to methods that rely on a reciprocal space description of the Fock exchange interaction, e.g., all methods that use plane wave basis sets. Furthermore, we present a detailed comparison of the performance of the HSE03 and PBE0 functionals for a set of archetypical solid state systems by calculating lattice parameters, bulk moduli, heats of formation, and band gaps. The results indicate that the hybrid functionals indeed often improve the description of these properties, but in several cases the results are not yet on par with standard gradient corrected functionals. This concerns in particular metallic systems for which the bandwidth and exchange splitting are seriously overestimated.
杂化福克交换/密度泛函理论泛函在描述广泛的分子性质方面已被证明非常成功。然而，对于周期性体系，福克交换相互作用的长程性质以及由此产生的巨大计算需求是一个主要缺点。对于需要密集布里渊区采样的金属体系来说尤其如此。最近，一种新的杂化泛函[HSE03，J. 海德、G. E. 斯库西亚和M. 恩策尔霍夫，《化学物理杂志》118, 8207 (2003)]被引入，它在实空间中评估福克交换的方法框架内解决了这个问题。我们讨论了HSE03泛函给依赖于福克交换相互作用倒易空间描述的方法（例如所有使用平面波基组的方法）带来的优势。此外，我们通过计算晶格参数、体模量、生成热和带隙，对一组典型固态体系的HSE03和PBE0泛函的性能进行了详细比较。结果表明，杂化泛函确实常常改善了对这些性质的描述，但在某些情况下，结果还未与标准梯度校正泛函相当。这尤其涉及金属体系，其带宽和交换分裂被严重高估。
