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

Abstract

Gross--Oliveira--Kohn (GOK) ensemble density-functional theory (GOK-DFT) is a time-\textit{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 \textit{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) weight-dependent 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.

11 pages, 4 figures (New horizons in density functional theory Faraday Discussion)

References in corpus (43)

• Progress in Time-Dependent Density-Functional Theory
• Fundamental gaps of finite systems from the eigenvalues of a generalized Kohn-Sham method
• A Mountaineering Strategy to Excited States: Highly-Accurate Reference Energies and Benchmarks
• Perspectives on double-excitations in TDDFT
• A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Medium Size Molecules
• Reference Energies for Double Excitations
• Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Multi-configuration time-dependent density-functional theory based on range separation
• Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations
• Assessment of Dressed Time-Dependent Density-Functional Theory for the Low-Lying Valence States of 28 Organic Chromophores
• On the "Causality Paradox" of Time-Dependent Density Functional Theory
• Two electrons on a hypersphere: a quasi-exactly solvable model
• 'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster
• Direct extraction of excitation energies from ensemble density-functional theory
• Exact and approximate Kohn-Sham potentials in ensemble density-functional theory
• Excitations and benchmark ensemble density functional theory for two electrons
• Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers
• Exact ensemble density functional theory for excited states in a model system: investigating the weight dependence of the correlation energy
• Ground state of two electrons on a sphere
• Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles
• Can ensemble density functional theory yield accurate double excitations?
• 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
• Generalized adiabatic connection in ensemble density-functional theory for excited states: example of the H2 molecule
• Excited states of spherium
• Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation
• Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory
• The flexible nature of exchange, correlation and Hartree physics: resolving "delocalization" errors in a 'correlation free' density functional
• Is ADC(3) as Accurate as CC3 for Valence and Rydberg Transition Energies?
• 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
• Uniform electron gases. I. Electrons on a ring
• Uniform electron gases
• Extension of many-electron theory and approximate density functionals to fractional charges and fractional spins
• Thinking outside the box: the uniform electron gas on a hypersphere
• Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer
• Uniform Electron Gases. II. The Generalized Local Density Approximation in One Dimension
• Near-locality of exchange and correlation density functionals for 1- and 2-electron systems
• Exchange functionals based on finite uniform electron gases
• Generalized local-density approximation and one-dimensional finite uniform electron gases
• 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

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• Accurate and Efficient Prediction of Double Excitation Energies Using the Particle-Particle Random Phase Approximation
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