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Assessment of quality in crystal structure determination entails analysis of global statistics. In data reduction, quality is assessed using Rmerge and mean I
σ(I). Progress in structure solution and refinement is checked by the goodness of fit, variants of the R index, Rcryst, and its cross-validation counterpart, Rfree. These statistics are useful and provide a convenient means of comparison but their scalar nature renders them unable to capture the essence of three-dimensional entities such as diffraction patterns and molecular models. A simple general method to quantify spatial variations in scalar statistics has been developed. In it, a symmetric matrix, the R tensor, is used to represent the local average residual as a function of diffraction geometry. An effective value of the statistic in question can then be found for any direction in reciprocal space. Differences between these effective R indices for individual reflections or groups of reflections can help to steer refinement strategy and assess the final structure.
σ(I). Progress in structure solution and refinement is checked by the goodness of fit, variants of the R index, Rcryst, and its cross-validation counterpart, Rfree. These statistics are useful and provide a convenient means of comparison but their scalar nature renders them unable to capture the essence of three-dimensional entities such as diffraction patterns and molecular models. A simple general method to quantify spatial variations in scalar statistics has been developed. In it, a symmetric matrix, the R tensor, is used to represent the local average residual as a function of diffraction geometry. An effective value of the statistic in question can then be found for any direction in reciprocal space. Differences between these effective R indices for individual reflections or groups of reflections can help to steer refinement strategy and assess the final structure.
