Even if determination of absolute configuration is not one of the aims of the structure determination, it is important to refine ANY non-centrosymmetric structure as the correct 'absolute structure' in order to avoid introducing systematic errors into the bond lengths etc. In some cases the absolute structure will be known with certainty (e.g. proteins), but in others it has to be deduced from the X-ray data. Generally speaking, a single phosphorus or heavier atom suffices to determine an absolute structure using Cu-K(alpha) radiation, and with accurate high-resolution low-temperature data including Friedel opposites such an atom may even suffice for Mo-K(alpha).

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 F^{2} 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

Ahead to Twinned Crystals and Refinement against Powder Data

Back to Macromolecules and Other Structures with a Poor Data/Parameter Ratio

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