Is it possible to derive quantitative information on polarization of electron density from the multipolar model?

The accuracy of electrostatic properties estimated from the Hansen-Coppens multipolar model was verified. Tests were carried out to determine whether the multipolar model is accurate enough to study changes of electrostatic properties under the influence of a crystal field. Perturbed and unperturbed electron densities of individual molecules of amino acids and dipeptides were obtained from cluster and perturbation theory calculations. This enabled the changes in electrostatic properties values caused by polarization of the electron density to be characterized. Multipolar models were then fitted to the subsequent theoretical electron densities. The study revealed that electrostatic properties obtained from the multipolar models are significantly different from those obtained directly from the theoretical densities. The electrostatic properties of isolated molecules are reproduced better by multipolar models than the electrostatic properties of molecules in a crystal. Changes of electrostatic properties caused by perturbation of electron density due to the crystal environment are barely described by the multipolar model. As a consequence, the electrostatic properties obtained from multipolar models fitted to the perturbed theoretical densities derived either from cluster or periodic calculations do not differ much from those estimated from multipolar models fitted to densities of isolated molecules. The main reason for this seems to be related to an inadequate description of electron-density polarization in the vicinity of the nuclei by the multipolar model.