A Many-Body Density Energy Functional

TL;DR

This paper reformulates density functional theory using a translationally invariant many-body density, providing a new approach for self-bound systems and demonstrating its application to helium clusters.

Contribution

It introduces a novel density functional framework based on a specific many-body density, extending DFT to self-bound systems with demonstrated practical application.

Findings

Unique relation between many-body density and potential established

Energy functional minimized to find ground-state energy

Application to $^4$He clusters shows advantages of the new formulation

Abstract

The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the basis of the Density Functional Theory, are reformulated in terms of a particular many-body density, which is translational invariant and therefore is relevant for self-bound systems. In a similar way that there is a unique relation between the one-body density and the external potential that gives rise to it, we demonstrate that there is a unique relation between that particular many-body density and a definite many-body potential. The energy is then a functional of this density and its minimization leads to the ground-state energy of the system. As a proof of principle, the analogous of the Kohn-Sham equation is solved in the specific case of $^4$He atomic clusters, to put in evidence the advantages of this new formulation in terms of physical insights.