On conjugated molecules with identical topological spectra

Abstract

Properties of molecular graphs having identical topological spectra are investigated in some detail. It has been established that whole families of isospectral graphs can be derived from a molecular skeleton of vinyl benzene. A pair of isospectral graphs are obtained by an exchange of two non-equivalent residuals attached to particular sites of the skeleton. Additional pairs of isospectral graphs can be derived from related skeletons in which ortho positions of vinyl benzene are occupied by substituents. No constraints have to be imposed on the nature and form of the residuals or the substituting groups. This allows construction of larger isospectral systems including polymeric species. The theoretical foundation for the construction of isospectral graphs described in this work rests on the factorization of the eigenvalue problem of the adjacency matrix associated with molecular graphs which is analogous to a fragmentation of a secular determinant of a Hückel MO problem as outlined some time ago by Heilbronner. A formal proof of the procedure, expressed in a symbolic form, is presented in the Appendix. A discussion of some interesting features of isospectral systems reflected in special properties of topological eigenfunctions is presented.

Reported in part at the Quantum Chemistry School, Leningrad, USSR, December 1973.

Reported in part at the Quantum Chemistry School, Leningrad, USSR, December 1973.

Notes

Reported in part at the Quantum Chemistry School, Leningrad, USSR, December 1973.

Additional information

Notes on contributors

M. Randić

Also visiting the Chemistry Department, University of Oxford, Oxford, England.