Analytic bond-order potential for open and close-packed phases

A recent analytic expression for the sigma bond order of sp-valent systems with open structures is generalized to close-packed structures. This requires the retention of both the four-member ring contribution and the second-order embedding-type terms which arise naturally within the tight-binding formalism of bond-order potential theory. This relatively simple analytic expression for the sigma bond order of sp-valent systems with half-full shells is shown to predict excellent bond orders over a wide range of coordination from the open graphitic and diamond lattices through simple cubic to the close-packed face-centered-cubic structures. The critical importance of the ring term on the structural stability of close-packed systems is demonstrated.