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

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