Optimal local axes and symmetry assignment for charge-density refinement

In the perspective of building an expanded electron-density library based on multipolar modelling for common chemical atom types, new consistent local axes systems are proposed. Optimal symmetry constraints can consequently be applied to atoms and a large number of multipole populations can be fixed to a zero value. The introduction of symmetry constraints in the multipolar refinement of small compounds allows a reduction in the number of multipolar parameters stored in the library and required for the description of the atomic electron density. In a refinement where the symmetry constraints are not applied, the use of optimal axes enables the deviations from the local pseudo-symmetry to be highlighted. The application of symmetry constraints or restraints on multipoles is more effective when the axes are in accordance with the local geometry of the atom and can lead to improved crystallographic R_free residuals. The new local axes systems, based on two or three atom neighbours, can also be usefully applied to the description of transition metal complexes.