Empirical correction for resolution- and temperature-dependent errors caused by factors such as thermal diffuse scattering

Charge density investigations of the compounds [Mg{(pz*)₃C}₂] (1) (pz* = 3,5-dimethylpyrazolyl) and (Ph₂P=S)C₁₄H₉ (2) show two disturbing features in each case. First, the models derived from high-resolution data sets at different temperatures differ significantly. Additionally, residual density appears close to or even at the atomic positions, especially for data sets measured at 100 K. This indicates significant errors that could be caused by thermal diffuse scattering (TDS). A reduction of the integration box size leads to a substantial improvement in the model quality and removes the differences in the models. At the same time it indicates TDS to be the reason for these errors. However, this method is very time consuming and an alternative is needed. In endeavouring to improve the method, it was noticed that the refinement of resolution-dependent scale factors can be employed as a validation tool to detect such errors. In a nested interval approach, a correction factor {α = a[sin(θ)/λ]² + b[sin(θ)/λ]³} is determined that minimizes these errors and improves the model quality. This model is now based on refinement of only a single scale factor.