CHEMICAL APPLICATIONS OF TOPOLOGY AND GROUP-THEORY - 33 - SYMMETRY-FORBIDDEN COORDINATION POLYHEDRA FOR SPHERICAL ATOMIC ORBITAL MANIFOLDS

The four chemically significant spherical manifolds of atomic orbitals are the sp(3), sd(5), sp(3)d(5), and sd(5)f(7) manifolds of 4, 6, 9, and 13 orbitals found in the chemistry of the main-group elements, the early transition metal homoleptic hydrides and alkyls, most other com pounds of the d-block transition metals, and the actinides; respective ly. Coordination geometries with an inversion center (e.g., the octahe dron) or a unique reflection plane passing through no vertices (e.g., the trigonal prism) are symmetry forbidden for the sd5 manifold thereb y accounting for some unusual experimental and computed geometries for six-coordinate early transition metal hydrides and alkyls. The maximu m coordination numbers for polyhedra with inversion centers for the ni ne-orbital sp(3)d(5),d 13-orbital sd(5)f(7) manifolds are 6 and 12 cor responding to the regular octahedron and regular icosahedron, respecti vely, for the most symmetrical manifestations of these coordination nu mbers.