Ring magnetic susceptibilities in conjugated hydrocarbons

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Abstract
In the context of an SCF π-electron theory an exact expression is derived which yields xπ ⊥, the total π-electron contribution to the magnetic susceptibility perpendicular to the plane of a polycyclic conjugated hydrocarbon. Once given the first-order correction to the bond-order matrix of the molecule in question (which, in the present calculation, is obtained via a coupled Hartree-Fock procedure), this expression makes no further appeal to the London integral approximation. The terms which occur in the expression for xπ ⊥ due to the ‘integrated current densities’ correspond to those which would have arisen if the London approximation had been invoked, the remaining terms being, in general, non-zero if this approximation is not made. The relative ‘integrated current densities’ associated with the various constituent rings in 12 molecules agree well with the corresponding ‘ring current’ intensities estimated via the London-Pople-McWeeny method. It is shown that for polycyclic conjugated systems which are predominantly diamagnetic, the total xπ ⊥ for a particular molecule can to a good approximation be partitioned into a sum of individual contributions from each of its constituent rings. Hence the intuitively appealing idea of a ‘ring susceptibility’ can be preserved, even when the whole of xπ ⊥, and not just that part of it due to ‘ring currents’, is calculated. When an appropriate set of Pascal-type constants is derived from the experimental data and calculated xπ ⊥ for benzene substantial agreement with experiment is found for a wide range of benzenoid hydrocarbons. This is evidence for regarding π-electron ‘ring susceptibility’ as an additive property within each individual molecule of this type.

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