Exact and approximate Kohn-Sham potentials in ensemble density-functional theory

Abstract

We construct exact Kohn-Sham potentials for the ensemble density-functional theory (EDFT) from the ground and excited states of helium. The exchange-correlation (XC) potential is compared with the quasi-localdensity approximation and both single-determinant and symmetry-eigenstate ghost-corrected exact exchange approximations. Symmetry-eigenstate Hartree exchange recovers distinctive features of the exact XC potential and is used to calculate the correlation potential. Unlike the exact case, excitation energies calculated from these approximations depend on ensemble weight, and it is shown that only the symmetry-eigenstate method produces an ensemble derivative discontinuity. Differences in asymptotic and near-ground-state behavior of exact and approximate XC potentials are discussed in the context of producing accurate optical gaps.

Calculating excitation energies by extrapolation along adiabatic connections

“…Indeed, several time-independent DFT approaches for calculating excitation energies exist and are currently being developed. These include ensemble DFT [7][8][9][10][11][12], ∆SCF [13][14][15][16][17] and related methods [18][19][20][21], or perturbation theory [22][23][24][25] along the standard adiabatic connection using the noninteracting Kohn-Sham (KS) Hamiltonian as the zero-order Hamiltonian.…”

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

“…EEXX calculations can yield good results in small atoms, [38][39][40] even for excitations that are very difficult for approximations to time-dependent Kohn-Sham theory. EEXX can be calculated in two ways: it can be obtained as a functional of the exact density, using the exact orbitals, which is the course we pursue in this work to avoid densitydriven errors 64 .…”

“…EDFT can yield energy differences directly, as discussed in detail below. Indeed, excited state EDFT has seen increasing interest of late [33][34][35][36][37][38][39][40] as a potential alternative to TDDFT for excitation energies. This recent resurgence of GOK EDFT mirrors a growing interest in more general forms of EDFT, which can deal, e.g., with degenerate ground states 30,[41][42][43][44] and "open" systems with a noninteger number of electrons.…”

Communication: Kohn-Sham theory for excited states of Coulomb systems

“…3-5), although several time-independent approaches have also been given to treat excited states within DFT. [6][7][8][9][10][11][12][13][14][15][16][17][18] The subspace theory of Theophilou 6 and its generalization by Gross, Oliveira, and Kohn 7 are complicated by the requirement that a whole ensemble of states has to be considered. Individual excitedstates can be targeted using time-independent approaches based on the adiabatic connection 19 or the constrained search.…”

“…(Nevertheless, approximate functionals for this bifunctional approach and the ensemble theory have been developed for and applied to atomic and molecular systems. [9][10][11]17,18 ) The time-independent Kohn-Sham theory that we give in this communication has the advantage that it employs a unifunctional.…”