Interatomic potentials: Achievements and challenges

TL;DR

This paper reviews various empirical interatomic potentials, discussing their design, constraints, and applications in simulating atomic systems, aiming to guide future advancements and combinations of these models.

Contribution

It provides a pedagogical overview of existing interatomic potentials, analyzing their functional forms, constraints, and potential for integration to enhance simulation capabilities.

Findings

Analysis of constraints from potential functional forms

Discussion on violations of Cauchy relations and their implications

Insights into the ratio of boiling to melting temperatures for different potentials

Abstract

Interatomic potentials approximate the potential energy of atoms as a function of their coordinates. Their main application is the effective simulation of many-atom systems. Here, we review empirical interatomic potentials designed to reproduce elastic properties, defect energies, bond breaking, bond formation, and even redox reactions. We discuss popular two-body potentials, embedded-atom models for metals, bond-order potentials for covalently bonded systems, polarizable potentials including charge-transfer approaches for ionic systems and quantum-Drude oscillator models mimicking higher-order and many-body dispersion. Particular emphasis is laid on the question what constraints ensue from the functional form of a potential, e.g., in what way Cauchy relations for elastic tensor elements can be violated and what this entails for the ratio of defect and cohesive energies, or why the ratio of boiling to melting temperature tends to be large for potentials describing metals but small for short-ranged pair potentials. The review is meant to be pedagogical rather than encyclopedic. This is why we highlight potentials with functional forms sufficiently simple to remain amenable to analytical treatments. Our main objective is to provide a stimulus for how existing approaches can be advanced or meaningfully combined to extent the scope of simulations based on empirical potentials.