USE OF X-RAY CRYSTALLOGRAPHY 685 are the only ones that are correctly described as being chi- simulated from the results of a single-crystal study allows the presence in the bulk of ne dia in erted point other tha n the ing racemic omerates.i the columns sih the tables any metho of these isomers sh single diffraction studies CHARACTERIZATION OF COMPOUNDS AND CRYSTALS EXPERIMENTATION AND ANALYSIS NEEDS The phase diagrams of enantiomeric mixtures can be IMPECCABLE TECHNIQUE Right-Handed Axe roe in It is for these rea that fo As emphasized and discussed previously. ric pu rity not only of analysis of absolute structure.Of particular danger for the tion o mmended Ther methods of characterization: any ba ran mation matrix mus OR:The sne ivity ive determin As the measureme n is a single-w e OR not ng the number of pos and negative ogram on the di must ha a positive me the after a hardware or soft of ac CD:The al st 他a nt of t scatter In fav orable cir Cture ution t give a flack pa v clos nents taken into so nfiguratio of the acid he the bull compound and p XRD Intensity Measurements pow red singl It has b man,to be hich ingly in the (EC sen estimates of the neri are result It hen imental con ns that the two ure both sepa members of each Friedel ay o nd is At the data age it is essential y (DSC)by vnthetic chemists and ructure ana stal r semi ing a pha se diagram.DSC measurements may be applied In pas ing,we also mention that powder diffraction can any Bra Chirality DOI 10.1002/chiare the only ones that are correctly described as being chi￾ral.5 Moreover, there are cases where for the standard set￾ting of the space group19 that the coordinates need to be inverted in some point other than the origin. The coordi￾nates of the appropriate inversion point can be found in the columns Inversion through a centre at of the tables of Euclidean normalizers of space groups.20 For nonstandard settings an algorithmic solution to this problem has been provided.16 CHARACTERIZATION OF COMPOUNDS AND CRYSTALS The phase diagrams of enantiomeric mixtures can be complicated,21,22 giving rise to solid and liquid phases of different composition. Also kinetic effects play an impor￾tant role in crystallization. It is for these reasons that for absolute-configuration determination, some characteriza￾tion or measurement of the enantiomeric purity not only of the bulk but also of the single crystal used for the diffrac￾tion studies is recommended. There are three principal methods of characterization: OR: The specific rotation of the optical activity in solution. As the measurement of specific rotation is a single-wave￾length technique, the presence and effect of impurities can easily go undetected. Moreover, OR can not be applied to microgram quantities (i.e., a single crystal used for diffraction studies). Also OR can only provide a measure of enantiomeric excess if the specific rotation of the enantiomerically pure compound is sufficiently strong and has been determined previously. CD: The visible and near-UV circular dichroism spectrum in solution. The presence and effect of impurities may be readily recognized in a CD spectrum. In favorable cir￾cumstances, CD may be applied to the single crystal used for the diffraction measurements taken into solu￾tion. For compounds that racemize rapidly in solution, solid-state CD in a KBr disk may be applied to the bulk compound and perhaps even to a powdered single crys￾tal.23–25 One may expect vibrational CD, either IR or Raman, to be used increasingly in the future. Enantioselective chromatography (EC): This sensitive technique is applicable to microgram quantities and pro￾vides estimates of the enantiomeric excess. It is of course necessary to establish that under the chosen ex￾perimental conditions that the two enantiomers are clearly separated. The retention times provide a satisfac￾tory characterization of the two enantiomers. Regrettably little use is made of differential scanning cal￾orimetry (DSC) by synthetic chemists and structure ana￾lysts. Nevertheless, the measurement of melting tempera￾tures and enthalpies is a valuable technique for establish￾ing a phase diagram. DSC measurements may be applied to the bulk. In passing, we also mention that powder diffraction can be useful. The simple expedient of comparing the X-ray powder diffraction pattern of the bulk product with that simulated from the results of a single-crystal study allows the presence in the bulk of polymorphs and crystalline dia￾stereoisomers to be revealed. Clearly although this tech￾nique is of no help for detecting racemic conglomerates, it is very helpful for other solid mixtures.26 As the presence of diastereoisomers has the capability of invalidating the determination of absolute configuration, any method which establishes the number and relative concentration of these isomers should be used to characterize the bulk compound and if possible the single crystal used for the diffraction studies. EXPERIMENTATION AND ANALYSIS NEEDS IMPECCABLE TECHNIQUE Right-Handed Axes As emphasized and discussed previously,27 right￾handed sets of axes must be used at every stage of an analysis of absolute structure. Of particular danger for the structure analyst are basis transformations performed to bring the unit cell into a standard setting. To maintain right-handed axes, any basis transformation matrix must have a positive determinant. A transformation matrix with a negative determinant will transform a right-handed set of axes into a left-handed set of axes, and conversely. The sign of the determinant cannot be spotted simply by count￾ing the number of positive and negative elements in the transformation matrix. The orientation matrix (UB) of the crystal on the diffractometer must have a positive determi￾nant. It is standard practice in our laboratory to calibrate every diffractometer after a hardware or software modifica￾tion with a well-defined reference material of a chiral crys￾tal structure and containing a sufficient amount of reso￾nant scattering. We use enantiomerically pure potassium hydrogen (2R, 3R) tartrate. With such a test material, structure solution must give a Flack parameter very close to zero for the (2R, 3R) configuration of the acid tartrate anion. XRD Intensity Measurements It has been established,13,14 under certain particular con￾ditions, which it is not necessary to detail here, that unless intensity measurements of both members, hkl and h k l of each pair of Friedel opposites are made and used sepa￾rately in the least-squares refinement, false values of the Flack parameter may result. It hence seems prudent, whether these particular conditions apply or not, to always measure both members of each Friedel pair. Fortunately, with modern-day equipment using area detectors this cri￾terion is easy to achieve and is often the default mode of operation. At the data-reduction stage it is essential for absolute-configuration determination not to average the intensities of Friedel opposites,6 to transform reflection indices only according to the symmetry operations of the crystal point group6 and not to use any semiempirical absorption correction which applies a different correction to the intensities of hkl and h k l. 1 In writing about pairs of Friedel opposites in this review, h k l should be taken in a general sense to mean h k l or any Bragg reflection symmetry-equivalent to it under the USE OF X-RAY CRYSTALLOGRAPHY 685 Chirality DOI 10.1002/chir