## Abstract

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 language | English |
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Article number | e26190 |

Pages (from-to) | 1-21 |

Number of pages | 21 |

Journal | International Journal of Quantum Chemistry |

Volume | 120 |

Issue number | 21 |

Early online date | 21 Feb 2020 |

DOIs | |

Publication status | Published - 1 Nov 2020 |

## Keywords

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