《有机化学》课程教学资源（文献资料）The use of X-ray crystallography to determine absolute configuration.pdf

Review Article The Use of X-ray Crystallography to Determine Absolute Configuration H. D. FLACK* AND G. BERNARDINELLI Laboratoire de Cristallographie, University of Geneva, Switzerland ABSTRACT Essential background on the determination of absolute configuration by way of single-crystal X-ray diffraction (XRD) is presented. The use and limitations of an internal chiral reference are described. The physical model underlying the Flack parameter is explained. Absolute structure and absolute configuration are defined and their similarities and differences are highlighted. The necessary conditions on the Flack parameter for satisfactory absolute-structure determination are detailed. The symmetry and purity conditions for absolute-configuration determination are discussed. The physical basis of resonant scattering is briefly presented and the insights obtained from a complete derivation of a Bijvoet intensity ratio by way of the mean-square Friedel difference are exposed. The requirements on least-squares refinement are emphasized. The topics of right-handed axes, XRD intensity measurement, software, crystal-structure evaluation, errors in crystal structures, and compatibility of data in their relation to absolute-configuration determination are described. Characterization of the compounds and crystals by the physicochemical measurement of optical rotation, CD spectra, and enantioselective chromatography are presented. Some simple and some complex examples of absolute-configuration determination using combined XRD and CD measurements, using XRD and enantioselective chromatography, and in multiply-twinned crystals clarify the technique. The review concludes with comments on absolute-configuration determination from light-atom structures. Chirality 20:681–690, 2008. VC 2007 Wiley-Liss, Inc. KEY WORDS: absolute structure; crystal structure; resonant scattering INTRODUCTION X-ray diffraction (XRD) of single crystals has the capacity to distinguish between the enantiomorphs of a chiral crystal structure and the enantiomers of a chiral molecule. The technique may be applied to compounds of a vast range of chemical composition. Essential chemical information such as the molecular geometry, bond distances and angles, and the packing of the molecules in the crystal are part and parcel of the results of the analysis. However there are limitations. Absolute-configuration determination is a fine detail of crystal-structure determination, which depends on being able to identify small diffraction intensity differences between two crystal-structure models of opposite chirality. With compounds containing only light atoms a significant difference is not guaranteed. The physical reason that these differences are small is described in the section Resonant scattering and its effect on the diffraction intensities. Clearly it makes no sense to claim that an absolute con- figuration has been determined unless the gross features of the structure and its determination, such as intensity measurements, symmetry, atomic positions, interatomic distances, and atomic displacement parameters have been evaluated and shown not to be in error. This review is written for the person who has sufficient knowledge of X-ray crystallography to accomplish this essential step. Of particular relevance in absolute-configuration determination are the following questions: • Does the model crystal structure properly represent the crystal structure inside the crystal(s) that have been measured? Is the crystal structure chiral? Is the model that of the real crystal structure and not its enantiomorph? Is the compound enantiomerically pure? Is the assumed space-group symmetry neither too low nor too high? • Does the model crystal structure properly represent the bulk product from which the crystal was grown? • Have the bulk and the measured single crystal been suf- ficiently characterized or fingerprinted to enable another experimentalist to correctly identify the material studied? *Correspondence to: H. D. Flack, Laboratoire de Cristallographie, 24 quai Ernest-Ansermet, CH-1211 Gene`ve 4, Switzerland. E-mail: howard.flack@unige.ch Received for publication 14 May 2007; Accepted 16 July 2007 DOI: 10.1002/chir.20473 Published online 8 October 2007 in Wiley InterScience (www.interscience.wiley.com). CHIRALITY 20:681–690 (2008) VC 2007 Wiley-Liss, Inc

