ArticleThe journal of physical chemistry letters2023
Exact Excited-State Functionals of the Asymmetric Hubbard Dimer.
Article in The journal of physical chemistry letters, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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- Excited-State Densities from Time-Dependent Density Functional Response Theory.Journal of chemical theory and computation · 2025Article
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Abstract
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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