Abstract
AbstractTwo (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.
Highlights
Density-functional theory (DFT) has become over the last two decades the method of choice for performing routine large-scale electronic structure calculations
DFT is applied to closed electronic systems, that is, systems with an integral number N of electrons
DFT is in principle able to describe systems with a fractional electron number, as shown in the pioneering work of Perdew, Parr, Levy, and Balduz (PPLB).[1]
Summary
Density-functional theory (DFT) has become over the last two decades the method of choice for performing routine large-scale electronic structure calculations. A direct consequence of Equations (15) and (16) is that the physical energy EðN Þ = Tr Γ^ðN ÞH^ of an open system can be extracted from a left or right N-centered ensemble as follows: dN e = N By deriving a DFT for left and right N-centered ensembles, we obtain from Equations (17)–(20) a novel and in-principle-exact density-functional description of open systems.
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