In a presentation of the way that absolute-configuration determination is undertaken by single-crystal XRD, the review provides essential background information and highlights those aspects which are the cause of confusion and error. Techniques to improve the capacity of singlecrystal XRD to determine absolute configuration are reviewed, along with a few examples of other more complex cases. The all-important topic of characterization of bulk and individual single crystals is treated and the concluding remarks contain comments on some current technical limitations. The current review does not go into any detail concerning the phase diagrams of enantiomeric mixtures as we have recently contributed detailed information on the absolute-configuration determination from binary enantiomeric mixtures1 which are neither enantiomerically pure nor racemates (scalemates). SINGLE-CRYSTAL XRD TECHNIQUES USING AN INTERNAL CHIRAL REFERENCE The presence in a crystal structure of enantiomerically pure chiral molecules, groups, or chiral centers of known absolute configuration leads directly to the determination of the absolute configuration of the other constituents of the crystal by making the image of the atomic arrangement correspond to that of the chiral molecules whose absolute configuration is known. The chiral molecules (or groups or centers) thus act as an internal reference. These may be introduced as part of the compound by chemical reaction or as part of the crystal by cocrystallization using an enantiomerically pure sample of the reference substance. It is important to stress that the correctness of absolute-configuration determination using an internal chiral reference depends crucially on the knowledge of the enantiomeric purity of the reference material and its indicated absolute configuration. It is not sufficient to assume that chemical reaction, crystallization, or operations of mechanochemistry (i.e., grinding) will necessarily conserve the chirality of the reference material. SINGLE-CRYSTAL XRD TECHNIQUES EXPLOITING RESONANT SCATTERING The Flack Parameter The distinction by single-crystal XRD of inversionrelated models of a noncentrosymmetric crystal structure relies on the phenomenon of resonant scattering (see section Resonant scattering and its effect on the diffraction intensities) and is measured by the Flack parameter.2 The physical model underlying the Flack parameter is that of a crystal twinned by inversion and composed of distinguishable domains, all of these being real phenomena well established in the fields of mineralogy, crystal growth, crystal physics, and solid-state physics.3 The macroscopic crystal is formed of two types of homogeneous and perfectly-oriented domains, the relationship between the two domain types being that of inversion. A simple way of picturing the crystal twinned by inversion is to imagine a racemic conglomerate in which the crystals have stuck together at growth in a perfectly oriented manner giving diffraction patterns that look like those of a single crystal. For a nice illustrative example see.4 Let X represent the model crystal structure as given by its cell dimensions, space group, and atomic coordinates and X its image inverted through a point. The macroscopic crystal may be represented as C 5 (1 2 x) X 1 x X for which the Flack parameter x measures respectively the mole fractions (12x) and x of the two types of domain X and X. When x 5 0, there is only one domain in the crystal which is that of the model X. When x 5 1, there is only one domain in the crystal which is that of the inverted model X. When x 5 0.3 both types of domain are present in the crystal in the proportion 70% of X to 30% of X. The physically meaningful values of x are 0 x 1, but due to statistical fluctuations and systematic errors, experimental values may lie a little outside of this range by a few standard uncertainties. A crystal of an enantiomerically pure compound in the correct absolute configuration has a value of the Flack parameter of zero. In crystallographic jargon one says that the Flack parameter measures the absolute structure of a noncentrosymmetric crystal and from this one may deduce the absolute configuration of the chiral molecules forming the crystal. What are Absolute Structure and Absolute Configuration? For convenience, the formal definitions of these quantities are reproduced5 in the glossary to this review. Absolute structure is a crystallographer’s term and applies to noncentrosymmetric crystal structures. Absolute configuration is a chemist’s term and refers to chiral molecules. Note particularly that both the entity under consideration, viz. crystal structure versus molecule, and the symmetry restrictions, viz. noncentrosymmetric versus lack of mirror reflection, inversion through a point, and rotoinversions, are different. Both terms concern the complete specification of the spatial arrangement of atoms with respect to inversion and require that the sample under investigation be characterized by some other physical measurement. Absolute-Structure Determination There are conditions under which one may say that the absolute structure of the crystal has been determined satisfactorily.6 Firstly one wants to know whether the absolute-structure determination is sufficiently precise by looking to see whether the standard uncertainty u of the Flack parameter x(u) is sufficiently small: in general u should be less than 0.04 but this value may be relaxed to 0.10 for a compound proven by other means to be enantiomerically pure. Secondly the value of the Flack parameter itself should be close to zero within a region of three standard uncertainties i.e. u < 0.04 (or u < 0.10 for a chemically proven enantiomeric excess of 100%) and |x|/u < 3.0. Moreover the crystal and bulk need to be characterized. The above criteria have been established by way of statistical reasoning6 to ensure that the structure analyst, by an examination of x(u) alone, does not claim an absolutestructure determination where none is valid. An unfortunate consequence of such a conservative or safe approach is that some borderline but valid absolute-structure deter- 682 FLACK AND BERNARDINELLI Chirality DOI 10.1002/chir

