Mosquera Martín A, Borca Carlos H, Ratner Mark A, Schatz George C
Department of Chemistry, Northwestern University , 2145 Sheridan Road, Evanston, Illinois 60208, United States.
Department of Chemistry, Purdue University , 560 Oval Drive, West Lafayette, Indiana 47907, United States.
J Phys Chem A. 2016 Mar 10;120(9):1605-12. doi: 10.1021/acs.jpca.5b10864. Epub 2016 Mar 1.
The exchange-correlation (XC) local density approximation (LDA) is the original density functional used to investigate the electronic structure of molecules and solids within the formulation of Kohn and Sham. The LDA is fundamental for the development of density-functional approximations. In this work we consider the generalized Kohn-Sham (GKS) theory of hybrid functionals. The GKS formalism is an extension of the Kohn-Sham theory for electronic ground states and leads to a vast set of alternative density functionals, which can be estimated by the LDA and related methods. Herein we study auxiliary electronic systems with parametrized interactions and derive (i) a set of exact equations relating the GKS XC energies in the parameter space and (ii) a formal relation between the parameters and the standard XC derivative discontinuity. In view of the new results and previously reported findings, we discuss why the inclusion of Fock exchange, and its long-range-corrected form (in the ground-state calculations and in linear-response Kohn-Sham equations), dominate over the generalized gradient corrections to enhance the quality of the fundamental gap and to enhance excitation-energy estimations. As an example, we show that the adiabatic CAM-LDA0 (a functional with 1/4 global and 1/2 long-range Hartree-Fock interaction, respectively, a range separation factor of 1/3, and pure LDA exchange and correlation) works for electronic excitations as well as the adiabatic CAM-B3LYP functional.
交换关联（XC）局域密度近似（LDA）是最初用于在科恩和沙姆的理论框架内研究分子和固体电子结构的密度泛函。LDA是密度泛函近似发展的基础。在这项工作中，我们考虑混合泛函的广义科恩 - 沙姆（GKS）理论。GKS形式体系是科恩 - 沙姆电子基态理论的扩展，它产生了大量可供选择的密度泛函，这些泛函可以通过LDA及相关方法来估计。在此，我们研究具有参数化相互作用的辅助电子系统，并推导（i）一组在参数空间中关联GKS XC能量的精确方程，以及（ii）参数与标准XC导数不连续性之间的形式关系。鉴于新的结果和先前报道的发现，我们讨论了为什么在基态计算和线性响应科恩 - 沙姆方程中，包含福克交换及其长程校正形式，在增强基本能隙质量和提高激发能估计方面比广义梯度校正更具优势。例如，我们表明绝热的CAM - LDA0（一种分别具有1/4全局和1/2长程哈特里 - 福克相互作用、范围分离因子为1/3以及纯LDA交换和关联的泛函）对于电子激发的效果与绝热的CAM - B3LYP泛函相同。
