Structure refinement

Hall, S. R.; Fitzgerald, P. M. D.; McMahon, B.

doi:10.1107/97809553602060000734

International
Tables for
Crystallography
Volume G
Definition and exchange of crystallographic data
Edited by S. R. Hall and B. McMahon

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. G. ch. 3.2, pp. 98-100

Section 3.2.3.1. Structure refinement

S. R. Hall,^a ^* P. M. D. Fitzgerald^b and B. McMahon^c

^a School of Biomedical and Chemical Sciences, University of Western Australia, Crawley, 6009, Australia,^bMerck Research Laboratories, Rahway, New Jersey, USA, and ^cInternational Union of Crystallography, 5 Abbey Square, Chester CH1 2HU, England
Correspondence e-mail: syd@crystal.uwa.edu.au

3.2.3.1. Structure refinement

| top | pdf |

The data items in these categories are as follows:

(a) REFINE [Scheme scheme26]

(b) REFINE_LS_CLASS [Scheme scheme27]

The bullet ( $[\bullet]$ ) indicates a category key. The arrow ( $[\rightarrow]$ ) is a reference to a parent data item. The dagger ( $[\dagger]$ ) indicates a deprecated item, which should not be used in the creation of new CIFs.

Example 3.2.3.1 shows how the data names in the REFINE category are used. Most of the dictionary entries are detailed and fully explanatory, so only a few points that might require special care are mentioned here.

Example 3.2.3.1. Summary of refinement results.

[Scheme scheme28]

Two groups of older data names have been superseded by new names that are functionally equivalent, but represent a more correct terminology. One group is of names that include the component `_obs' used to indicate `observed' reflections; this has been replaced by the component `_gt' indicating that the measured values are greater than a threshold recorded elsewhere (as the value of _reflns_threshold_expression). The other group replaces the component `_esd' (for estimated standard deviation) with `_su' (for standard uncertainty).

A number of data names describe the extinction coefficient and the method used to determine it. Note that a default value ( Zachariasen) is given in the dictionary for the method ( _refine_ls_extinction_method); this only makes sense if this data item is missing from the data block but a value of _refine_ls_extinction_coef is present. This can complicate the design of software to read CIFs, which might assign to any missing data name a default value given by the dictionary.

Care is also needed with _refine_ls_hydrogen_treatment, which describes the treatment of hydrogen atoms in the refinement. Clearly, the data item only has meaning if there were hydrogen atoms in the model (although, since in this case the default value is undef for `undefined', it could be argued that the default is appropriate even when hydrogen atoms were not included in the model).

The weighting scheme used in the refinement is described by the two data names _refine_ls_weighting_scheme and _refine_ls_weighting_details. The first of the two can take only one of the three values sigma (weights assigned based on measured standard uncertainties), unit (unit or no weights applied) or calc (calculated weights applied). The actual mathematical expression used in the weighting scheme should be stated in _refine_ls_weighting_details.

A wide variety of `residual structure-factor difference measures', referred to as R factors, are used in crystallography as indicators of refinement quality. The core CIF dictionary contains definitions for the three most commonly used R factors. The `conventional R factor' is defined as $[R = {{ \textstyle\sum|F({\rm meas}.)-F({\rm calc}.)|} \over {\textstyle\sum|F({\rm meas}.)|}},]$ where $[F(\rm{meas}.)]$ and $[F(\rm{calc}.)]$ are the measured and calculated structure factors, respectively. In the data item _refine_ls_R_factor_all, the sum used in the calculation is taken over all the reflections collected, whereas in the data item _refine_ls_R_factor_gt, the sum is taken over reflections with a value greater than the limit specified by _refine_threshold_expression. In both cases, the reflections included in the calculation may be limited to those between specified resolution limits.

This R factor is calculated from the F values, regardless of whether the structure-factor coefficient [|F|] , [|F|^2] or I was actually used in the refinement, and is often taken as a convenient indicator of the relative quality of a structure determination. As most structure refinements used to be performed on [|F|] , it allows a structure determined today to be compared with an older study.

Many refinements are now carried out on [|F|^2] , although some may still use the absolute value of the structure factor $|F|$ or the net intensity I. The weighted residual factor wR and goodness of fit S for a refinement should be reported according to the coefficients actually used in the refinement. For example, the weighted residual over all reflections, _refine_ls_wR_factor_all, is defined as $[wR=\Bigg({{\sum w[Y({\rm meas}.)-Y({\rm calc}.)]^2} \over {\sum wY({\rm meas}.)^2 }}\Bigg)^{1/2},]$ where w represents the weights and Y represents the structure-factor coefficient, either [|F|] , [|F|^2] or I as specified by _refine_ls_structure_factor_coef.

This distinction between the conventional R factor, which is invariably calculated using F values, and the wR and S factors also holds for similar expressions defined on subsets of the reflections, e.g. _reflns_class_wR_factor_all.

Note that data names are also provided for reporting unweighted residuals on [|F|^2] or I, but these are rarely used in practice, with the exception of R(I) in Rietveld refinements against powder data, where it is generally called the Bragg R factor, R_Bragg or R_B.

The data items in the REFINE_LS_CLASS category are similar to several in the general REFINE category, but correspond to values for separate reflection classes as described in the REFLNS_CLASS category. The data name _refine_ls_class_code identifies the individual classes through a direct match with a corresponding value of _reflns_class_code.

References

International Tables for Crystallography (2006). Vol. G. ch. 3.2, pp. 98-100