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.

中文翻译：

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评估交换相关函数的准确固体密度。


Kohn-Sham 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研究中无处不在的关键。该理论的核心是交换相关泛函，它只能使用少数精确约束以近似形式表示。最近对这些近似值的批评是，它们旨在以牺牲密度的糟糕表示为代价来准确描述能量，这与密度泛函理论的精神背道而驰。这些结论是从原子或小分子的研究中得出的，在这些研究中可以获得确切的结果。为了阐明这个问题，我们使用三种原型固体（半导体、硅、绝缘体、氯化钠和金属、铜）的几乎精确的密度和能量来比较雅各布阶梯各个梯级的交换相关泛函的性能。通过检查它们在再现能量和密度方面的错误，我们表明几种混合体和半局部泛函表现始终如一。此外，为再现精确约束而构建的函数式往往是所有测试材料类别中表现最好的函数之一，这加强了在函数构造中使用这些约束的论点。平均而言，截至 2000 年代初发表的泛函同时改进了对密度和能量的预测。对于最近的泛函来说，情况往往并非如此，尽管能量和密度的误差继续以相关方式演变。