The Interplay Between Graph Theory and Molecular Orbital Theory

Abstract

Molecular orbital (MO) theory, at various levels of approximation, is nowadays a standard tool of chemists.1,2 Similarly, chemical graph theory is also becoming a powerful device in the hands of chemists.3-5 A graph-theoretical analysis of the MO theory at the level of the Huckel approximation was carried out by a number of authors, e.g.6-10 A pioneering work on the relationship between graph theory and the MO theory at the PPP level was recently accomplished by Balasubramanian.11 The complexity of this analysis is much higher than that in the case of graph-theoretical analysis of Huckel MO theory. However, this result is very valuable, because it shows that the graph-theoretical analysis of the MO theory at the higher levels of approximation is also possible. Nevertheless, we will consider in the present article only the interplay between the MO theory at the Huckel level and graph theory. In this way the analysis will be simple, clear and easily understood by a chemical community at large. Besides, the HMO theory in spite of all of its shortcomings’ is still being used by many a chemist, e.g.,12–21 as a convenient device for qualitative rationalization of a variety of chemical phenomena.