Rapidly convergent bond order expansion for atomistic simulations.

An O(N) and rapidly convergent method for calculating the bond order potential and forces for the atomistic simulation of covalent systems is described. A derivation of a novel many-atom expansion, which allows the Green's functions, not only to handle the symmetry problem correctly but also to retrieve equivalence between the site-diagonal and intersite descriptions for the bond energy, is given. The convergence of the bond orders and bond energies is demonstrated for d-valent transition metals.