Optimization of the main-group and late-transition-metal elemental structures: Gallium, boron, zinc, cadmium, and manganese

We demonstrate that a tight-binding Hamiltonian, to which a pairwise additive repulsive potential has been added, can qualitatively and semiquantitatively account for the elemental structures of gallium, boron, zinc, cadmium, and manganese. These structures represent the most complex structures found in the lighter elements of the Periodic Table (N<40). We show that these structures result from the interplay of the number of valence electrons, the overlap of atomic orbitals, and geometrical features such as the number of triangles of bonded atoms and the angles between bonds. To illustrate this last point, we use the method of moments in a useful quantitative fashion. Finally, we account for the variation in cell parameters observed in binary noble-metal and main-group hexagonal closest-packed structures.