N-centered ensemble density-functional theory for open systems

Abstract

Two (so-called left and right) variants of N-centered ensemble density-functional theory (DFT) [Senjean and Fromager, Phys. Rev. A 98, 022513 (2018)] are presented. Unlike the original formulation of the theory, these variants allow for the description of systems with a fractional electron number. While conventional DFT for open systems uses only the true electron density as basic variable, left/right N-centered ensemble DFT relies instead on (i) a fictitious ensemble density that integrates to a central (integral) number N of electrons, and (ii) a grand canonical ensemble weight $\alpha$ which is equal to the deviation of the true electron number from N. Within such a formalism, the infamous derivative discontinuity that appears when crossing an integral number of electrons is described exactly through the dependence in $\alpha$ of the left and right N-centered ensemble Hartree-exchange-correlation density functionals. Incorporating N-centered ensembles into existing density-functional embedding theories is expected to pave the way towards the in-principle-exact description of an open fragment by means of a pure-state N-electron many-body wavefunction. Work is currently in progress in this direction

15 pages, 4 figures, 1 table

References in corpus (26)

• Fractional charge perspective on the band-gap in density-functional theory
• Understanding and reducing errors in density functional calculations
• Partition Density Functional Theory
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Delocalization errors in density functional theory are essentially quadratic in fractional occupation number
• The Hubbard Dimer: A density functional case study of a many-body problem
• 'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster
• 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
• Prediction of the derivative discontinuity in density functional theory from an electrostatic description of the exchange and correlation potential
• Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles
• 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
• Molecular Binding Energies from Partition Density Functional Theory
• Ground-State Energy as a Simple Sum of Orbital Energies in Kohn-Sham Theory: A Shift in Perspective through a Shift in Potential
• Linear response time-dependent density functional theory of the Hubbard dimer
• Local density approximation in site-occupation embedding theory
• Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF
• The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect
• Kohn-Sham potential for a strongly correlated finite system with fractional occupancy
• Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer
• Exchange functionals based on finite uniform electron gases
• Frozen density embedding with non-integer subsystems' particle numbers
• Accuracy of electron densities obtained via Koopmans-compliant hybrid functionals
• Spectroscopy of the Hubbard dimer: the spectral potential

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• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
• 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
• Improving the exchange and correlation potential in density functional approximations through constraints
• Density-functional approach to the band gaps of finite and periodic two-dimensional systems
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities