Structure of phosphorus clusters using simulated annealing—P2 to P8

The geometries of low-lying isomers of phosphorus clusters P2 to P8 have been calculated using a density functional (DF) method, combined with molecular dynamics (MD) and simulated annealing techniques. The structures and vibration frequencies are in excellent agreement with experiment in those cases (P2, P4) where spectroscopic data are available. A roof-shaped tetramer is a prominent structural unit in low-lying states of P5, P6, P7, and P8. Contrary to widespread belief, the most stable isomer of P8 is not cubic, but the ‘‘wedge’’ or ‘‘cradle’’ structure found as a structural unit in violet (monoclinic, Hittorf) phosphorus. The energetic ordering and geometrical shapes of the P8 isomers show striking analogies to the corresponding valence-isoelectronic hydrocarbons (CH)8 cubane, cuneane, and 2,2′:4,4′-bis-(bicyclobutyl). The bonding and structural trends in phosphorus clusters are discussed in detail.