Comparison of analytic and numerical bond-order potentials for W and Mo

TL;DR

This paper compares numerical and analytic bond-order potentials for tungsten and molybdenum, showing that analytic BOPs provide better force calculations and improved predictions of defect energies and phonons.

Contribution

It provides a detailed comparison demonstrating that analytic BOPs offer exact force calculations and enhanced accuracy over numerical BOPs for refractory metals.

Findings

Analytic BOPs and numerical BOPs agree well on energy calculations.

Forces in analytic BOPs are exact negative energy gradients.

Analytic BOPs improve defect and phonon predictions.

Abstract

Bond-order potentials (BOPs) are derived from the tight-binding (TB) approximation and provide a linearly-scaling computation of the energy and forces for a system of interacting atoms. While the numerical BOPs involve the numerical integration of the response (Green's) function, the expressions for the energy and interatomic forces are analytical within the formalism of the analytic BOPs. In this paper we present a detailed comparison of numerical and analytic BOPs. We use established parametrisations for the bcc refractory metals W and Mo and test structural energy differences; tetragonal, trigonal, hexagonal and orthorhombic deformation paths; formation energies of point defects as well as phonon dispersion relations. We find that the numerical and analytic BOPs generally are in very good agreement for the calculation of energies. Different from the numerical BOPs, the forces in the analytic BOPs correspond exactly to the negative gradients of the energy. This makes it possible to use the analytic BOPs in dynamical simulations and leads to improved predictions of defect energies and phonons as compared to the numerical BOPs.