ABSTRACT
In the early days of quantum chemistry, two distinct theoretical approaches emerged: the molecular orbital (MO) theory and the valence bond (VB) theory. The former is an extension of the notion of atomic orbitals from atoms to molecules, which led to the Hückel molecular orbital (HMO) calculations, which were applied to benzene and similar conjugated systems by Hückel and others. The representative book on this is E. Hückel’s Fundamentals of Theory of Unsaturated Aromatic Compounds, published in 1938 [1]. The second theory is a generalization of the calculations of Heitler and London on the H2 molecule extended to conjugated systems of organic chemistry. The representative book on this is Pauling’s The Nature of the Chemical Bond and the Structure of Molecules and Crystals, to be published in 1939, the next year [2]. Interestingly, although conceptually and computationally different, both methods, the MO and VB, found early contact with graph theory. As already mentioned, only 12 years after Kekulé introduced a cyclic valence structure for benzene, Sylvester recognized the graph theoretical content of Kekulé valence structures [3,4]. The graph theoretical content of HMO is, in this respect, of a more recent time, the 1970s, which is almost 100 years later, although in 1956 Günthard and Primas published a paper on the connection between the theory of graphs and the MO theory of molecules with conjugated bond. However, by mid-1970, graph theory was confused and identied by many with HMO although HMO, at best, parallels certain sections of spectral graph theory.
