Variational generalized Kohn-Sham approach combining the random-phase-approximation and Green's-function methods
Variational generalized Kohn-Sham approach combining the random-phase-approximation and Green's-function methods
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DOI：
10.1103/physreva.99.012518
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发表时间：
2019-01
影响因子：
2.9
通讯作者：
Vamsee K. Voora;S. Balasubramani;F. Furche
中科院分区：
文献类型：
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作者：
Vamsee K. Voora;S. Balasubramani;F. Furche
作者：Voora, Vamsee K；巴拉苏布拉马尼 (Balasubramani)、斯里·甘内什 (Sree Ganesh)；菲利普·弗什 |摘要：介绍了一种广义 Kohn-Sham (GKS) 方案，该方案相对于 GKS 单粒子密度矩阵可变地最小化随机相位近似 (RPA) 基态能量。我们引入了函数自洽（FSC）方案的概念，该方案改变单粒子Kohn-Sham（KS）势进入给定密度的显式势依赖交换相关（XC）能量泛函，并将其与轨道自洽（OSC）方案区分开来，后者改变密度或轨道、密度矩阵或生成密度的KS势。结果表明，对于显式依赖势的 XC 泛函，现有的 OSC 方案（例如优化的有效势方法）违反了密度的 Hellmann-Feynman 定理，从而在 KS 密度和近似泛函的正确 Hellmann-Feynman 密度之间产生了虚假差异。导出了功能自洽条件，该条件通过要求 XC 能量相对于固定密度下的 KS 势保持稳定来解决这种差异。我们通过 PBE KS 哈密顿量的半正则投影 (sp) 近似地强加函数自一致性。所得 GKS-spRPA 能量泛函的变分 OSC 最小化导致非局域相关势，其非对角块对应于轨道旋转梯度，而其对角块与真实频率下的 RPA 自能相关。准粒子引力波能量是 GKS-spRPA 轨道能量的一阶微扰极限；总能量的最低阶变化捕获了对 RPA 的重整化单激元激励校正。研究发现，GKS-spRPA 轨道能量比半局域密度泛函近似 (SL DFA) 或 G0W0 更准确地近似原子和分子的电离势和基本能隙，并纠正 SL DFA 对负离子的杂散行为。 GKS-spRPA 能量差均比 SL-RPA 更准确；对于共价键来说，改进是有限的，但对于弱结合系统来说，改进是显着的。 GKS-spRPA 能量最小化还消除了 Be 2 的 SL-RPA 势能曲线中的虚假最大值，并在 H 2 平衡键长的 ∼ 2.7 倍处产生单个库尔森-费歇尔点。因此，GKS-spRPA 纠正了 SL-RPA 的大多数密度驱动误差，提高了电子对守恒过程的 RPA 能量差异的准确性，并提供直观的单电子 GKS 图片，产生电离势能量和 GW 质量的间隙。
Author(s): Voora, Vamsee K; Balasubramani, Sree Ganesh; Furche, Filipp | Abstract: A generalized Kohn–Sham (GKS) scheme which variationally minimizes the random phase approximation (RPA) ground state energy with respect to the GKS one-particle density matrix is introduced. We introduce the notion of functional-selfconsistent (FSC) schemes, which vary the one- particle Kohn–Sham (KS) potential entering an explicitly potential-dependent exchange-correlation (XC) energy functional for a given density, and distinguish them from orbital-selfconsistent (OSC) schemes, which vary the density, or the orbitals, density matrix, or KS potential generating the density. It is shown that, for explicitly potential-dependent XC functionals, existing OSC schemes such as the optimized effective potential method violate the Hellmann-Feynman theorem for the density, producing a spurious discrepancy between the KS density and the correct Hellmann-Feynman density for approximate functionals. A functional selfconsistency condition is derived which resolves this discrepancy by requiring the XC energy to be stationary with respect to the KS potential at fixed density. We approximately impose functional selfconsistency by by semicanonical projection (sp) of the PBE KS Hamiltonian. Variational OSC minimization of the resulting GKS-spRPA energy functional leads to a nonlocal correlation potential whose off-diagonal blocks correspond to orbital rotation gradients, while its diagonal blocks are related to the RPA self-energy at real frequency. Quasiparticle GW energies are a first-order perturbative limit of the GKS-spRPA orbital energies; the lowest-order change of the total energy captures the renormalized singles excitation correction to RPA. GKS-spRPA orbital energies are found to approximate ionization potentials and fundamental gaps of atoms and molecules more accurately than semilocal density functional approximations (SL DFAs) or G0W0 and correct the spurious behavior of SL DFAs for negative ions. GKS-spRPA energy differences are uniformly more accurate than the SL-RPA ones; improvements are modest for covalent bonds but substantial for weakly bound systems. GKS-spRPA energy minimization also removes the spurious maximum in the SL-RPA potential energy curve of Be 2 , and produces a single Coulson-Fischer point at ∼ 2.7 times the equilibrium bond length in H 2 . GKS-spRPA thus corrects most density-driven errors of SL-RPA, enhances the accuracy of RPA energy differences for electron-pair conserving processes, and provides an intuitive one-electron GKS picture yielding ionization potentials energies and gaps of GW quality.