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#### Exact Density Functional Obtained via the Levy Constrained Search

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##### Citation

Mori-Sánchez, P., & Cohen, A. J. (2018). Exact Density Functional Obtained via
the Levy Constrained Search.* The Journal of Physical Chemistry Letters,* *9*(17),
4910-4914.

Cite as: https://hdl.handle.net/21.11116/0000-000E-DA8A-1

##### Abstract

A stochastic minimization method for a real-space wave function, psi(r(1), r(2)...r(n)), constrained to a chosen density, rho(r), is developed. It enables the.,explicit calculation of the Levy constrained search, F[rho] = min(psi ->rho)<psi vertical bar(T) over cap + (V) over cap (ee) vertical bar psi >, which gives the exact functional of density functional theory. This general method is illustrated in the evaluation of F[rho] for densities in one dimension with a soft-Coulomb interaction, Additionally, procedures are given to determine the first and second functional derivatives, delta F/delta rho(r) and delta F-2/[delta rho(r)delta rho(r')]. For a chosen external potential, v(r), the functional and its derivatives are used in minimizations over densities to give the exact energy, E-v, without needing to solve the Schrodinger equation.