Section 25.2.10.4.3. Full-matrix estimates of standard uncertainties

Inversion of the full normal matrix (or of large matrix blocks, e.g. for all positional parameters) enables the precision of individual parameters to be estimated (Rollett, 1970), either with or without the inclusion of the restraints in the matrix. The standard uncertainties in dependent quantities (e.g. torsion angles or distances from mean planes) are calculated in SHELXL using the full least-squares correlation matrix. These standard uncertainties reflect the data-to-parameter ratio, i.e. the resolution and completeness of the data and the percentage of solvent, and the quality of the agreement between the observed and calculated F² values (and the agreement of restrained quantities with their target values when restraints are included).

Full-matrix refinement is also useful when domains are refined as rigid groups in the early stages of refinement (e.g. after structure solution by molecular replacement), since the total number of parameters is small and the correlation between parameters may be large.