Exact static linear response of excited states from ensemble density functional theory

2025/06/19 by Dupuy, Lucien, Fromager, Emmanuel · 2 citations
#Chemical Physics (physics.chem-ph) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2506.16363

Abstract

Following a recent work [E. Fromager, J. Phys. Chem. A 2025, 129, 4, 1143-1155] on the ensemble density functional theory (DFT) of excited electronic energy levels, we derive in this paper the ensuing static linear response theory, thus allowing for an in-principle exact evaluation of excited-state density-density linear response functions in a completely frequency-independent setting. Once individual-state components of the inverse ensemble linear response function have been introduced, a working Dyson-type equation naturally emerges for each state, individually. By considering the zero-weight limit of the theory, which infinitesimally deviates from standard Kohn--Sham DFT, exact excited-state corrections to ground-state linear response DFT can be identified. They involve the first-order weight derivatives of the ensemble Hartree-exchange-correlation (Hxc) potential and kernel, thus confirming the importance in ensemble DFT of both weight and density-functional derivatives of the ensemble Hxc energy functional.

Citations

• Ensemble Time-Dependent Density Functional Theory
• Excited State Densities from Time-Dependent Density Functional Response Theory
• "Ensemblization" of density functional theory
• Excited States of the Uniform Electron Gas
• Freeze-and-release direct optimization method for variational calculations of excited electronic states
• Capturing the elusive curve-crossing in low-lying states of butadiene with dressed TDDFT
• State-specific density functionals for excited states from ensembles
• Orbital-optimized Density Functional Calculations of Molecular Rydberg Excited States with Real Space Grid Representation and Self-Interaction Correction
• Oscillator strengths and excited-state couplings for double excitations in time-dependent density functional theory
• Exact Conditions for Ensemble Density Functional Theory
• Local density approximation for excited states
• Calculations of Excited Electronic States by Converging on Saddle Points Using Generalized Mode Following
• DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science
• Double and Charge-Transfer Excitations in Time-Dependent Density Functional Theory
• Progress in Time-Dependent Density-Functional Theory
• Self-Consistent Equations Including Exchange and Correlation Effects

Cited by

• How an Equi-ensemble Description Systematically Outperforms the Weighted-ensemble Variational Quantum Eigensolver
• Ensemble Time-Dependent Density Functional Theory

Related

• Ensemble density functional theory of excited states: Exact N -centered formalism and practical opportunities
• State-specific density functionals for excited states from ensembles
• An accurate exchange energy functional in excited-state density\n functional theory
• Excited State Densities from Time-Dependent Density Functional Response Theory
• Local density approximation for excited states