Density-functional theory for ensembles of fractionally occupied states. II. Application to the He atom

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

“…Thus, E now equals a statistical average of the lowest lying energy eigenvalues E κ [v] ofĤ v = T +Ŵ + n(r)v(r)dr for weights W = {w κ } obeying w κ = 1, 0 ≤ w κ ≤ 1, w κ ≥ w κ for E κ ≤ E κ ′ and other conditions discussed in detail in the original GOK articles [24][25][26] and in more recent work.…”

“…DFT was later generalized to the case of ensembles 27,28 , which can be broadly categorized into three forms: First, there are ensemble of states with different numbers of electrons in each state; 29 Second, ensembles may be required to deal with degenerate ground states 62 ; and finally, Gross, Oliveira and Kohn (GOK) ensembles [24][25][26] extend density functional theory to statistical ensembles of eigenstates.…”

“…One different, low-cost route to the CT problem is afforded by the Gross, Oliveira, and Kohn (GOK) [24][25][26] ensemble density functional theory (EDFT), [27][28][29][30][31][32][33] which offers a statistical ensembles of quantum states that can be treated similarly to a ground state. EDFT can yield energy differences directly, as discussed in detail below.…”

Ensemble density variational methods with self- and ghost-interaction-corrected functionals

“…It has been recognized that spurious self-interaction may be responsible for yielding too large ensemble energies if local density functionals are employed. 20 Apart from self-interaction ensemble functionals can be plagued by another kind of spurious interaction that has no counterpart in the ground-state theory, namely, the so-called ghost-interaction (GI). 24,28,29 Ghost-interaction terms are unambiguously identified in case of a one-electron system.…”

“…11 and 12. Substantial theoretical investigation of the ensemble DFT 7,8,10,[13][14][15][16][17][18][19] has not been paralleled by its practical implementations and the amount of numerical examples is rather scarce. Initial attempts of computing excitation energies have been mainly limited to atoms and small molecules and they involved using either local and semi-local functionals, [20][21][22][23][24][25][26][27] or the exact-exchange functional. 15,28,29 Calculations have been carried out via the Kohn-Sham (KS) scheme and, in case of the exact exchange functional, optimal effective potential (OEP) methods have been developed.…”