Broad Motivation and Aim - Graph Theory

Valence-Bond (VB) and Molecular-Orbital (MO) theories both were clearly formulated by the end of the first decade of quantum mechanics. Of course VB theory is connected to early conceptual roots in chemistry, as emphasized by Rumer [1] and more particularly by Pauling, in a review [2] and then in his masterwork [3] The Nature cfiJte Chemical Bond. Thence for some jjeriod of time VB theory seems in the chemical community to have been viewed quite favorably. 

The chemical relevance of MO theory was perhaps clearly demonstrated first by Hiickel [4] in the early 1930s, but the dominance of MO theory did not set in until after further conceptual development from the English school and the systematic computational self-consistent-field format of Roothaan [5] (and Hall [6]). Still within the MO-theoretic firamework various theorems were found [7,8], the Woodward-Hofftnann rules for concerted reactions were developed [9,10], and powerful black-box MO-based computer programs became both widely available and widely utilized. 

But presumably because of VB theory s connections to classical chemical bonding concepts, work continued in this area and has even intensified in recent decades, there now being many new-theorematic, conceptual, and computational developments, as evidenced in the reviews in the-book [11] 

Valence Bond Theory and Chemical Structure, where also some further detail in the here highly summarized history is provided. 

Here then it is intended to note some inter-relations between VB and MO theories, particularly as regards general predictive correspondences. With the focus on generality of correspondences the emphasis naturally shifts to the simpler (typically semiempirical) models for which it is easier to obtain general (e.g. theorematic) results. Thence here attention is focused on the rather well studied such models for n-electron networks in neutral (i.e. non-ionic) organic molecules. 

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