Practical schemes for distributed polarizabilities

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Abstract
A general formalism for distributed molecular polarizabilities has already been established [1]. It requires the matrix elements of the multipole moment operators to be partitioned between a number of regions of the molecule. In the present paper, various partitioning methods are investigated. One partitioning scheme, based on Gauss-Hermite quadrature, stands out as more stable than others which can be applied to general geometries. Symmetry requirements, however, are not automatically fulfilled when this scheme is used, so symmetrization schemes are also discussed. Calculations of the Rayleigh-Schrödinger induction energy using these distributed polarizabilities are used as a guide for judging the usefulness of the partitioning schemes. Morokuma analysis is used as a standard for comparison. The results support the view that the partitioning scheme based on Gauss-Hermite quadrature is preferred because of its greater stability.