Determination of distributed polarizabilities from a statistical analysis of induction energies

A method is proposed to determine models of distributed polarizabilities fr om induction energies calculated quantum chemically for a molecule polarize d by a point charge running over a grid of points. Once a polarizability mo del is chosen, sets of distributed polarizability components recovering exa ctly the induction energy for a selection of grid points are obtained by a matrix inversion. Distribution functions of the polarizability components a re then built and the set of the most probable values for each polarizabili ty component of the model is determined. The quality of a model is assessed by its ability to reproduce molecular polarizabilities and induction energ ies as accurately as possible. In addition, the distribution function appro ach provides valuable help to detect ill-defined components and, thus, sele ct the optimal models. Several models of distributed polarizabilities for t he water? methanol, and acetonitrile molecules are presented to illustrate the proposed approach.