A weight-dependent local correlation density-functional approximation for ensembles

Abstract

We report a local, weight-dependent correlation density-functional approximation that incorporates information about both ground and excited states in the context of density-functional theory for ensembles (eDFT). This density-functional approximation for ensembles is specially designed for the computation of single and double excitations within Gross--Oliveira--Kohn (GOK) DFT (i.e., eDFT for neutral excitations), and can be seen as a natural extension of the ubiquitous local-density approximation in the context of ensembles. The resulting density-functional approximation, based on both finite and infinite uniform electron gas models, automatically incorporates the infamous derivative discontinuity contributions to the excitation energies through its explicit ensemble weight dependence. Its accuracy is illustrated by computing single and double excitations in one-dimensional many-electron systems in the weak, intermediate and strong correlation regimes. Although the present weight-dependent functional has been specifically designed for one-dimensional systems, the methodology proposed here is general, i.e., directly applicable to the construction of weight-dependent functionals for realistic three-dimensional systems, such as molecules and solids.

arXiv comment13 pages, 8 figures, supporting information available

References in corpus (51)

• Luttinger Liquid Behavior in Carbon Nanotubes
• Progress in Time-Dependent Density-Functional Theory
• Wigner Crystal in One Dimension
• Perspectives on double-excitations in TDDFT
• Reference Energies for Double Excitations
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Wigner crystal physics in quantum wires
• The Hubbard Dimer: A density functional case study of a many-body problem
• 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
• Coupled-cluster theory for atoms and molecules in strong magnetic fields
• 'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster
• Direct extraction of excitation energies from ensemble density-functional theory
• Density functional theory for strongly-interacting electrons: Perspectives for Physics and Chemistry
• 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
• Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles
• Exact wave functions of two-electron quantum rings
• Can ensemble density functional theory yield accurate double excitations?
• Ground-state energy of the electron liquid in ultrathin wires
• 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
• On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation
• Ground-State Energy as a Simple Sum of Orbital Energies in Kohn-Sham Theory: A Shift in Perspective through a Shift in Potential
• Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory
• Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation
• The flexible nature of exchange, correlation and Hartree physics: resolving "delocalization" errors in a 'correlation free' density functional
• Correlation energy of two electrons in the high-density limit
• 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
• Invariance of the correlation energy at high density and large dimension in two-electron systems
• 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
• N-centered ensemble density-functional theory for open systems
• A Tale of Two Electrons: Correlation at High Density
• High-density correlation energy expansion of the one-dimensional uniform electron gas
• Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer
• Uniform Electron Gases. II. The Generalized Local Density Approximation in One Dimension
• 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
• Uniform electron gases: III. Low-density gases on three-dimensional spheres
• Symmetry-broken local-density approximation for one-dimensional systems
• Excited-State Wigner Crystals in One Dimension

Cited by in corpus (23)

• Individual correlations in ensemble density-functional theory: State-driven/density-driven decompositions without additional Kohn-Sham systems
• Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle
• Ensemble Density Functional Theory of Neutral and Charged Excitations
• Foundation of one-particle reduced density matrix functional theory for excited states
• Machine learning the derivative discontinuity of density-functional theory
• Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems
• Electronic excited states in extreme limits via ensemble density functionals
• Exact Excited-State Functionals of the Asymmetric Hubbard Dimer
• Dynamical Kernels for Optical Excitations
• Ground and Excited States from Ensemble Variational Principles
• Second-order perturbative correlation energy functional in the ensemble density-functional theory
• 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
• Variations of the Hartree-Fock fractional-spin error for one electron
• Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons
• Extended $N$-centered ensemble density functional theory of double electronic excitations
• Excited States of the Uniform Electron Gas
• Exact static linear response of excited states from ensemble density functional theory
• Approaching Periodic Systems in Ensemble Density Functional Theory via Finite One-Dimensional Models
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities
• Transient Uniform Electron Gases
• Solving one-body ensemble N-representability problems with spin
• Refining ensemble $N$-representability of one-body density matrices from partial information