N‐centered ensemble density‐functional theory for open systems

• Published in: International journal of quantum chemistry Vol. 120; no. 21
• Main Authors: Senjean, Bruno, Fromager, Emmanuel
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.11.2020; Wiley Subscription Services, Inc; Wiley
• Subjects: Chemical Sciences; Chemistry; Condensed Matter; Density functional theory; Derivatives; Electron density; embedding; ensemble density‐functional theory; fractional electron number; grand canonical energy; Integrals; Open systems; or physical chemistry; Physical chemistry; Physics; Quantum physics; Strongly Correlated Electrons; Theoretical and; Wave functions
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.26190

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. Describing an open system remains a challenge in density‐functional theory, as standard density functionals do not exhibit the infamous derivative discontinuity that appears when crossing an integral number of electrons. By referring to N‐centered ensembles in the context of density‐functional theory, a more explicit (ensemble weight‐dependent) density‐functional expression for the derivative discontinuity is derived and, most importantly, an open‐system problem can also be mapped onto a pure‐state closed one, in principle exactly.