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.

• Received 9 September 1993

DOI:https://doi.org/10.1103/PhysRevLett.71.3842