About systematic errors in charge-density studies.

The formerly introduced theoretical R values [Henn & Schönleber (2013). Acta Cryst. A69, 549-558] are used to develop a relative indicator of systematic errors in model refinements, R(meta), and applied to published charge-density data. The counter of R(meta) gives an absolute measure of systematic errors in percentage points. The residuals (Io - Ic)/σ(Io) of published data are examined. It is found that most published models correspond to residual distributions that are not consistent with the assumption of a Gaussian distribution. The consistency with a Gaussian distribution, however, is important, as the model parameter estimates and their standard uncertainties from a least-squares procedure are valid only under this assumption. The effect of correlations introduced by the structure model is briefly discussed with the help of artificial data and discarded as a source of serious correlations in the examined example. Intensity and significance cutoffs applied in the refinement procedure are found to be mechanisms preventing residual distributions from becoming Gaussian. Model refinements against artificial data yield zero or close-to-zero values for R(meta) when the data are not truncated and small negative values in the case of application of a moderate cutoff Io > 0. It is well known from the literature that the application of cutoff values leads to model bias [Hirshfeld & Rabinovich (1973). Acta Cryst. A29, 510-513].