Electronic excited states in extreme limits via ensemble density functionals

Abstract

Density functional theory (DFT) has greatly expanded our ability to affordably compute and understand electronic ground states, by replacing intractable {\em ab initio} calculations by models based on paradigmatic physics from high- and low-density limits. But, a comparable treatment of excited states lags behind. Here, we solve this outstanding problem by employing a generalization of density functional theory to ensemble states (EDFT). We thus address important paradigmatic cases of all electronic systems in strongly (low-density) and weakly (high-density) correlated regimes. We show that the high-density limit connects to recent, exactly-solvable EDFT results. The low-density limit reveals an unnoticed and most unexpected result -- density functionals for strictly correlated {\em ground} states can be reused {\em directly} for excited states. Non-trivial dependence on excitation structure only shows up at third leading order. Overall, our results provide foundations for effective models of excited states that interpolate between exact low- and high-density limits, which we illustrate on the cases of singlet-singlet excitations in H${}_2$ and a ring of quantum wells.

References in corpus (14)

• Regularized Orbital-Optimized Second-Order Møller-Plesset Perturbation Theory: A Reliable Fifth-Order Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers
• Exact conditions and scaling relations in finite temperature density functional theory
• 'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster
• Density functional theory for strongly-interacting electrons: Perspectives for Physics and Chemistry
• Individual correlations in ensemble density-functional theory: State-driven/density-driven decompositions without additional Kohn-Sham systems
• Can ensemble density functional theory yield accurate double excitations?
• Density-driven correlations in many-electron ensembles: theory and application for excited states
• Smoothing of transport plans with fixed marginals and rigorous semiclassical limit of the Hohenberg-Kohn functional
• Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory
• U(1)$\times$SU(2) Gauge Invariance Made Simple for Density Functional Approximations
• A weight-dependent local correlation density-functional approximation for ensembles
• Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems
• Second-order perturbative correlation energy functional in the ensemble density-functional theory
• Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory

Cited by in corpus (13)

• Exact Excited-State Functionals of the Asymmetric Hubbard Dimer
• Quantum simulation of excited states from parallel contracted quantum eigensolvers
• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
• Ensemble density functional theory of ground and excited energy levels
• Extended $N$-centered ensemble density functional theory of double electronic excitations
• Stationary conditions for excited states: the surprising impact of density-driven correlations
• State-specific density functionals for excited states from ensembles
• Density functional theory beyond the Born-Oppenheimer approximation: Exact mapping onto an electronically non-interacting Kohn-Sham molecule
• Excited States of the Uniform Electron Gas
• Exact static linear response of excited states from ensemble density functional theory
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities
• Solving one-body ensemble N-representability problems with spin
• Refining ensemble $N$-representability of one-body density matrices from partial information