Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer

Abstract

Building on our recent study [https://doi.org/10.1021/acs.jpclett.3c02052, J. Phys. Chem. Lett. 14, 8780 (2023)], we explore the generalization of the ground-state Kohn-Sham (KS) formalism of density-functional theory (DFT) to the (singlet) excited states of the asymmetric Hubbard dimer at half-filling. While we found that the KS-DFT framework can be straightforwardly generalized to the highest-lying doubly-excited state, the treatment of the first excited state presents significant challenges. Specifically, using a density-fixed adiabatic connection, we show that the density of the first excited state lacks non-interacting $v$-representability. However, by employing an analytic continuation of the adiabatic path, we demonstrate that the density of the first excited state can be generated by a complex-valued external potential in the non-interacting case. More practically, by performing state-specific KS calculations with exact and approximate correlation functionals -- each state possessing a distinct correlation functional -- we observe that spurious stationary solutions of the KS equations may arise due to the approximate nature of the functional.

14 pages, 10 figures

References in corpus (17)

• Time-dependent density functional theory: Past, present, and future
• Charge-Transfer in Time-Dependent Density Functional Theory
• Exact ensemble density functional theory for excited states in a model system: investigating the weight dependence of the correlation energy
• Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems
• Orbital-optimized versus time-dependent density functional calculations of intramolecular charge transfer excited states
• The structure of the density-potential mapping. Part I: Standard density-functional theory
• Exact Excited-State Functionals of the Asymmetric Hubbard Dimer
• Exploring Foundations of Time-Independent Density Functional Theory for Excited-States
• Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
• Density-to-potential map in time-independent excited-state density-functional theory
• Ensemble density functional theory of ground and excited energy levels
• Density-potential inversion from Moreau-Yosida regularization
• Geometry of Degeneracy in Potential and Density Space
• Geometrical Perspective on Spin-Lattice Density-Functional Theory
• Stationary conditions for excited states: the surprising impact of density-driven correlations
• Kohn-Sham inversion with mathematical guarantees
• Lieb variation principle in density-functional theory

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