Determination of Forces from a Potential in Molecular Dynamics

TL;DR

This paper details the precise derivation of forces from potentials in molecular dynamics, ensuring energy preservation and addressing implementation issues in multi-scale MD systems.

Contribution

It provides a rigorous derivation of forces from potentials and demonstrates energy conservation within a multi-scale MD framework.

Findings

Forces derived from potentials preserve energy in MD simulations.

Implementation details ensure local mechanical equilibrium.

Supports development of multi-scale MD systems.

Abstract

In Molecular Dynamics (MD), the forces applied to atoms derive from potentials which describe the energy of bonds, valence angles, torsion angles, and Lennard-Jones interactions of which molecules are made. These de finitions are classic; on the contrary, their implementation in a MD system which respects local equilibrium of mechanical conditions is usually not described. The precise derivation of the forces from the potential and the proof that their application preserves energy is the object of this note. This work is part of the building of a multi-scale MD system, presently under development.