Bond-order potential and cluster recursion for the description of chemical bonds: Efficient real-space methods for tight-binding molecular dynamics

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Abstract
The tight-binding model is presented as a successful theory for describing cohesion. It allows for rapid, but accurate, evaluation of electronic properties, total energies, and forces, while being simple enough to allow insight into the nature of bonding. The problem of applying this model to very large systems by diagonalizing the Hamiltonian matrix is discussed. Moments methods provide an efficient way to evaluate energies and forces from the Hamiltonian, even for large systems. However, for systems with sharp features in a broad density of states, many moments are required to achieve convergence. By reference to a moments method [the bond-order potential (BOP)] and a cluster-based method [cluster recursion (CR)], the origin of the need for many moments is explained. In particular, it is found that the inclusion of an exact description of the first-neighbor shell is important for obtaining accurate forces. For strongly covalent systems it also improves the energy convergence. Whereas CR gives rapid convergence with respect to number of levels, BOP is found to give more rapid convergence with respect to CPU time. © 1996 The American Physical Society.