A novel proof of the DFT formula for the interatomic force field of Molecular Dynamics

TL;DR

This paper presents a new, straightforward proof of the DFT-based interatomic force formula used in Molecular Dynamics, establishing its exactness through the Legendre transform relationship between energy functionals.

Contribution

It introduces a novel proof connecting the Hellmann-Feynman force formula to the Legendre transform of energy functionals, clarifying its theoretical foundation.

Findings

The Hellmann-Feynman formula is proven to be exact for interatomic forces.

The proof is based on the Legendre transform relationship between energy functionals.

The approach simplifies understanding of force calculations in Molecular Dynamics.

Abstract

We give a novel and simple proof of the DFT expression for the interatomic force field that drives the motion of atoms in classical Molecular Dynamics, based on the observation that the ground state electronic energy, seen as a functional of the external potential, is the Legendre transform of the Hohenberg-Kohn functional, which in turn is a functional of the electronic density. We show in this way that the so-called Hellmann-Feynman analytical formula, currently used in numerical simulations, actually provides the exact expression of the interatomic force.