Density-functional theory requires ever better exchange-correlation (xc)functionals for the ever more precise description of many-body effects onelectronic structure. Universal constraints on the xc energy are importantingredients in the construction of improved functionals. Here we investigateone such universal property of xc functionals: the Lieb-Oxford lower bound onthe exchange-correlation energy, $E_{xc}[n] \ge -C \int d^3r n^{4/3}$, where$C\leq C_{LO}=1.68$. To this end, we perform a survey of available exact ornear-exact data on xc energies of atoms, ions, molecules, solids, and somemodel Hamiltonians (the electron liquid, Hooke's atom and the Hubbard model).All physically realistic density distributions investigated are consistent withthe tighter limit $C \leq 1$. For large classes of systems one can obtainclass-specific (but not fully universal) similar bounds. The Lieb-Oxford boundwith $C_{LO}=1.68$ is a key ingredient in the construction of modern xcfunctionals, and a substantial change in the prefactor $C$ will haveconsequences for the performance of these functionals.
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机译：密度泛函理论要求更好的交换相关（xc）泛函，以更精确地描述电子结构上的多体效应。对xc能量的通用约束是构造改进功能时的重要意义。在这里，我们研究了xc泛函的这种通用性质：交换相关能量的利布-牛津下界$ E_ {xc} [n] \ ge -C \ int d ^ 3r n ^ {4/3} $，其中C \ leq C_ {LO} = 1.68 $。为此，我们对原子，离子，分子，固体和某些模型哈密顿量（电子液体，胡克原子和哈伯德模型）的xc能量的可用精确精确数据进行了调查。与更严格的限制$ C \ leq 1 $一致。对于大型类系统，可以获取特定于类（但不是完全通用）的相似范围。 Lieb-Oxford与$ C_ {LO} = 1.68 $的界线是构建现代xc功能的关键要素，并且前因子$ C $的实质性变化将对这些功能的性能产生影响。
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