Exact exchange-correlation potentials from ground-state electron densities

Kanungo, Bikash; Zimmerman, Paul M.; Gavini, Vikram

doi:10.1038/s41467-019-12467-0

Cited by 79 publications

(112 citation statements)

References 51 publications

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“…To justify this choice quantitatively, we recall that we can obtain directly the Gaussian representation of the LDA grid potential using Eq. (16). As a measure to gauge the quality of defining the potential in a given basis set, we use the Coulomb energy U [ρ ga − ρ gr ] (1), where ρ ga and ρ gr are the densities arising from defining the potential in a Gaussian basis set and on the grid respectively.…”

Section: Appendix A: Choice Of Basis Set Representation For ρScrmentioning

confidence: 99%

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Density-inversion method for the Kohn–Sham potential: Role of the screening density

Callow

Lathiotakis

Gidopoulos

2020

The Journal of Chemical Physics

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We present a method to invert a given density and find the Kohn-Sham (KS) potential in Density Functional Theory (DFT) which shares that density. Our method employs the concept of screening density, which is naturally constrained by the inversion procedure and thus ensures the density being inverted leads to a smooth KS potential with correct asymptotic behaviour. We demonstrate the applicability of our method by inverting both local (LDA) and non-local (Hartree-Fock and Coupled Cluster) densities; we also show how the method can be used to mitigate the effects of self-interactions in common DFT potentials with appropriate constraints on the screening density.

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Section: Appendix A: Choice Of Basis Set Representation For ρScrmentioning

confidence: 99%

“…Often, we can compare with experiment or a higher level calculation; however, it is also valuable to know what an 'exact' KS result is. This is commonly done by inverting an accurate density to find the corresponding KS potential [10][11][12][13][14][15][16] .…”

Section: Introductionmentioning

confidence: 99%

Density-inversion method for the Kohn–Sham potential: Role of the screening density

Callow

Lathiotakis

Gidopoulos

2020

The Journal of Chemical Physics

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“…In KS theory, such development has been greatly advanced by studies of exact definitions and relations, e.g., the adiabatic connection theorem [24] and the precise distinction between exchange and correlation [10]. Furthermore, for KS theory there is a long and distinguished history of aiding such an exact analysis by examining the properties of exact potentials, obtained through the inversion of accurate reference densities, for practical systems [25][26][27][28][29][30][31][32][33][34][35][36]. To the best of our knowledge, neither analytical nor numerical analysis of this kind has been performed for GKS theory.…”

Section: Introductionmentioning

confidence: 99%

Exact Generalized Kohn-Sham Theory for Hybrid Functionals

et al. 2020

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Hybrid functionals have proven to be of immense practical value in density-functional-theory calculations. While they are often thought to be a heuristic construct, it has been established that this is in fact not the case. Here, we present a rigorous and formally exact analysis of generalized Kohn-Sham (GKS) density-functional theory of hybrid functionals, in which exact remainder exchange-correlation potentials combine with a fraction of Fock exchange to produce the correct ground-state density. First, we extend formal GKS theory by proving a generalized adiabatic connection theorem. We then use this extension to derive two different definitions for a rigorous distinction between multiplicative exchange and correlation components-one new and one previously postulated. We examine their density-scaling behavior and discuss their similarities and differences. We then present a new algorithm for obtaining exact GKS potentials by inversion of accurate reference electron densities and employ this algorithm to obtain exact potentials for simple atoms and ions. We establish that an equivalent description of the many-electron problem is indeed obtained with any arbitrary global fraction of Fock exchange, and we rationalize the Fock-fraction dependence of the computed remainder exchange-correlation potentials in terms of the new formal theory. Finally, we use the exact theoretical framework and numerical results to shed light on the exchange-correlation potential used in approximate hybrid functional calculations and to assess the consequences of different choices of fractional exchange.

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“…To do this, several inversion schemes have been proposed. [ 26–42 ] Most of them utilize optimization approaches based on the fundamental principles of DFT. [ 1,43,44 ] These approaches either minimize the noninteracting kinetic energy

T_{S} (][, ρ) = \sum_{i = 1}^{N} f_{i} (〉〈||, ϕ_{i}, - \frac{1}{2} \nabla^{2}, ϕ_{i})

of electrons with the constraint that the corresponding orbitals lead to the given density ρ 0 ( r ) [ 30,31,43 ] or maximize the functional given in Equation ) by varying the KS potential.…”

Section: Introductionmentioning

confidence: 99%

A general penalty method for density‐to‐potential inversion

Kumar

Harbola

2020

Int J of Quantum Chemistry

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A general penalty method is presented for the construction of the Kohn-Sham system for a given density through Levy's constrained search. The method uses a functional S[ρ] of one's choice. Different forms of S[ρ] are used to calculate the kinetic energy and exchange-correlation potential of atoms, jellium spheres, and the Hookium, and consistency among results obtained from them is shown for each system.

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Exact exchange-correlation potentials from ground-state electron densities

Cited by 79 publications

References 51 publications

Density-inversion method for the Kohn–Sham potential: Role of the screening density

Density-inversion method for the Kohn–Sham potential: Role of the screening density

Exact Generalized Kohn-Sham Theory for Hybrid Functionals

A general penalty method for density‐to‐potential inversion

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