2024/03/07 by Weitao Yang, Paul W. Ayers, Yang, Weitao +1
Engineering · #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Phase Equilibria and Thermodynamics
paper · pdf · doi:10.48550/arxiv.2403.04604
openalex publication_date 2024/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend ground-state density-functional theory to excited states and provide the theoretical formulation for the widely used ΔSCF method for calculating excited-state energies and densities. As the electron density alone is insufficient to characterize excited states, we formulate excited-state theory using the defining variables of a noninteracting reference system, namely (1) the excitation quantum number ns and the potential ws(r) (excited-state potential-functional theory, nPFT), (2) the noninteracting wavefunction Φ (Φ-functional theory, ΦFT), or (3) the noninteracting one-electron reduced density matrix γs(r,r') (density-matrix-functional theory, γsFT). We show the equivalence of these three sets of variables and their corresponding energy functionals. Importantly, the ground and excited-state exchange-correlation energy use the same universal functional, regardless of whether (ns,ws(\boldsymbolr)), Φ, or γs(r,r') is selected as the fundamental descriptor of the system. We derive the excited-state (generalized) Kohn-Sham equations. The minimum of all three functionals is the ground-state energy and, for ground states, they are all equivalent to the Hohenberg-Kohn-Sham method. The other stationary points of the functionals provide the excited-state energies and electron densities, establishing the foundation for the ΔSCF method.