In the course of the final structure factor calculation the program calculates the Flack absolute structure parameter x and its esd (it is a bonus of the refinement against F2 that this calculation is a 'hole in one' and doesn't require expensive iteration). A comparison of x with its esd provides an indication as to whether the refined absolute structure is correct or whether it has to be 'inverted' (the program prints a suitable warning should this be necessary). This attempt to refine x 'on the cheap' is reliable when the true value of x is close to zero, but may produce a (possibly severe) underestimate of x for structures which have to be inverted, because x is correlated with positional and other parameters which have not been allowed to vary. Effectively these parameters have adapted themselves to compensate for the wrong (zero) value of x in the course of the refinement, and need to be refined with x to eliminate the effects of correlation. These effects will tend to be greater when the correlation terms are greater, e.g. for pseudo-symmetric structures and for poor data to parameter ratios (say less than 8:1). x can be refined at the same time as all the other parameters using the TWIN and BASF instructions; this implies racemic twinning and so is discussed under TWIN below (see also H.D. Flack, Acta Cryst., (1983) A39, 876-881).
For most space groups 'inversion' of the structure simply involves inserting an instruction MOVE 1 1 1 -1 before the first atom. Where the space group is one of the 11 enantiomorphous pairs [e.g. P3(1) and P3(2)] the translation parts of the symmetry operators need to be inverted as well to generate the other member of the pair. There are seven cases for which, if the standard setting of the International Tables for Crystallography has been used, inversion in the origin does NOT lead to the inverted absolute structure (in fact, in some cases it leads to a totally different structure: H.D. Flack, personal communication, 1992)! This problem was drawn to the author's attention by D. Rogers in about 1980, but was probably first discussed in print by E. Parthe and L.M. Gelato, Acta Cryst., A40 (1984) 169-183 and by G. Bernardinelli and H.D. Flack, Acta Cryst., A41 (1985) 500-511. The offending space groups and corresponding correct MOVE instructions are:
Fdd2 MOVE .25 .25 1 -1 I4(1) MOVE 1 .5 1 -1 I4(1)22 MOVE 1 .5 .25 -1 I4(1)md MOVE 1 .5 1 -1 I4(1)cd MOVE 1 .5 1 -1 I-42d MOVE 1 .5 .25 -1 F4(1)32 MOVE .25 .25 .25 -1
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