Foundation for the ΔSCF Approach in Density Functional Theory
arxiv(2024)
摘要
We extend ground-state density-functional theory to excited states and
provide the theoretical formulation for the widely used Δ SCF 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 n_s and the potential
w_s(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
γ_s(𝐫,𝐫') (density-matrix-functional theory,
γ_sFT). 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 (n_s,w_s(r)),
Φ, or γ_s(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 Δ
SCF method.
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