# Levy-Lieb constrained-search formulation as a minimization of the correlation functional

## TL;DR

This paper demonstrates that the Levy-Lieb constrained-search formulation of density functional theory is equivalent to minimizing the correlation functional over the N-1 conditional probability density, providing new insights into the theoretical foundation.

## Contribution

It establishes the equivalence between the Levy-Lieb constrained-search approach and the minimization of the correlation functional, offering a novel perspective on the foundational formulation.

## Key findings

- Shows the equivalence between Levy-Lieb constrained-search and correlation functional minimization
- Analyzes implications through a practical example
- Provides theoretical insights into density functional theory

## Abstract

The constrained-search formulation of Levy and Lieb, which formally defines the exact Hohenberg-Kohn functional for any N-representable electron density, is here shown to be equivalent to the minimization of the correlation functional with respect to the N-1 conditional probability density, where N is number of electrons of the system. The consequences and implications of such a result are here analyzed and discussed via a practical example.