Distributed Multipole Analysis:  Stability for Large Basis Sets

The distributed multipole analysis procedure, for describing a molecular charge distribution in terms of multipole moments on the individual atoms (or other sites) of the molecule, is not stable with respect to a change of basis set, and indeed, the calculated moments change substantially and unpredictably when the basis set is improved, even though the resulting electrostatic potential changes very little. A revised procedure is proposed, which uses grid-based quadrature for partitioning the contributions to the charge density from diffuse basis functions. The resulting procedure is very stable, and the calculated multipole moments converge rapidly to stable values as the size of the basis is increased.