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

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.

References in corpus (10)

• Orbital Optimized Density Functional Theory for Electronic Excited States
• 'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster
• Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers
• Ensemble Density Functional Theory of Neutral and Charged Excitations
• Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems
• Electronic excited states in extreme limits via ensemble density functionals
• Exact Excited-State Functionals of the Asymmetric Hubbard Dimer
• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
• Ensemble density functional theory of ground and excited energy levels
• Extended $N$-centered ensemble density functional theory of double electronic excitations

Cited by in corpus (6)

• Freeze-and-release direct optimization method for variational calculations of excited electronic states
• Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
• State-specific density functionals for excited states from ensembles
• Excited States of the Uniform Electron Gas
• Exact static linear response of excited states from ensemble density functional theory
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities