Interatomic Potentials and Force Fields

A molecular dynamics simulation is only as good as the forces it uses, and those come from interatomic potentials and force fields, mathematical models of how atoms attract, repel and bond as a function of their arrangement.

Definition

An interatomic potential or force field is a function giving the potential energy of a system of atoms in terms of their positions, whose negative gradient provides the forces used to drive a molecular dynamics or Monte Carlo simulation.

Scope

This topic covers the models that supply forces in classical simulation: pair potentials such as Lennard-Jones, many-body metallic potentials such as the embedded-atom method, and molecular force fields with bonded and non-bonded terms. It addresses how potentials are parametrized, their transferability, and how long-range interactions are handled.

Core questions

• How do pair potentials like Lennard-Jones capture repulsion and attraction between atoms?
• Why do metals and covalent solids require many-body rather than pairwise potentials?
• How are molecular force fields decomposed into bonded and non-bonded terms?
• How are long-range electrostatic interactions summed efficiently?

Key theories

Pair potentials

The Lennard-Jones potential models a steep short-range repulsion and a weaker long-range attraction with two parameters, giving a simple yet realistic description of noble gases and a standard model for simulation.

Many-body and embedded-atom potentials

In metals the energy of an atom depends on the local electron density from all its neighbors, captured by the embedded-atom method and related many-body potentials that pairwise models cannot reproduce.

Molecular force fields

Force fields for molecules sum bonded terms for bond stretching, angle bending and torsion with non-bonded van der Waals and electrostatic terms, parametrized against experiment and quantum calculations.

Clinical relevance

The choice of potential determines whether a simulation faithfully reproduces structure, phase behavior, mechanical response and reaction energetics, making force-field development central to materials modeling, soft matter and biomolecular simulation.

History

Lennard-Jones introduced his pair potential in the 1920s from gas equation-of-state data; richer many-body potentials such as the embedded-atom method appeared in the 1980s for metals, and biomolecular force fields were developed in parallel, with machine-learned potentials emerging more recently.

Debates

Transferability versus accuracy of force fields

Potentials fit to one set of conditions may not transfer to others, and there is ongoing tension between simple, transferable forms and highly accurate but narrowly fitted potentials, including modern machine-learned ones.

Key figures

• John Lennard-Jones
• Murray Daw
• Michael Baskes

Seminal works

• lennardjones1924
• daw1984

Frequently asked questions

Why can't a single potential describe all materials?

Different bonding types, metallic, ionic, covalent and van der Waals, have qualitatively different physics, so a form tuned for one tends to fail for another. Potentials are therefore developed and validated for specific classes of systems and conditions.

Why are long-range electrostatics treated specially?

Coulomb interactions decay slowly and cannot simply be truncated without artifacts, so methods such as Ewald summation and its mesh-based variants are used to sum them accurately and efficiently under periodic boundary conditions.