Symmetry Rules in the Graph Theory of Molecular Orbitals

Abstract

This chapter explores that the use of graph theory for studying problems in quantum chemistry was developed and established as the well-known pairing theorem of the alternant molecules. Huckel molecular orbitals (HMO) have had many applications to organic chemistry and quantum chemists study HMO in various aspects. Because the molecular graphs of HMO have the most apparent topological properties, great success has been achieved using graph theory to study HMO. The pairing theorem can easily be proved by graph theory, stabilities of conjugated molecules is discussed and the (4n + 2) rule is established in the chapter. In correspondence with a molecular graph, there is a characteristic matrix representing the topological properties. The characteristic values of the topological matrix or the characteristic roots of the characteristic equation are also the eigenvalues of the molecule, so it is especially effective to use the method of graph theory in the search for the eigenvalue spectra of a molecule. It emphasizes the structural characteristics of the characteristic matrices and the solutions of the characteristic equations of the molecular graphs, especially those of the symmetrical molecular graphs.