  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.
