Tensor Formalism for Coulomb Interactions and Asymptotic Properties of Multipole Expansions

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Abstract
A tensor notation for electric multipole interactions between molecular charge distributions is developed and applied to the evaluation of first- and second-order interaction energies. An equivalence theorem between cylindrically symmetric and linear assemblies of charge is established. The mathematical implications of using a multipole Taylor expansion in regions of configuration space where the series has no validity is discussed for the first and second orders of perturbation theory.

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