From atoms to a data bank: optimizing transferability of electron-density symmetry.

The multipole model provides a significantly improved description of electron density compared with the spherical atom approximation and is widely applied in the crystallographic refinement of X-ray diffraction data. The multipolar atom types from theory and statistical clustering (MATTS) data bank collects multipole model parameters for atom types. These parameters are derived from quantum chemical calculations performed on experimental geometries of model molecules and rely on the concept of transferability between chemically similar atoms. An essential component of each atom type is the definition of the local coordinate system (LCS) and the symmetry of the electron density, which so far have been selected individually using expert judgment during data bank construction. In this work, we focus on the electron densities of atoms from model molecules and atom types from the MATTS data bank. We introduce a systematic procedure in which symmetry constraints are removed during multipole model refinement of model molecules and multiple types of LCS are tested using chemically meaningful directions. We examine how different LCS choices influence the pseudosymmetry, the apparent symmetry of electron density, identified empirically based on the refined multipole model parameters and their statistical significance. Our results show that refinement without symmetry constraints improves the representation of pseudosymmetry and, in some cases, leads to changes in both the values of the multipole model parameters and the assigned symmetry of the electron density. We propose an optimal LCS for each topological kind of atom type and provide clear criteria for symmetry assignment. This work contributes to the future development of the MATTS data bank with improved descriptions of LCSs and transferability of electron-density symmetry.