A databank of atomic densities calculated using Hirshfeld partition has been developed which allows for refinement with similar accuracy to Hirshfeld atom refinement without the need for time-consuming wavefunction calculations.

The multipolar model of the valence-electron-density distribution for sulfur has been optimized based on theoretical structure factors for six organic molecules. It is shown that: (a) the ratio of the n(l) values for different l is more important than their absolute values, and (b) the (2,4,6,8) set of n(l) with κ′ refined as a single value is an optimal choice of radial function parameters for S atoms.

A possible model of one-electron reduced density matrices is presented. Potential benefits from a joint refinement of the model from X-ray diffraction and deep inelastic scattering data are illustrated.

An aspherical atom (multipole) refinement model with two sets of atomic deformation functions on each atom is tested with ab initio crystal structure factors on four different molecular crystals. The flexible model provides a quantitatively improved fit to the density and its topological parameters in the bonding regions between atoms.

Cartesian real spherical harmonics for l ≤ 20 and the corresponding normalization factors for the deformation density functions with an accuracy to 35 significant figures have been generated using the Wolfram Mathematica software and converted to a Fortran90 code.

A three part paper on charge density analysis of actinide containing compounds is presented that covers experimental protocols, augmented multipole model building and a comparison of topological analysis of experimental and theoretical electron densities.

Embedded within the MoProViewer program, a new code library, Charger, contains an implementation of the analytical computation of the electrostatic interaction energy based on the multipolar atom. It was used to investigate the electrostatic interaction energies of benchmark dimers and glutathione transferase–benzophenone complexes.

Accurate, simple and efficient formulae for calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model of electron density are presented. The expressions are applied to the determination of the nuclear quadrupole moment of the Fe atom in Fe(CO)₅.

A new aspherical scattering factor formalism was implemented in SHELXL. It relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. The automated atom-type assignment was derived from the invariom formalism.

Refinement of a small-molecule crystal structure against electron diffraction data is now available in the MoPro software with the implementation of electron scattering factors, using a spherical or multipolar atom model.