Quantum Mechanics of Mobile Electrons in Conjugated Bond Systems. III. Topological Matrix as Generatrix of Bond Orders

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Abstract
It is shown that in homonuclear conjugated systems the various bond orders and similar quantities can be written as matrix functions of the topological incidence matrix. This entails the existence of a number of useful general relations between these various quantities. The relations include as special cases: Coulson and Rushbrooke's theorem on charge orders in alternants; G. G. Hall's theorem on bond orders in alternants; McWeeny's theorem on the formal charges; Ham and Ruedenberg's correlation between Coulson and Mulliken bond orders for neighbors in alternants; closely related is Ham‐Ruedenberg‐Platt's relation between valence‐bond bond orders and molecular orbital theory. A number of new relations between bond orders are derived and discussed. The generalization from alternants to nonalternants is given particular attention.

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