Multistate-Averaged Kohn-Sham ΔSCF Method for Excitation Energies, Transition Properties, and Absorption Spectra and Its Relation to Ensemble Density Functional Theory.

Authors

Oliver Bertleff, Egor Trushin, Andreas Görling

Published in

Journal of chemical theory and computation. Oct 28, 2026. Epub Oct 28, 2026.

Abstract

The ΔSCF (Δ-Self-Consistent-Field) approach is an attractive alternative to time-dependent density-functional theory (TDDFT) for excited-state calculations, particularly for Rydberg, charge-transfer, and doubly excited states, for which conventional linear-response TDDFT performs poorly. However, conventional ΔSCF methods based on the unrestricted Kohn-Sham formalism suffer from spin- and spatial-symmetry breaking, optimize the ground- and excited-state determinants independently, leading to nonorthogonal Kohn-Sham determinants that complicate the calculation of transition properties, and require a separate SCF procedure for each excited state of interest. In order to address these limitations, we present a potential-averaged multistate-averaged Kohn-Sham (pa-MSTA-KS) method, which averages the Hartree-exchange-correlation potential of the ground state with state-averaged Hartree-exchange-correlation potentials of one or several excited states during a single SCF procedure. Unlike restricted open-shell Kohn-Sham (ROKS) approaches, pa-MSTA-KS yields canonical SCF equations and can be implemented in any standard KS code with minimal effort. The pa-MSTA-KS method avoids spin-symmetry breaking by construction, yields orbitals that describe ground and excited states simultaneously, and enables the direct evaluation of transition dipole moments and the simulation of full UV/vis absorption spectra based on a single SCF calculation. For excitation energies of the QUEST1 data set and for absorption spectra of water, ethylene, and ammonia, pa-MSTA-KS outperforms TDDFT in accuracy. By combining the generalized-adiabatic-connection Kohn-Sham formalism with ensemble density-functional theory, we provide a formal basis for the pa-MSTA-KS method and derive a new decomposition of the ensemble correlation energy into state- and density-driven contributions.

PMID:
42956333
Bibliographic data and abstract were imported from PubMed on 30 Oct 2026.

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