Exact and approximate Kohn-Sham potentials in ensemble density-functional theory

Abstract

We construct exact Kohn-Sham potentials for the ensemble density-functional theory (EDFT) from the ground and excited states of helium. The exchange-correlation (XC) potential is compared with the quasi-local-density approximation and both single determinant and symmetry eigenstate ghost-corrected exact exchange approximations. Symmetry eigenstate Hartree-exchange recovers distinctive features of the exact XC potential and is used to calculate the correlation potential. Unlike the exact case, excitation energies calculated from these approximations depend on ensemble weight, and it is shown that only the symmetry eigenstate method produces an ensemble derivative discontinuity. Differences in asymptotic and near-ground-state behavior of exact and approximate XC potentials are discussed in the context of producing accurate optical gaps.

9 pages, 13 figures

References in corpus (2)

• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Excitations and benchmark ensemble density functional theory for two electrons

Cited by in corpus (28)

• 'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster
• Direct extraction of excitation energies from ensemble density-functional theory
• Exact ensemble density functional theory for excited states in a model system: investigating the weight dependence of the correlation energy
• Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles
• 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?
• How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?
• Density-driven correlations in many-electron ensembles: theory and application for excited states
• Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation
• Origin of static and dynamic steps in exact Kohn-Sham potentials
• Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory
• A weight-dependent local correlation density-functional approximation for ensembles
• Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states
• Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems
• Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer
• Exact Excited-State Functionals of the Asymmetric Hubbard Dimer
• Ghost interaction correction in ensemble density-functional theory for excited states with and without range separation
• Combining linear interpolation with extrapolation methods in range-separated ensemble density-functional theory
• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
• Second-order perturbative correlation energy functional in the ensemble density-functional theory
• Calculating excitation energies by extrapolation along adiabatic connections
• Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons
• Excitation energies from G{ö}rling-Levy perturbation theory along the range-separated adiabatic connection
• Inverting the Kohn-Sham equations with physics-informed machine learning
• Full Quantum Work Statistics for Non-Homogeneous Many-Body Systems
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities
• Approaching Periodic Systems in Ensemble Density Functional Theory via Finite One-Dimensional Models
• Warming Up Density Functional Theory