论文标题
Lieb-oxford在库仑能量上的下限，它们对电子密度功能理论的重要性以及猜想的紧密结合
The Lieb-Oxford Lower Bounds on the Coulomb Energy, Their Importance to Electron Density Functional Theory, and a Conjectured Tight Bound on Exchange
论文作者
论文摘要
Lieb and Oxford（1981）以电子密度的局部功能的形式得出了严格的下限，在库仑排斥能的间接部分上。给定电子数n的最大下限在单调上取决于n，n->无穷大限制均与所有n结合。这些边界已显示适用于交换和交换相关能量的确切密度函数，必须近似于精确和计算高效的原子，分子和固体的效率描述。在其两电子接地态下，已得出了确切的交换能的紧密结合，并猜想适用于所有自旋 - 非极化电子接地态。其中一些和其他确切的约束已被用于构建超出局部密度近似之外的两代非经验密度函数：Perdew-Burke-Ernzerhof（PBE）广义梯度近似（GGA），以及强烈的约束和适当的范围（SCAN）META-GGGA。
Lieb and Oxford (1981) derived rigorous lower bounds, in the form of local functionals of the electron density, on the indirect part of the Coulomb repulsion energy. The greatest lower bound for a given electron number N depends monotonically upon N, and the N-> infinity limit is a bound for all N. These bounds have been shown to apply to the exact density functionals for the exchange- and exchange-correlation energies that must be approximated for an accurate and computationally efficient description of atoms, molecules, and solids. A tight bound on the exact exchange energy has been derived therefrom for two-electron ground states, and is conjectured to apply to all spin-unpolarized electronic ground states. Some of these and other exact constraints have been used to construct two generations of non-empirical density functionals beyond the local density approximation: the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the strongly constrained and appropriately normed (SCAN) meta-GGA.
