Crystal structure refinements with generalized scattering factors. III. Refinement of 1, 1′-azobiscarbamide and melamine, 2,4,6-triamino-s- triazine, at the octopole level

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Abstract
Single crystal x‐ray diffraction data for 1,1′‐azobiscarbamide, C2H4N4O2, and melamine (2,4,6‐triamino‐s‐triazine), C3N6H6, have been refined using one‐center generalized x‐ray scattering factors through the octopole level. This work is an extension of previous work in which the crystal structures of these compounds were refined using one‐center dipole and quadrupole population parameters and two‐center monopole paramaters to account for the bonding electron density. The one‐center octopole model accounts for bonding electron density more efficiently than the two‐center model. Radial parameters in the Slater‐type functions used to compute scattering factors were also refined. In both compounds, radial parameters about 7% smaller than molecular optimized values were found. Interatomic distances are not very sensitive to the model. In melamine, all C–N distances increase by about 0.004 Å for models with octopoles. Also, if octopoles are used on the nitrogen atoms, all N–H distances become approximately equal and have values consistent with the centroid of the hydrogen atom electron density being displaced about 0.07–0.08 Å into the bond. By using the molecular symmetry and applying appropriate linear constraints to the least‐squares matrix, dramatic improvements can be made over a spherical atom model with very few additional parameters. Electric field gradients at the nuclei (i.e., atomic positions determined by the refinement of the x‐ray data) have been calculated for all atoms. These calculations included penetration integrals from the multipole functions of all atoms within a 7 Å radius.