Analytical and numerical calculations of interatomic forces and stresses

Abstract

Atomistic simulation methods such as molecular dynamics require an efficient calculation of interatomic forces and stresses from pre–defined interatomic potentials. Both analytical and numerical approaches can be used to do this. Analytical approach directly calculates forces and stresses using analytical formulae, and can therefore yield accurate results. However, the force and stress expressions may become extremely complicated as the complexity level of the potential increases, resulting in a prolonged development cycle to implement new potentials. Numerical approach uses finite difference method to evaluate forces and stresses through simple calculation of energies at selected perturbations of crystal configurations. The method can be quickly implemented and tested for any potentials. However, it may result in significant numerical errors. We have compared analytical and numerical calculations of interatomic forces and stresses in molecular dynamics, and identified the conditions where numerical method can be successfully used without significant errors.

Keywords:

• Molecular dynamics
• Interatomic potential
• Semiconductors
• Stress