Aouina Ayoub, Borlido Pedro, Marques Miguel A L, Botti Silvana
Research Center Future Energy Materials and Systems of the University Alliance Ruhr and Interdisciplinary Centre for Advanced Materials Simulation, Ruhr University Bochum, Universitätsstraße 150, D-44801 Bochum, Germany.
Institut für Festkörpertheorie und -optik, Friedrich-Schiller-Universität Jena, D-07743 Jena, Germany.
J Chem Theory Comput. 2024 Dec 24;20(24):10852-10860. doi: 10.1021/acs.jctc.4c01042. Epub 2024 Dec 3.
The success of Kohn-Sham density functional theory in predicting electronic properties from first-principles is key to its ubiquitous presence in condensed matter research. Central to this theory is the exchange-correlation functional, which can only be written in an approximate form using a handful of exact constraints. A recent criticism of these approximations is that they are designed to give an accurate description of the energy at the expense of a poor representation of the density, which is contrary to the spirit of density functional theory. These conclusions are drawn from studies of atoms or small molecules, where exact results are available. To shed light on this issue, we use the almost exact densities and energies of three prototypical solids (a semiconductor, silicon, an insulator, sodium chloride, and a metal, copper) to compare the performance of exchange-correlation functionals from all rungs of Jacob's ladder. By examining their errors in reproducing both energy and density, we show that several hybrids and semilocal functionals perform consistently well. Furthermore, functionals built to reproduce exact constraints tend to be among the top performers for all tested material classes, strengthening the argument for using these constraints in functional construction. On average, functionals published up to the early 2000s simultaneously improve the prediction of both densities and energies. This is often not the case for more recent functionals, although errors in energy and density continue to evolve in a correlated manner.
科恩-沈密度泛函理论在从第一性原理预测电子性质方面的成功，是其在凝聚态物质研究中普遍存在的关键。该理论的核心是交换关联泛函，它只能用少数精确约束以近似形式写出。最近对这些近似的批评是，它们旨在给出能量的准确描述，却以密度表示不佳为代价，这与密度泛函理论的精神相悖。这些结论是从对原子或小分子的研究中得出的，在这些研究中有精确结果。为了阐明这个问题，我们使用三种典型固体（一种半导体，硅；一种绝缘体，氯化钠；以及一种金属，铜）几乎精确的密度和能量，来比较雅各布天梯各层级的交换关联泛函的性能。通过检查它们在再现能量和密度方面的误差，我们表明几种杂化泛函和半局域泛函表现一直良好。此外，为再现精确约束而构建的泛函往往是所有测试材料类别中表现最佳的，这加强了在泛函构建中使用这些约束的论据。平均而言，2000年代初之前发表的泛函同时改进了对密度和能量的预测。对于更新的泛函，情况通常并非如此，尽管能量和密度的误差仍以相关方式演变。
