Molecular orbitals of solids

The molecular orbital contains, in general, a linear combination of orbitals of all equivalent atoms in the molecule, and for its construction one can use the method projection operators or induced representation. In this paper, for the expansion of space group representations obtained on induction of representation of local symmetry groups into a space group, the authors use the Mackey linkage theory and the generalized Frobenius reciprocity theorem. On the basis of the Mackey theory a classification of the chemical interactions in crystals composed of one orbital was obtained. Molecular orbitals for the O/sub h//sup 7/ groups of diamond were obtained, and a symmetric analysis of the zone structure of diamond, silicon, and germanium was performed.