Net atomic charges and molecular dipole moments from spherical-atom X-ray refinements, and the relation between atomic charge and shape

Refinement of the population and radial dependence of the spherical atomic valence shell is introduced in a general crystallographic least-squares program. The radial dependence is described by an expansion-contraction parameter κ, which, in the nine data sets tested, indicates contraction of positively and expansion of negatively charged atoms in agreement with theoretical concepts such as those incorporated in Slater's analytical rules for atomic orbitals. H atoms appear more contracted than concluded previously on the basis of a comparison of X-ray and neutron thermal parameters of sucrose. An average value of 1.40 for the radial contraction of H is used in structures for which no neutron thermal parameters are available. The resulting net charges are used to calculate X-ray molecular dipole moments whose magnitude and direction are in good agreement with theoretical and other experimental results, though some differences may be expected because of matrix effects. Net molecular charges in the one-dimensional conductor TTF-TCNQ agree with results obtained earlier by direct integration of the charge density over the molecular volume. A charge transfer from Si to V in the superconducting alloy V₃Si is also in agreement with earlier results.