Critical examination of the radial functions in the Hansen–Coppens multipole model through topological analysis of primary and refined theoretical densities

A double-zeta (DZ) multipolar model has been applied to theoretical structure factors of four organic molecular crystals as a test of the ability of the multipole model to faithfully retrieve a theoretical charge density. The DZ model leads to significant improvement in the agreement with the theoretical charge density along the covalent bonds and its topological parameters, and eliminates some of the bias introduced by the limited flexibility of the radial functions when a theoretical density is projected into the conventional multipole formalism. The DZ model may be too detailed for analysis of experimental data sets of the accuracy and resolution typically achieved at present, but provides guidance for the type of algorithms to be adapted in future studies.