Koopmans-Compliant Spectral Functionals for Extended Systems

Abstract

Koopmans-compliant functionals have been shown to provide accurate spectral properties for molecular systems; this accuracy is driven by the generalized linearization condition imposed on each charged excitation, i.e., on changing the occupation of any orbital in the system, while accounting for screening and relaxation from all other electrons. In this work, we discuss the theoretical formulation and the practical implementation of this formalism to the case of extended systems, where a third condition, the localization of Koopmans's orbitals, proves crucial to reach seamlessly the thermodynamic limit. We illustrate the formalism by first studying one-dimensional molecular systems of increasing length. Then, we consider the band gaps of 30 paradigmatic solid-state test cases, for which accurate experimental and computational results are available. The results are found to be comparable with the state of the art in many-body perturbation theory, notably using just a functional formulation for spectral properties and the generalizedgradient approximation for the exchange and correlation functional.

Dielectric-dependent hybrid functionals for heterogeneous materials

“…The functionals PBE0 [42] and HSE [43][44][45] are among the most popular hybrid functionals used for condensed systems, and lately dielectric dependent hybrid functionals [46][47][48][49] have been increasingly used to predict structural and electronic properties of solids [46,47,[49][50][51][52][53][54][55][56][57] and liquid [58][59][60] and of several molecules [47,48,61]. Another category of orbital dependent functionals recently proposed is that of Koopmans-compliant functionals, used for both molecules and solids [62][63][64].…”

Improved band gaps and structural properties from Wannier–Fermi–Löwdin self-interaction corrections for periodic systems

“…The WFL-SIC procedure for another intermediate band gap semiconductor material, cubic boron phosphide, gives a band gap of 2.5 eV, which is within one percent of the experimental value (2.4 ev) and also outperforms the HSE result (2.13 eV). [30,5] This is a significant improvement over the PBE result of 1.2 eV, which severely underestimates the experimental benchmark. Similarly, the band gap of diamond, a wide band gap insulator, shows a significant improvement in which the PBE band gap of 4.10 eV is increased to 5.3 eV, which matches well with the experimental value of 5.47 eV.…”

“…[3] Although the Kohn-Sham formalism has been used for a variety of chemical/material systems, it suffers from several issues: the XC potential decays too fast at asymptotic internuclear distances, the total energy of the system varies nonlinearly as a function of fractional occupation numbers, the band gaps of periodic systems are underestimated, and unphysical fractional charges appear for stretched internuclear distances (to name a few). [3,4,5] There have been ongoing attempts to obtain better approximations for these XC functionals; however, the inaccuracy of all these Kohn-Sham DFT approaches can be traced to their inherent self-interaction error, which we describe further below. [6] For a one-electron hydrogen atom, the total energy should not have any contributions from electron-electron repulsions, i.e., the E H and E XC energies should exactly cancel each other: E H [ρ α ] + E XC [ρ α , 0] = 0.…”

Density-functional theory methods for electronic band structure properties of materials

“…的工作, 包括Wang等 [26] 发展的Wannier-Koopmans方 法, Ferreira等 [27] 发展的LDA+1/2方法, Marzari等 [28] 发 展的Koopmans-compliant functional方法, Zheng [35,37] , 但这组方程过于复杂, 对任何非平庸体系都 难以精确求解, 因此必须引入近似才能应用于实际体 系. 在最常用的近似中, 自能函数在时间-空间域上表 达为单体格林函数G和屏蔽库仑作用W的乘积, 即所谓 GW近似 [35] .…”