Acta Cryst. (2013). A69, 549-558 [ doi:10.1107/S0108767313022514 ]
Abstract: The usual residual values are complemented by expectation values based solely on the experimental data and the number of model parameters. These theoretical R values serve as benchmark values when all of the basic assumptions for a least-squares refinement, i.e. no systematic errors and a fully adequate model capable of describing the data, are fulfilled. The prediction of R values as presented here is applicable to any field where model parameters are fitted to data with known precision. For crystallographic applications, F2-based residual benchmark values are given. They depend on the first and second moments of variance, intensity and significance distributions, <2>, <Io2>, <Io2/2>. Possible applications of the theoretical R values are, for example, as a data-quality measure or the detection of systematic deviations between experimental data and model predicted data, although the theoretical R values cannot identify the origin of these systematic deviations. The change in R values due to application of a weighting scheme is quantified with the theoretical R values.
Keywords: theoretical residual values; data-quality indicators; fit-quality indicators; quality indicators.
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