Consequences of extending 1-matrix energy functionals from pure–state representable to all ensemble representable 1 matrices

Valone, Steven M.

doi:10.1063/1.440249

Cited by 230 publications

(130 citation statements)

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“…The exchange-correlation functional collects the errors made in the approximations of the kinetic energy and of the interactions between electrons by respectively the first and third terms of the Kohn-Sham functional. It follows from the Hohenberg-Kohn theorem [20,26,28,33], that there exists an exact exchange-correlation functional, that is a functional of the electronic density ρ for which solving (1.4) provides the ground state electronic energy and density of the N -body electronic Schrödinger equation. Unfortunately, no mathematical expression of the exchange-correlation functional amenable to numerical simulations is known.…”

Section: Rapide Notementioning

confidence: 99%

Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models

Cancès¹,

Chakir

Maday

2011

ESAIM: M2AN

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Abstract.In this article, we provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the electronic density, and allows for a comprehensive analysis. This is not the case for the Kohn-Sham LDA model, for which the uniqueness of the ground state electronic density is not guaranteed. We prove that, for any local minimizer Φ 0 of the Kohn-Sham LDA model, and under a coercivity assumption ensuring the local uniqueness of this minimizer up to unitary transform, the discretized Kohn-Sham LDA problem has a minimizer in the vicinity of Φ 0 for large enough energy cut-offs, and that this minimizer is unique up to unitary transform. We then derive optimal a priori error estimates for the spectral discretization method.Mathematics Subject Classification. 65N25, 65N35, 65T99, 35P30, 35Q40, 81Q05.

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Section: Rapide Notementioning

confidence: 99%

Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models

Cancès¹,

Chakir

Maday

2011

ESAIM: M2AN

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“…Third, the typical situation is that there are many wavefuctions and many electron densities that are consistent with a particular q. To define a unique energy from among the possible choices, we adhere to constrained search density functional theory (CS-DFT) 41,53 rather than appealing to a maximum entropy principle.…”

Section: 1933mentioning

confidence: 99%

“…Rigorously speaking, it should be optimal in the sense of Levy CS-DFT. 41,53 The constraint is that Γ * A should yield the lowest energy for all other ensemble density matrices which integrate to ρ * A :…”

Section: Definition Of Pseudo-atom Energiesmentioning

confidence: 99%

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An empirical charge transfer potential with correct dissociation limits

Valone

Atlas

2004

The Journal of Chemical Physics

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The empirical valence bond (EVB) method [J. Chem. Phys. 52, 1262Phys. 52, (1970] has always embodied charge transfer processes. The mechanism of that behavior is examined here and recast for use as a new empirical potential energy surface for large-scale simulations. A two-state model is explored. The main features of the model are: (1) Explicit decomposition of the total system electron density is invoked; (2) The charge is defined through the density decomposition into constituent contributions; (3) The charge transfer behavior is controlled through the resonance energy matrix elements which cannot be ignored; and (4) A reference-state approach, similar in spirit to the EVB method, is used to define the resonance state energy contributions in terms of "knowable" quantities. With equal validity, the new potential energy can be expressed as a nonthermal ensemble average with a nonlinear but analytical charge dependence in the occupation number. Dissociation to neutral species for a gas-phase process is preserved. A variant of constrained search density functional theory is advocated as the preferred way to define an energy for a given charge.PACS numbers: 71.15.-m, 34.70.+e, 34.20.-b, 31.15.-p

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“…Blöchl et al [9] have proposed such a hybrid approach with the help of reduced density-matrix functional theory (RDMFT, [10][11][12][13]). RDMFT uses the one-particle reduced density matrix (1-RDM) as a natural variable and thus emphasizes orbital occupations.…”

Section: Introductionmentioning

confidence: 99%

Reduced density-matrix functionals from many-particle theory

Schade

Kamil

Blöchl

2017

Eur. Phys. J. Spec. Top.

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Abstract. In materials with strong electron correlation the proper treatment of local atomic physics described by orbital occupations is crucial. Reduced density-matrix functional theory is a natural extension of density functional theory for systems that are dominated by orbital physics. We review the current state of reduced density-matrix functional theory (RDMFT). For atomic structure relaxations or abinitio molecular dynamics the combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) possesses a number of disadvantages, like the cumbersome evaluation of forces. We therefore describe a method, DFT+RDMFT, that combines many-particle effects based on reduced density-matrix functional theory with a density functional-like framework. A recent development is the construction of density-matrix functionals directly from many-particle theory such as methods from quantum chemistry or many-particle Green's functions. We present the underlying exact theorems and describe current progress towards quantitative functionals.

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Consequences of extending 1-matrix energy functionals from pure–state representable to all ensemble representable 1 matrices

Abstract: Erratum: "Explicit pure-state density operator structure for quantum tomography" [

Cited by 230 publications

References 7 publications

Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models

Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models

An empirical charge transfer potential with correct dissociation limits

Reduced density-matrix functionals from many-particle theory

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