View source for SHELXL

== 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, 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. <br>

If high resolution data are available, it may be possible to obtain rigorous standard uncertaintiess by matrix inversion. The structure should first be refined to convergence with CGLS, setting the second parameter to –1 to keep the free-R data separate, then a further refinement should be performed against all data by deleting the second CGLS parameter, and finally a single full-matrix cycle should be performed (‘L.S. 1’) with zero damping and a zero shift multiplier (‘DAMP 0 0’). Often ‘BLOC 1’ will be used so that the (anisotropic) displacement parameters are fixed in this final cycle, which makes the matrix appreciably smaller and more stable on inversion, but still allows the estimation of realistic standard deviations on all geometrical parameters. BOND, RTAB, HTAB and MPLA instructions may be needed to define the dependent parameters for which esds are required, and the connectivity table used by BOND may need to have extra 'bonds' (e.g. to metal ions) added by BIND if they are not generated automatically (rare).<br>

Given high-resolution data (better than say 1.5 &Aring;) all restraints should be removed: lines begining with SIMU, DELU, ISOR, BUMP, DFIX, DANG, CHIV, FLAT and NCSY should be deleted or preceded by "REM". Alternatively, one can determine standard uncertainties in the Bayesian sense that take all available knowledge into account by retaining all the restraints. This may be done at more modest resolution (say 2.5A or better). To obtain mean values and s.u. of e.g. distances or chiral volumes that occur several times in a structure, use DFIX or CHIV with "free variables" (see below).<br>