Expansion of scalar validation criteria to three dimensions: The R tensor

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42 Scopus citations


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.

Original languageEnglish
Pages (from-to)157-162
Number of pages6
JournalActa Crystallographica Section A: Foundations of Crystallography
Issue number2
StatePublished - 2000

ASJC Scopus subject areas

  • Structural Biology


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