LCAO Description of Symmetric Molecules by Unified Theory of Finite Graphs

Abstract

LCAO MO descriptions of symmetric molecules have topological and energetic aspects. Topological effects include the point symmetry of the nuclear configuration and the various connections between these points (connectedness). An appropriate mathematical tool for a discussion of molecular topoligies is given by the general theory of graphs. This theory anticipates various properties connected with the topological matrix. Special graphs and their matrix representations which reflect all topological properties of symmetric molecules serve to determine the molecular-orbital-term scheme and the symmetry orbitals for various sorts of molecules. In particular, tetrahedral, square planar, trigonal prismatic, and octahedral molecules are investigated. Finally some remarks are made on the relative choice of parameters in the semiempirical theory as suggested by the consideration of the virial theorem.