ANGULARLY DEPENDENT EMBEDDING POTENTIALS AND STRUCTURAL PREDICTION

The binding energies of equivalent, symmetric lattices such as the thr ee-dimensional f.c.c., b.c.c., simple-cubic and diamond structures, th e two-dimensional hexagonal, square and graphite layers and the one-di mensional linear chain are compared using a first-nearest-neighbour em bedding potential for the bond order which retains the first term in a recently derived many-atom expansion. Unexpectedly we find that the b ond energy of angularly dependent sp-valent systems with identical dim ensionality shows the same square-root dependence on coordination numb er as that predicted by the conventional embedded atom potential or th e angularly independent bond order potentials for s-valent systems. Th us the inclusion of the predicted angular character in the first term of the many-atom expansion for the bond order does not provide any add itional differentiation between the binding energies of different isod imensional structure types.