minations are deemed to be unacceptable. Some of the above criteria may be relaxed somewhat by taking account of a broader spectrum of knowledge over a class of compounds in conjunction with other nondiffraction data or accumulated knowledge of a particular instrument but this needs exceedingly careful, individual and expert evaluation. Absolute-Configuration Determination Once the absolute structure has been determined satisfactorily, it is only then the moment to see whether something can be said about the absolute configuration of its constituent molecules, as not all valid determinations of absolute structure can necessarily lead to the assignment of an absolute configuration. Although the following description of restrictions7 is self-sufficient, it has to be admitted that more background knowledge on chiral and achiral crystal structures5 helps in its understanding. The weakest and most easily-applicable restriction is given first and the strongest one is given last. In fact the third restriction is sufficient in itself, the other two not so. Space-group restriction. The simplest restriction is one of space-group symmetry. If the space group contains symmetry operations of the second kind (i.e., rotoinversions or rotoreflections, glide reflections), it must occur that these operate either intramolecularly, forcing the individual molecules to be achiral, or intermolecularly, forcing an arrangement of pairs of opposite enantiomers. Thus, in the first case, the molecules are achiral and in the second a racemate is present. Consequently it is only in crystals displaying space groups containing exclusively symmetry operations of the first kind (i.e., pure or proper rotations, screw rotations) that the determination of absolute configuration is possible (geometric crystal classes: 1, 2, 222, 4, 422, 3, 32, 6, 622, 23, and 432). Chiral molecular entity restriction. To comply with the definition of absolute configuration,5 one needs to identify a chiral molecular entity and its spatial arrangement in the crystal structure. For example, in a couple of alkali tartrate salts,8,9 the absolute configuration of the tartrate anion (a chiral molecule) was established but correctly no claims to have done so for the sodium or rubidium atoms were made as these are achiral cations and not molecules. The symmetry group of an achiral molecule contains rotoinversion or rotoreflection operations, and these may or may not be part of the space-group symmetry of the crystal. So one must always examine the spatial arrangement of a candidate molecule for noncrystallographic rotoinversion or rotoreflection symmetry operations and if any are found, the molecule is achiral and its absolute configuration cannot be determined. For example any planar molecule has mirror symmetry and is achiral whether the mirror plane is part of the space-group symmetry or not. Solid-state enantiomeric purity restriction. One needs to verify that all occurrences of the chiral molecular entity in the crystal structure are the same enantiomer for an absolute-configuration assignment to be valid. This is of particular concern when the asymmetric unit contains more than one occurrence of the chiral molecule (Z 0 > 1). Some of the above criteria may be relaxed, but such studies need exceedingly careful, individual and expert evaluation as described in the section Absolute-configuration determination from a bulk racemate by combined CD and XRD. 10 Bulk samples which are mixtures of diastereoisomers may give rise to crystals which contain several of the diastereoisomers either in an ordered or disordered arrangement. The crystal structure may clearly and distinctly show the configuration of some of the elements of chirality common to all of the diastereoisomers whereas those elements which vary amongst the diastereoisomers may be in doubt due to disordered atomic positions arising from the superposition of more than one diastereoisomer. The space-group restriction mentioned earlier implies that absolute configuration may only be undertaken from chiral crystal structures. The latter are necessarily noncentrosymmetric, but not all noncentrosymmetric crystal structures are chiral. Achiral noncentrosymmetric crystal structures exist and the absolute structure of their crystals may be determined. However, it is not possible to deduce the absolute configuration of their constituent molecules for the reasons given above. As we have explained previously,5 chiral crystal structures are found formed either of enantiomerically pure (chiral) molecules, or of chiral molecules as a racemate, or of achiral molecules. Achiral crystal structures, which may be either centrosymmetric or noncentrosymmetric, are found formed either of chiral