Successive refinement of structures with data of increasing resolution: a theoretical study for triclinic space groups

The method of least squares could be used to refine an imperfectly related trial structure by adoption of one of the following two procedures: (i) using all the observed at one time or (ii) successive refinement in stages with data of increasing resolution. While the former procedure is successful in the case of trial structures which are sufficiently accurate, only the latter has been found to be successful when the mean positional error (i.e. 〈|Δr|〉) for the atoms in the trial structure is large. This paper makes a theoretical study of the variation of the R index, mean phase-angle error, etc. as a function of 〈|Δr|〉 for data corresponding to different resolutions in order to find the best refinement procedure [i.e. (i) or (ii)] which could be successfully employed for refining trial structures in which 〈|Δr|〉 has large, medium and low values. It is found that a trial structure for which the mean positional error is large could be refined only by the method of successive refinement with data of increasing resolution.