Bond-order potentials: Theory and implementation

The background theory and the details required for implementation of bond-older potentials are presented in a systematic fashion. The theory is an O(N) implementation of tight binding that is naturally parallelizable. Further, it is straightforward to show how the lowest-order approximation to the two-site expansion can reproduce the Tersoff potential. The accuracy of the forces is demonstrated by means of constant-energy molecular dynamics, for which the energy is found to be very well conserved. Thus, the method is both an efficient computational method and a useful analytic tool for the atomistic simulation of materials.