From Kohn-Sham to many-electron energies via step structures in the exchange-correlation potential

Abstract

Accurately describing excited states within Kohn-Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy (∆), which relates a many-electron energy difference to the corresponding KS energy difference. We demonstrate, analytically and numerically, how the relationship between KS and many-electron energies leads to the step structures observed in the exact xc potential, in four scenarios: electron addition, molecular dissociation, excitation of a finite system, and charge transfer. We further show that steps in the potential can be obtained also with common xc approximations, as simple as the LDA, when addressed from the ensemble perspective. The article therefore highlights how capturing the relationship between KS and manyelectron energies with advanced xc approximations is crucial for accurately calculating excitations, as well as the ground-state density and energy of systems which consist of distinct subsystems.

Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons

“…(1). Figure 1 shows that as δ → 0 + the change in the KS potential (v N +δ s (x) − v N s (x)) tends to a uniform constant of magnitude ∆ [52,66]. In this case the N -electron KS potential is defined such that v N +δ s (|x| → ∞) = 0. v N +δ s (x) possess a discontinuous shift which elevates the potential in the central region of the system.…”

Charge-transfer steps in Density Functional Theory from the perspective of the Exact Electron Factorization

“…It was found previously that steps can appear in the exact KS potential v KS during dissociation and charge transfer (see, e.g., [10][11][12][13][14] and citations therein), that they are related to the derivative distcontinuity and the problem of describing charge-transfer in DFT [15], and that many density functionals do not describe these steps correctly [16]. Steps were also found in the Pauli potential v P [17] that appears in another variant of DFT, orbital-free (OF) DFT [18][19][20][21].…”