Interrelations of Quantum-Mechanical Quantities Concerning Chemical Reactivity of Conjugated Molecules

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Abstract
It is attempted here to disclose the interrelations underlying the parallelism found in several quantum‐mechanical methods previously proposed to explain chemical reactivity in conjugated molecules. This is carried out mathematically in alternant hydrocarbons and hetero‐alternant molecules mainly by the use of Coulson's integral formulas. In an alternant hydrocarbon, provided a condition is satisfied between minors of the secular determinant, the orders of reactivity of each position predicted by the self‐polarizability, free valence, superdelocalizability, Wheland's localization energy, and Dewar's approximate localization energy by NBMO are shown to be in complete agreement with one another. The relation of the frontier electron density and superdelocalizability is discussed. It is also demonstrated that a nonperturbation treatment for the so‐called static method leads us to the same conclusion as the perturbation treatment. The parallelism of various quantities is discussed in their relation to the effect of heteroatom in heteroalternant molecules.