What determines the structures of the group 15 elements?

The structures of black phosphorus (orthorhombic), As, Sb, and Bi (rhombohe dral) have been traditionally interpreted as resulting from a Peierls disto rtion from an ideal simple cubic structure, We examine this idea in detail by calculating the Fermi surfaces of simple cubic phosphorus with the exten ded Huckel tight-binding method and by looking at some simpler models to un derstand the trends. The calculated Fermi surfaces for cubic P are not nest ed, which argues strongly that the structural distortion in black phosphoru s has little to do with Peierls instability. Within the (simple) Huckel app roximation for p-orbital interactions, the Fermi surface nesting is still p erfect, even when interchain (pi-type) interactions are included, Next-near est-neighbor interaction and s-p mixing completely destroy the Fermi surfac e nesting. The observed strong s-p mixing implies that it is just this mixi ng that causes the deformation to the highly stable black phosphorus struct ure, forming lone pairs in the process. We suggest that in order to underst and the trend in the magnitude of distortions in the structures of the grou p 15 elements (P > As > Sb > Ri) s-p mixing should not be neglected even in the heavier elements. (C) 1999 Academic Press.