molecules as a racemate or of achiral molecules. Enantiomerically pure compounds are found to crystallize exclusively in chiral crystal structures. Resonant Scattering and Its Effect on the Diffraction Intensities Optical systems working with visible light distinguish objects of opposite chirality without difficulty i.e., one can easily see the difference between ones own right and left hand. The major difference in the diffraction pattern of the right and left hand occurs in the phases of the inversionrelated reflections whereas their amplitudes are identical in the absence of any resonant effects. Differences in intensities of the latter occur only if a resonant frequency of the diffracting object is near to that of the incident electromagnetic radiation. Therein lies the essential difficulty for chirality distinction using X-rays. As no lens exists for focusing X-rays, one has to rely only on the intensity of the reflections in the Fraunhofer diffraction pattern. Moreover, if the frequency of the incident X-rays is close to that of some of the atomic electrons which cause diffraction, it will be only a small proportion of these electrons which are resonant, and the intensity difference between inversion-related reflections (Friedel opposites in crystallographic jargon) is small. A further complication is that the resonant frequencies of light atoms occur at long X-ray wavelengths which are very difficult to access experimentally. It helps to remember that resonant scattering is no more or no less than the response of a forced damped harmonic oscillator of which there are numerous examples in nature. There is nothing anomalous about resonant scatUSE OF X-RAY CRYSTALLOGRAPHY 683 Chirality DOI 10.1002/chir

tering (apart perhaps from the commonly-used names anomalous dispersion and anomalous scattering). An important tool11 in understanding resonant-scattering effects in XRD and of use in the planning of experimentation and the evaluation of results has been provided very recently in an analytical expression for the meansquare Friedel intensity difference for a noncentrosymmetric crystal structure with a centrosymmetric substructure. A related Bijvoet intensity ratio v gives a measure of Friedel differences relative to the average intensity of Friedel opposites. A spreadsheet application available with the publication11 undertakes the necessary calculations from the elemental composition of the compound for some common X-ray wavelengths. Values of 104 v called Friedif11 are calculated both for the case of all atoms arranged noncentrosymmetrically and also allowing for atoms arranged on a centrosymmetric substructure if it is possible to identify these. We now rapidly pass in review some of the principal insights that this work has provided: • The Bijvoet ratio is largest when all atoms are arranged noncentrosymmetrically and zero when all atoms are arranged centrosymmetrically. • The Bijvoet ratio is zero when all atoms are of the same chemical element regardless of whether the structure is noncentrosymmetric or centrosymmetric. Such is the case, in the spherical atom approximation, for the chiral crystal structure of elemental Se in the form of a helix.12 • The Bijvoet ratio quantifies a contrast and needs both resonant and nonresonant atoms to attain large values. • Rather surprisingly the presence in an otherwise noncentrosymmetric structure of a centrosymmetric arrangement of resonant atoms of one (heavy) chemical element does not diminish the value of the Bijvoet intensity ratio, an observation which had already been con- firmed experimentally.13,14 • The analytical form of the Bijvoet ratio shows that there are no classes of Bragg reflections having particularly large or small values. Consequently, in the absence of a model of the crystal structure, no particular reflections nor any specific regions of reciprocal space on average are established as showing large Friedel differences. Calculation of the Bijvoet ratio at different wavelengths enables an optimal choice of X-ray wavelength to be made prior to experimentation. Further it allows the molecular composition of the crystal to be optimized. Suppose for example that a compound is found to have a Bijvoet ratio that is too small for absolute-configuration determination. One may envisage the synthesis of a suitable derivative or the fabrication of a solvate or cocrystal of the compound having a higher Bijvoet ratio. As has been shown above it is unimportant if the solvent or cocrystal molecule takes an essentially centrosymmetric arrangement in the crystal as this does not tend to diminish the Bijvoet ratio. Moreover we have found,14 using an approximate form of the Bijvoet ratio15 and a small set of pseudocentrosymmetric structures, a relationship between the Bijvoet ratio and the standard uncertainty on the Flack parameter. This relationship allows a priori estimates of the standard uncertainty of the Flack parameter. Work is currently in progress to establish the corresponding relationship between the full Bijvoet ratio and the standard uncertainty on the Flack parameter for a much larger set of