Using complex degrees of freedom in the Kohn-Sham self-interaction correction

Hofmann, Detlef W. M.; Klüpfel, Simon; Klüpfel, P.; Kümmel, Stephan

doi:10.1103/physreva.85.062514

Cited by 55 publications

(52 citation statements)

References 78 publications

(122 reference statements)

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“…3 For atoms of the first three rows of the periodic table, the FODs are connected to the hybridization of the s-p n orbitals with n= 1,2, or 3 depending upon p filling. [14] As for the case of most generalized-gradient approximations, FLOSIC as well as the versions of the PZ functional which account for unitary transformations [7,[10][11][12][13][14][33][34][35][36][37][38][39][40][41][42][43] favors integer occupied p valences over perfectly spherical atoms with fractionally occupied p valences. However, especially when starting new calculations, it is necessary to account for the fact that starting points derived from spherical potentials will always provide fractionally occupied starting orbitals in open-shell systems.…”

Section: Resultsmentioning

confidence: 99%

Full self-consistency in the Fermi-orbital self-interaction correction

2017

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The Perdew-Zunger self-interaction correction cures many common problems associated with semilocal density functionals, but suffers from a size-extensivity problem when Kohn-Sham orbitals are used in the correction. Fermi-Löwdin-orbital self-interaction correction (FLOSIC) solves the size-extensivity problem, allowing its use in periodic systems and resulting in better accuracy in finite systems. Although the previously published FLOSIC algorithm [J. Chem. Phys. 140, 121103 (2014)] appears to work well in many cases, it is not fully self-consistent. This would be particularly problematic for systems where the occupied manifold is strongly changed by the correction. In this paper we demonstrate a new algorithm for FLOSIC to achieve full self-consistency with only marginal increase of computational cost. The resulting total energies are found to be lower than previously reported non-self-consistent results.

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Section: Resultsmentioning

confidence: 99%

Full self-consistency in the Fermi-orbital self-interaction correction

2017

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“…In these cases, the variational orbitals fjφ i ig that minimize the functional are different from the eigenstates or canonical orbitals fjϕ m ig that diagonalize the orbitaldensity-dependent Hamiltonian, as discussed, e.g., in Refs. [30,31,[51][52][53][54][55]. The algorithm that we advocate to minimize these functionals consists of two nested steps [35], following the ensemble-DFT approach [56]: First, (i) a minimization is performed with respect to all unitary transformations of the orbitals (the so-called "inner loop"; this minimization enforces the Pederson condition [53,57]).…”

Section: A Linearization In Koopmans-compliant Functionalsmentioning

confidence: 99%

Koopmans-Compliant Spectral Functionals for Extended Systems

et al. 2018

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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.

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“…Self-interaction correction [22] schemes lead to a significant improvement in the interpretation of KS eigenvalues [50]. Yet, their performance for ground-state energetics is debatable [51][52][53][54][55]. Approaches that approximate directly the xc potential [56][57][58][59] yield eigenvalues that satisfactorily reproduce the experimental IP, due to modified long-range properties of the potential.…”

Section: Introductionmentioning

confidence: 99%

Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue

Kraisler

Schmidt

Kümmel

et al. 2015

The Journal of Chemical Physics

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There are several approximations to the exchange-correlation functional in density-functional theory that accurately predict total energy-related properties of many-electron systems, such as binding energies, bond lengths, and crystal structures. Other approximations are designed to describe potential-related processes, such as charge transfer and photoemission. However, the development of a functional which can serve the two purposes simultaneously is a long-standing challenge. Trying to address it, we employ in the current work the ensemble generalization procedure proposed in Phys. Rev. Lett. 110, 126403 (2013). Focusing on the prediction of the ionization potential via the highest occupied Kohn-Sham eigenvalue, we examine a variety of exchange-correlation approximations: the local spin-density approximation, semi-local generalized gradient approximations, and global and local hybrid functionals. Results for a test set of 26 diatomic molecules and single atoms are presented. We find that the aforementioned ensemble generalization systematically improves the prediction of the ionization potential, for various systems and exchange-correlation functionals, without compromising the accuracy of total energy-related properties. We specifically examine hybrid functionals. These depend on a parameter controlling the ratio of semi-local to non-local functional components. The ionization potential obtained with ensemble-generalized functionals is found to depend only weakly on the parameter value, contrary to common experience with non-generalized hybrids, thus eliminating one aspect of the so-called 'parameter dilemma' of hybrid functionals.

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Using complex degrees of freedom in the Kohn-Sham self-interaction correction

Cited by 55 publications

References 78 publications

Full self-consistency in the Fermi-orbital self-interaction correction

Full self-consistency in the Fermi-orbital self-interaction correction

Koopmans-Compliant Spectral Functionals for Extended Systems

Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue

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