Deriving density-matrix functionals for excited states

Liebert, Julia; Schilling, Christian

doi:10.21468/scipostphys.14.5.120

Cited by 7 publications

(2 citation statements)

References 61 publications

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“…Alternatively, a time‐independent and variational approach to excited states that has recently gained an increasing interest is the theory of many‐electron ensembles 23–48 . Ensemble DFT, which extends regular ground‐state DFT to ensembles of ground and (neutral) excited states, was originally introduced by Theophilou 24,49 for equi‐ensembles and then further generalized by Gross, Oliveira and Kohn, 26,50,51 hence the name TGOK‐DFT 52 .…”

Section: Introductionmentioning

confidence: 99%

Extended N‐centered ensemble density functional theory of double electronic excitations

Cernatic,

Fromager

2024

J Comput Chem

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A recent work (arXiv:2401.04685) has merged N‐centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in‐principle exact (so‐called extended N‐centered) ensemble density functional theory of neutral and charged electronic excitations. This formalism made it possible to revisit the concept of density‐functional derivative discontinuity, in the particular case of single excitations from the highest occupied Kohn–Sham (KS) molecular orbital, without invoking the usual “asymptotic behavior of the density” argument. In this work, we address a broader class of excitations, with a particular focus on double excitations. An exact implementation of the theory is presented for the two‐electron Hubbard dimer model. A thorough comparison of the true physical ground‐ and excited‐state electronic structures with that of the fictitious ensemble density‐functional KS system is also presented. Depending on the choice of the density‐functional ensemble as well as the asymmetry of the dimer and the correlation strength, an inversion of states can be observed. In some other cases, the strong mixture of KS states within the true physical system makes the assignment “single excitation” or “double excitation” irrelevant.

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Section: Introductionmentioning

confidence: 99%

Extended N‐centered ensemble density functional theory of double electronic excitations

Cernatic,

Fromager

2024

J Comput Chem

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“…In recent times, EDFT has undergone significant developments that are crucial to its advancement. − However, it suffers from the disadvantages that, to treat a high-lying excited state, it is usually required to include all lower-lying states in the ensemble and that the weight dependence of the exchange-correlation functional is hard to model. Another ensemble theory that has been receiving increasing attention and shares some of the problems of EDFT is w -ensemble one-body reduced density matrix functional theory. − …”

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confidence: 99%

Exact Excited-State Functionals of the Asymmetric Hubbard Dimer

Giarrusso,

Loos

2023

J. Phys. Chem. Lett.

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The exact functionals associated with the (singlet) ground state and the two singlet excited states of the asymmetric Hubbard dimer at half-filling are calculated using both Levy’s constrained search and Lieb’s convex formulation. While the ground-state functional is, as is commonly known, a convex function with respect to the density, the functional associated with the doubly excited state is found to be concave. Also, because the density-potential mapping associated with the first excited state is noninvertible, its “functional” is a partial, multivalued function composed of one concave and one convex branch that correspond to two separate domains of the external potential. Remarkably, it is found that, although the one-to-one mapping between density and external potential may not apply (as in the case of the first excited state), each state-specific energy and corresponding universal functional are “functions” whose derivatives are each other’s inverse, just as in the ground state formalism.

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Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction

Giarrusso,

Gori‐Giorgi,

Agostini

2024

ChemPhysChem

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We generalize the definitions of local scalar potentials named vkin and vN−1, which are relevant to properly describe phenomena such as molecular dissociation with density‐functional theory, to the case in which the electronic wavefunction corresponds to a complex current‐carrying state. In such a case, an extra term in the form of a vector potential appears which cannot be gauged away. Both scalar and vector potentials are introduced via the exact factorization formalism which allows us to express the given Schrödinger equation as two coupled equations, one for the marginal and one for the conditional amplitude. The electronic vector potential is directly related to the paramagnetic current density carried by the total wavefunction and to the diamagnetic current density in the equation for the marginal amplitude. An explicit example of this vector potential in a triplet state of two non‐interacting electrons is showcased together with its associated circulation, giving rise to a non‐vanishing geometric phase. Some connections with the exact factorization for the full molecular wavefunction beyond the Born‐Oppenheimer approximation are also discussed.

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Deriving density-matrix functionals for excited states

Cited by 7 publications

References 61 publications

Extended N‐centered ensemble density functional theory of double electronic excitations

Extended N‐centered ensemble density functional theory of double electronic excitations

Exact Excited-State Functionals of the Asymmetric Hubbard Dimer

Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction

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