Application of tight-binding and bond-order potentials to interfaces and complex phases
Bond-order potentials (BOPs), which are based on the tight-binding approximation for determining the energy of a system of many interacting atoms, allow for solving this problem in the real space. While the previously developed BOPs involve numerical evaluation of the response (Green's) function, the expressions for the bond energy and related interatomic forces are analytical within the formalism of the analytic BOPs.We constructed analytic BOPs for four transition metals Mo, W, Nb and Ta. The parameters entering the potentials are optimised for the equilibrium bcc structure and extensively tested for atomic environments far from equilibrium that have not been included in the fitting procedure. These tests include structural energy differences for different competing structures; tetragonal, trigonal, hexagonal and orthorhombic deformation paths; formation energies of point defects and phonon dispersion relations. Comparison of these calculations with corresponding calculations based on both a DFT method and numerical BOPs demonstrates a very good transferability of the analytic BOPs to atomic structures encountered in lattice defects.