Extracting charge density distributions from diffraction data: a model study on urea

The quality of the extraction of electron density distributions by means of a multipole refinement method is investigated. Structure factors of the urea crystal have been obtained from an electron density distribution (EDD) resulting from a density function calculation with the CRYSTAL95 package. To account for the thermal motion of the atoms, the stockholder-partioned densities of the atoms have been convoluted with thermal smearing functions, which were obtained from a neutron diffraction experiment. A POP multipole refinement yielded a good fit, R = 0.6%. This disagreement factor is based on magnitudes only. Comparison with the original structure factors gave a disagreement of 0.8% owing to differences in magnitude and phase. The fitted EDD still showed all the characteristics of the interaction density. After random errors corresponding to the experimental situation were added to the structure factors, the refinement was repeated. The fit was R = 1.1%. This time the resulting interaction density was heavily deformed. Repetition with another set of random errors from the same distribution yielded a widely different interaction density distribution. The conclusion is that interaction densities cannot be obtained from X-ray diffraction data on non-centrosymmetric crystals.