Exact Density Functional Obtained via the Levy Constrained Search.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Density Functional Theory

Background:

• Density functional theory (DFT) offers a computationally tractable approach to electronic structure.
• Calculating the exact functional remains a significant challenge in DFT.

Purpose of the Study:

• To develop a general stochastic minimization method for calculating the exact functional in DFT.
• To enable explicit computation of the Levy constrained search, F[ρ].

Main Methods:

• A stochastic minimization technique is applied to a real-space wave function constrained to a target electron density.
• The method explicitly calculates the Levy constrained search, F[ρ] = minΨ→ρ⟨Ψ| T̂ + V̂ee|Ψ⟩.
• Procedures for determining the first and second functional derivatives are also provided.

Main Results:

• The developed method successfully evaluates the exact functional F[ρ] for one-dimensional densities with soft-Coulomb interactions.
• The functional and its derivatives can be used to find the exact ground-state energy without solving the Schrödinger equation.

Conclusions:

• This stochastic minimization approach provides a pathway to the exact functional in DFT.
• The method offers a novel route to accurate electronic structure calculations, circumventing direct solution of the Schrödinger equation.