Classical Potentials and Simulation Methods

This 1994 handbook chapter serves as a practical user guide for the Embedded-Atom Method (EAM). It details the theoretical derivation from density-functional theory, synthesizes related methods like the Glue Model, and provides a complete tutorial on fitting potentials, illustrated with a specific implementation for the Ni-Al-B system.

This 1993 review systematizes the Embedded-Atom Method (EAM) as a practical semi-empirical approach for metallic systems. It synthesizes theory, applications, and connections to related methods while addressing the limitations of pair potentials.

This paper validates the homogeneous Evans method for calculating thermal conductivity against experimental Argon data. It demonstrates broad agreement across the phase diagram but identifies significant non-monotonic behavior and enhanced long-time tails near the critical point.

Proposes the Hyperbolic Algorithm for Euclidean field theory simulations. By adding a second-order fictitious time derivative to the Langevin equation, the method reduces systematic errors from O(ε) down to O(ε²).

Stillinger and Weber propose a 3-body interaction potential that stabilizes the diamond crystal structure of silicon and reproduces liquid properties through molecular dynamics, addressing the inability of standard pair potentials to model tetrahedral semiconductors.

This work validated classical Molecular Dynamics for simulating liquids, revealing the ‘cage effect’ in velocity autocorrelation and establishing predictor-corrector integration algorithms for N-body problems.

A two-dimensional analytical potential energy surface introduced in 1979 for testing optimization algorithms. It features three minima and curved transition pathways that evaluate an algorithm’s ability to navigate non-trivial topologies.

The foundational 1984 paper introducing EAM, a semi-empirical many-body interatomic potential that incorporates density functional theory concepts to accurately simulate metallic systems while maintaining computational efficiency comparable to pair potentials.

Torrie and Valleau’s 1977 paper introducing importance sampling with non-physical distributions to overcome the sampling gap problem in Monte Carlo free-energy calculations, particularly for phase transitions.

Lennard-Jones’s 1932 theoretical paper applying quantum mechanical potential energy surfaces to gas-solid interactions, providing the first unified framework explaining both physisorption and chemisorption as different regions of the same energy landscape.