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

TL;DR

This paper explores how step structures in the exchange-correlation potential of Kohn-Sham DFT are essential for accurately describing excited states and charge transfer, highlighting the importance of the derivative discontinuity and ensemble approaches.

Contribution

It analytically and numerically demonstrates the origin of step structures in the xc potential and shows that common approximations can capture these steps from an ensemble perspective.

Findings

Step structures are linked to the relationship between KS and many-electron energies.

Common xc approximations like LDA can produce steps when viewed ensemble-wise.

Capturing these steps improves excitation and subsystem energy calculations.

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 ($\Delta$), 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 many-electron 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.