686 FLACK AND BERNARDINELII symmetric the t ere ol el the ing into this trap.Ofeqal rel equivale nt to it,has b achiral crystal structure of a racemate (often disordered) lent to it has not been measured then the Friedel coverage has err is 0%. Getting the best out of you ent of al in t cycl un re ing an abs de n is h uses by default a spars rom an qu PLATON mic coordinates and cell pa ter.SHELXL pace group of too low syr has been chosen at it may be poss to add refin to th to invert the structur tion .sho ould be rejec if the evid mestandard uncertaintyis e in stalline state the same value of x(). of the real On The o Framework mated ourrecent study f 135 publsne ing the data me nts and the In general.for these incom mination.Syst s can be d ade n on close to an to.contrad and s in the in. ues of the Flack parameter close to 0.5.with a low stand Vith the aid ard saoehohnedtb nay be completed and justified.An W dete minations that either the are hac opp ha s orded to liminate intensity dif operated by the One should ear in mind that SOME EXAMPLES TO STRETCH ONE'S roneous.Ar with which or should be familia Experimental values of the flack parameter has been toa noncentros mme We owe a debt of gratitude to the referees of this article space group w he crys ng t of theg the inte crys e,the conditions for ly yet aga that eter.is to scrutinize the output of a system such as check Chirality DOI 10.1002/chir point group of the crystal. For a noncentrosymmetric crys￾tal hkl and h k l are not symmetry-equivalent under the point group of the crystal. Later on in this review the term Friedel coverage is also used. If in the intensity data, for each reflection hkl the reflection h k l, or one symmetry￾equivalent to it, has been measured then the Friedel cover￾age is 100%. If for each hkl, h k l or one symmetry-equiva￾lent to it has not been measured then the Friedel coverage is 0%. Getting the Best Out of Your Software In the section Least-squares refinement above it was pointed out that full-matrix simultaneous refinement of all variables should be used in the final cycles to obtain reli￾able results. One widely-used least-squares refinement programme, SHELXL93/97,28 uses by default a sparse-ma￾trix technique,6 called hole-in-one, for the refinement of the Flack parameter. SHELXL may nevertheless be coaxed into doing the appropriate full-matrix calculation.13,29 One may make one or two simple checks of any refine￾ment software. The first is to invert the structure and check that a value of the Flack parameter of 1 2 x with the same standard uncertainty is obtained. A second check is to undertake the refinement using a different starting value of the Flack parameter which should lead to exactly the same value of x(u). Crystal-Structure Evaluation The results of a crystal-structure determination are transmitted nowadays by means of computer-readable files viz. a Crystallographic Information Framework30 (CIF) file which may be used for display, analysis, evaluation, and archiving. A great deal may be achieved by the automated evaluation of the information contained in a CIF file con￾cerning the data measurements and the crystal-structure determination. Systems can be designed to make use of a considerable amount of general and specific crystallo￾graphic knowledge and know-how in the evaluation of a structure determination, and to alert the structure analyst to ambiguities, contradictions, and shortcomings in the in￾formation encapsulated in a CIF file. With the aid of these alerts, the data-measurement and structure-refinement procedures may be improved, completed and justified. An essential element is the examination of a graphical repre￾sentation of the atomic displacement parameters.31 The most elaborate system currently in operation for the evalu￾ation of crystal-structure determinations is the free-of￾charge online checkCIF/PLATON32,33 operated by the International Union of Crystallography. Erroneous Crystal Structures One should bear in mind that a structure analysis may be erroneous. An error with which one should be familiar is the one in which the symmetry of a crystal structure has been incorrectly assigned to a noncentrosymmetric space group whereas the crystal structure itself is really centrosymmetric. In an erroneous noncentrosymmetric description of a crystal structure, the conditions for abso￾lute-configuration determination may apparently be achieved which do not of course apply in the true centro￾symmetric description.13,14 The measurement of a whole sphere of reflection intensities (see section XRD intensity measurements) is a prudent approach to help avoiding fall￾ing into this trap. Of equal relevance to absolute-configura￾tion determination are those cases of analysis in which an achiral crystal structure of a racemate (often disordered) with a space group containing rotoinversion operations has erroneously been assigned to a crystal which has in fact a chiral crystal structure of an enantiomerically pure compound with a space group containing only rotation and screw rotation operations. This latter case may arise when a bulk racemate crystallizes by spontaneous resolution and the structure analyst force-feeds the structure solution with a racemate. The possibility of undertaking an abso￾lute-configuration is hence lost. From an analysis of the atomic coordinates and cell pa￾rameters, checkCIF/PLATON may provide an alert that a space group of too low symmetry has been chosen. The most common situation is that it may be possible to add a center of symmetry to the chosen space group. This prop￾osition should be rejected if there is strong evidence to show that the compound is enantiomerically pure in the crystalline state. Partial-polar ambiguities34 have the capacity to falsify an absolute-configuration determination. In a crystal-structure solution suffering from a partial-polar ambiguity, some of the atoms are correctly located but the others are images of the real atoms inverted in a point. One may be able to recognize this type of error by a study of interatomic dis￾tances and angles. Compatibility of Chemical and Crystallographic Data In our recent study1 of 135 published crystal structures of metallacycles an appalling 26% had incompatible chemi￾cal and crystallographic data. In general, for these incom￾patible crystal structures, the chemical evidence was adequate to convince us that the bulk products had a com￾position close to an enantiomeric excess of 100%. The crys￾tal structures were determined as being chiral but with val￾ues of the Flack parameter close to 0.5, with a low stand￾ard uncertainty, indicative of a crystal twinned by inversion with an overall composition near to that of the racemate, in contradiction to the chemical evidence. We hypothesized that for the incompatible crystal-structure determinations that either the data-reduction software had averaged Friedel opposites or that an empirical absorption correction procedure had tended to eliminate intensity dif￾ferences between Friedel opposites. Other considerations have also been highlighted.14 SOME EXAMPLES TO STRETCH ONE’S UNDERSTANDING Experimental Values of the Flack Parameter We owe a debt of gratitude to the referees of this article for suggesting the inclusion of this section giving the inter￾pretation of some typical values of the Flack parameter. We cannot stress sufficiently yet again that a necessary step, prior to examining and interpreting the Flack param￾eter, is to scrutinize the output of a system such as check- 686 FLACK AND BERNARDINELLI Chirality DOI 10.1002/chir