Stationary conditions for excited states: the surprising impact of density-driven correlations

TL;DR

This paper uncovers that individual excited states in density functional theory have specific stationary conditions influenced by density-driven correlations, challenging traditional assumptions and impacting self-consistent calculations.

Contribution

It reveals the complex state-specific stationary conditions for excited states in DFT and PFT, highlighting the role of density-driven correlations neglected in common approaches.

Findings

Excited states have unique stationary conditions derived from ensemble solutions.

Density-driven correlations significantly affect the non-interacting Kohn-Sham PFT excited state conditions.

Implications for self-consistency in both exact and approximate DFT/PFT are discussed.

Abstract

Typical density functional theory (DFT) and approximations thereto solve the many-electron ground state problem by working from a numerically efficient non-interacting Kohn-Sham reference system; and benefit from useful minimization conditions that allow iteration (i.e. self-consistency) to the optimal energy and density. Ensembles of ground and excited states can also benefit from similar minimization conditions [see in source]. This work reveals that individual excited states also have state-specific stationary conditions, that can be deduced from the ensemble solution and apply to DFT and its interacting potential functional theory (PFT) counterpart. However, the state-specific stationary condition for the non-interacting Kohn-Sham PFT is revealed to be more complicated than the ground state problem, due in part to a contribution from density-driven correlations [Phys. Rev. Lett. 123, 016401 (2019); 124, 243001 (2020); 125, 233001 (2020)] that are neglected in ``$\Delta$SCF'' approaches. Some implications for self-consistency in exact theory and approximations are discussed.