N-centered ensemble density-functional theory for open systems

Bruno Senjean*, Emmanuel Fromager

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


Two (so-called left and right) variants of N-centered ensemble density-functional theory (DFT) 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 (a) a fictitious ensemble density that integrates to a central (integral) number N of electrons, and (b) a grand canonical ensemble weight α 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 α 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 toward 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.

Original languageEnglish
Article numbere26190
Pages (from-to)1-21
Number of pages21
JournalInternational Journal of Quantum Chemistry
Issue number21
Early online date21 Feb 2020
Publication statusPublished - 1 Nov 2020


  • embedding
  • ensemble density-functional theory
  • fractional electron number
  • grand canonical energy
  • open systems


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