Exact density functional obtained via the Levy constrained search

2017/09/29 by Mori-Sánchez, Paula, Cohen, Aron J.
#Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1709.10284

Abstract

A stochastic minimization method for a real-space wavefunction, Ψ(\bf r₁,\bf r₂…\bf r_n), constrained to a chosen density, ρ(\bf r), is developed. It enables the explicit calculation of the Levy constrained search F[ρ]=min_Ψ→ρ⟨Ψ|T+V_ee|Ψ⟩ (Proc. Natl. Acad. Sci. 76 6062 (1979)), that gives the exact functional of density functional theory. This general method is illustrated in the evaluation of F[ρ] for two-electron densities in one dimension with a soft-Coulomb interaction. Additionally, procedures are given to determine the first and second functional derivatives, \fracδFδρ(\bf r) and \fracδ²Fδρ(\bf r)δρ(\bf r'). For a chosen external potential, v(\bf r), the functional and its derivatives are used in minimizations only over densities to give the exact energy, E_v without needing to solve the Schrödinger equation.

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