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 (7)

• Fractional charge perspective on the band-gap in density-functional theory
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• '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
• Kohn-Sham potential for a strongly correlated finite system with fractional occupancy
• Frozen density embedding with non-integer subsystems' particle numbers