AI 中文总结
本文通过求解逆广义Kohn-Sham问题，利用高精度从头算密度获得原子和分子的精确交换-关联势与能量，发现KS与GKS关联量在强关联系统中差异显著，为GKS框架下开发下一代XC泛函提供了有力工具。
AI 中文摘要
密度泛函理论（DFT）的Kohn-Sham（KS）表述是从多电子问题到有效单电子问题的映射，该单电子问题由局域乘法势控制。广义Kohn-Sham（GKS）形式将其扩展，允许任意单电子算符——非局域、局域非乘法、局域乘法或它们的任意组合。这样做扩大了DFT中交换-关联（XC）泛函建模的范围和简便性，该泛函将复杂的多电子相互作用编码为电子密度的平均场。然而，与KS理论不同，GKS理论中XC泛函的发展因缺乏相应的精确XC势和能量而受阻。我们通过求解逆GKS问题，利用高精度的关联从头算密度，给出了原子和分子的精确XC势和能量。我们的方法在弱关联和强关联系统中均得到验证。我们进一步检验了一个常见但未经检验的假设，即KS和GKS关联势和能量相似，结果发现它们在强关联系统中差异显著。总体而言，这项工作为在DFT的GKS形式中建模下一代XC泛函提供了有力工具。
英文摘要
The Kohn-Sham (KS) formulation of density functional theory (DFT) is a map from the many-electron problem to an effective single-electron problem that is governed by a local multiplicative potential. The generalized-Kohn-Sham (GKS) formalism extends it to permit any single-electron operator---nonlocal, local non-multiplicative, local multiplicative, or any combination of them. Doing so expands the scope and ease of modeling the exchange-correlation (XC) functional in DFT, which encodes the complicated many-electron interactions into a mean-field of the electron density. However, unlike KS theory, development of XC functionals in GKS theory has been hindered by the absence of corresponding exact XC potentials and energies. We present the exact XC potentials and energies for atoms and molecules by solving the inverse GKS problem, using highly accurate correlated \textit{ab initio} densities. Our approach is validated across weakly and strongly correlated systems. We further examine a common, yet untested, assumption that KS and GKS correlation potentials and energies are similar, finding instead that they differ substantially in strongly correlated systems. Overall, this work offers a powerful tool to model next-generation of XC functionals within the GKS formalism of DFT.
Comments20 pages, 9 figures
