Verification of the Kuhn—Thomas Sum Rule in the Framework of Some Recent Polarizability Theories for Molecular Aggregates

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Abstract
The semiclassical formalism for molecular aggregates, presented by Nesbet, is compared to the corresponding classical treatment of DeVoe. A development of the first theory allows the determination of the complex polarizability tensor representing a given electronic transition. Another development allows the computation of the energy absorbed by a molecular aggregate. This energy expression is of quadratic form with respect to the incident field, which permits the definition of a tensorial extinction coefficient and a tensorial oscillator strength. The same results are obtained with the theory of DeVoe. The preceding tensors are calculated for an aggregate of two nonidentical molecules (each molecule is assumed to be represented by only one polarizability). A special class of spatial configurations of the molecules of an aggregate is found, for which the tensorial oscillator strength remains invariant. The scalar oscillator strength is invariant whatever the aggregate spatial configuration is. These results show that the Kuhn—Thomas sum rule is verified in this particular case (a molecular dimer) of two electrons coupled by Coulombic forces.

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