Characteristic Polynomial Expression and Integral Expression for Imaginary Bond–Bond Polarizability. Rules for London Susceptibility and for Ring Current

Abstract

Abstract The McWeeny theory for calculating magnetic properties of conjugated hydrocarbons is studied from a graph-theoretical point of view. Imaginary bond–bond polarizability is expressed in terms of characteristic polynomial. The expression clarifies the dependence of imaginary bond–bond polarizability on the structure. It is shown that the expression enables one easily to derive the equations for the quantity proved in two previous papers. The characteristic polynomial expression for imaginary bond–bond polarizability is rewritten in Coulson’s integral form. The rules for London susceptibility and for ring current are proved from the integral expression.