Investigation of exchange-correlation potentials in ensemble density functional theory: parameter fitting and excitation energy

Paragi, Gábor; Gyémánt, I.; VanDoren, V.E.

doi:10.1016/s0166-1280(01)00561-9

Cited by 13 publications

(11 citation statements)

References 17 publications

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“…We believe that it is partly due to the lack of accurate approximations for GOK-DFT. In particular, to the best of our knowledge, although several attempts have been made, 82,83 an explicitly weight-dependent density-functional approximation for ensembles (eDFA) has never been developed for atoms and molecules from first principles. The present contribution paves the way towards this goal.…”

Section: Introductionmentioning

confidence: 99%

Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems

Marut,

Senjean,

Fromager

et al. 2020

Preprint

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Gross-Oliveira-Kohn (GOK) ensemble density-functional theory (GOK-DFT) is a time-independent extension of density-functional theory (DFT) which allows to compute excited-state energies via the derivatives of the ensemble energy with respect to the ensemble weights. Contrary to the time-dependent version of DFT (TD-DFT), double excitations can be easily computed within GOK-DFT. However, to take full advantage of this formalism, one must have access to a weight-dependent exchange-correlation functional in order to model the infamous ensemble derivative contribution to the excitation energies. In the present article, we discuss the construction of first-rung (i.e., local) weightdependent exchange-correlation density-functional approximations for two-electron atomic and molecular systems (He and H 2 ) specifically designed for the computation of double excitations within GOK-DFT. In the spirit of optimally-tuned range-separated hybrid functionals, a two-step system-dependent procedure is proposed to obtain accurate energies associated with double excitations.

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Section: Introductionmentioning

confidence: 99%

Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems

Marut,

Senjean,

Fromager

et al. 2020

Preprint

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“…The GOK principle provided a basis 062501-1 1050-2947/2013/87(6)/062501 (11) ©2013 American Physical Society for the ensemble DFT method [7,8] and its variants which employ the optimized effective potential (exchange only) [9][10][11]. Despite the substantial theoretical investigations of the ensemble variational theories, the practical implementations of the method have been rather scarce and limited to the calculation of excitation energies of atoms and small molecules at equilibrium geometries [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Calculation of electronic excited states of molecules using the Helmholtz free-energy minimum principle

2013

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“…According to Eqs. (24) and (25), the ensemble exchange-correlation energy can be expanded through second order in w as follows,…”

Section: Generalized Adiabatic Connection For Ensemblesmentioning

confidence: 99%

“…(40). For the purpose of constructing ensemble DFAs from regular ground-state DFAs, as proposed by Nagy [36] and Paragi et al [24,25], Eqs. (41) and (42) should be taken in the w = 0 limit.…”

Section: Exact Ensemble and Excitation Energiesmentioning

confidence: 99%

Generalised adiabatic connection in ensemble density-functional theory for excited states: example of the H₂ molecule

Franck

Fromager

2013

Molecular Physics

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A generalized adiabatic connection for ensembles (GACE) is presented. In contrast to the traditional adiabatic connection formulation, both ensemble weights and interaction strength can vary along a GACE path while the ensemble density is held fixed. The theory is presented for non-degenerate two-state ensembles but it can in principle be extended to any ensemble of fractionally occupied excited states. Within such a formalism an exact expression for the ensemble exchange-correlation density-functional energy, in terms of the conventional ground-state exchange-correlation energy, is obtained by integration over the ensemble weight. Stringent constraints on the functional are thus obtained when expanding the ensemble exchange-correlation energy through second order in the ensemble weight. For illustration purposes, the analytical derivation of the GACE is presented for the H 2 model system in a minimal basis, leading thus to a simple density-functional approximation to the ensemble exchange-correlation energy. Encouraging results were obtained with this approximation for the description in a large basis of the first 1 Σ + g excitation in H 2 upon bond stretching. Finally, a range-dependent GACE has been derived, providing thus a pathway to the development of a rigorous state-average multi-determinant density-functional theory.

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Investigation of exchange-correlation potentials in ensemble density functional theory: parameter fitting and excitation energy

Cited by 13 publications

References 17 publications

Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems

Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems

Calculation of electronic excited states of molecules using the Helmholtz free-energy minimum principle

Generalised adiabatic connection in ensemble density-functional theory for excited states: example of the H₂ molecule

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Investigation of exchange-correlation potentials in ensemble density functional theory: parameter fitting and excitation energy

Cited by 13 publications

References 17 publications

Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems

Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems

Calculation of electronic excited states of molecules using the Helmholtz free-energy minimum principle

Generalised adiabatic connection in ensemble density-functional theory for excited states: example of the H2 molecule

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Product

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Generalised adiabatic connection in ensemble density-functional theory for excited states: example of the H₂ molecule