non-pseudosymmetric structures. Unfortunately as this review goes to press, we have not yet completed the data analysis to determine the values of Friedif corresponding to our limiting values of u of 0.04 and 0.10, and to investigate in more detail the influence of pseudosymmetry. Least-Squares Refinement Early results16,17 and subsequent experience from many crystal-structure determinations have shown that the Flack parameter is robust and converges in only a few cycles to its final value during least-squares refinement. However, as the Flack parameter is one of many parameters of the physical model of a crystal structure, the values of which are to be found by optimization based on some general criterion, it is essential in the final cycles of optimization that all parameters be varied jointly and simultaneously. If this prescription is not followed, two effects may occur separately or together: (a) the value of the Flack parameter may not correspond to the best value for the optimization criterion and (b) its standard uncertainty may be incorrectly estimated, most frequently underestimated. In the case of least-squares minimization, the final refinement needs to be undertaken by full-matrix least-squares (all parameters varied jointly and simultaneously) and needs to have converged. Another important aspect of least-squares minimization which needs some words of explanation is that of stabilization and damping.18 To avoid a least-squares refinement becoming unstable and failing to converge, certain numerical techniques, grouped together under the general term damping, are often applied automatically or manually. A side effect of these techniques is that stabilized parameters stay close to their starting or target values with standard uncertainties that are systematically underestimated. Biased (wrong) parameter estimates and underestimated standard uncertainties are the result. Inverting a Model Structure It sometimes happens that a model crystal structure yields a value of the Flack parameter larger than 0.5. To represent the majority component in the crystal, the model needs to be inverted so the Flack parameter takes a value less than 0.5. In general this inversion is obtained by inversion in the origin by just changing all atomic coordinates x, y, z into 2x, 2y, 2z or some point symmetry-equivalent to it. However, for the chiral crystal structures which are necessary for absolute-configuration determination, there are some cases where this simple change of coordinates is insufficient or inappropriate. So in the case of a space group belonging to one of the 11 pairs of enantiomorphic space groups (P41–P43; P4122–P4322; P41212–P43212; P31– P32; P3121–P3221; P3112–P3212; P61–P65; P62–P64; P6122– P6522; P6222–P6422; P4132–P4332), the space group should also be changed into the other member of the pair. As they occur in enantiomorphic pairs, these 22 space groups 684 FLACK AND BERNARDINELLI Chirality DOI 10.1002/chir

are the only ones that are correctly described as being chiral.5 Moreover, there are cases where for the standard setting of the space group19 that the coordinates need to be inverted in some point other than the origin. The coordinates 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 important role in crystallization. It is for these reasons that for absolute-configuration determination, some characterization or measurement of the enantiomeric purity not only of the bulk but also of the single crystal used for the diffraction 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-wavelength 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 circumstances, CD may be applied to the single crystal used for the diffraction measurements taken into solution. 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 crystal.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 provides estimates of the enantiomeric excess. It is of course necessary to establish that under the chosen experimental conditions that the two enantiomers are clearly separated. The retention times provide a satisfactory characterization of the two enantiomers. Regrettably little use is made of differential scanning calorimetry (DSC) by synthetic chemists and structure analysts. Nevertheless, the measurement of melting temperatures and enthalpies is a valuable technique for establishing 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 diastereoisomers to be revealed. Clearly although this technique 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 righthanded 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 counting 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 determinant. It is standard practice in our laboratory to calibrate every diffractometer after a hardware or software modification with a well-defined reference material of a chiral crystal structure and containing a sufficient amount of resonant 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 conditions, 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 separately 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 criterion 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