Research: Science & Education
Molecules, Crystals, and Chirality Il-Hwan Suh and Koon Ha Park Departments of Physics and Chemistry, Chungnam National University, Taejon, 305-764 Korea William P. Jensen and David E. Lewis* Department of Chemistry and Biochemistry, South Dakota State University, Brookings, SD 57007
The terms chiral and chirality, both derived from the Greek χειρ (cheir, a hand), are commonplace in modern chemistry. Indeed, chirality, or handedness, is a fact of everyday existence, as illustrated by the number and variety of chiral objects and situations that one can find in daily life. Gloves and shoes are designed to fit only one hand or foot; golf clubs and many musical instruments are designed to be right- or left-handed; doors swing open to the right or the left. Screws, bolts, and nuts are threaded in a right- or left-handed manner (how often does one try to remove a nut, only to find that it has a left-hand thread?). Automobiles are also chiral (the steering wheel is on the left-hand side in the U.S. and on the right-hand side in Great Britain), as are books (try holding this page up to a mirror) and even clothing (men’s shirts button left-over-right and women’s shirts button right-over-left). Nor is chirality restricted to macroscopic systems, as was discovered more than a century ago. The B form of the DNA double helix, which may be the most famous molecule known owing to its almost ubiquitous appearance in TV programs and videos on science, is always right-handed. Furthermore, every protein known contains chiral α-amino acids whose configurations are all the same (with a few rare, notable exceptions). Many drugs display desired activity only as one of the two mirror-image forms. The drug thalidomide provided one of the most horrific examples of handedness being critical to function: while one form of the drug is a mild analgesic, the mirror image is a powerful teratogen, which resulted in babies being born without limbs. Historical Perspective In 1815 Jean Baptiste Biot discovered that solutions of certain organic compounds were able to rotate the plane of plane polarized light, a property which he called optical activity (1). The same property is exhibited by certain forms of crystalline quartz, indicating that it is not restricted to the solution state. Although optical activity is still the defining characteristic of chiral compounds, optical rotations at a single wavelength are seldom used in modern chemistry, having been largely superseded by optical rotatory dispersion and circular dichroism. The possible origins of optical activity were first linked to molecular structure by the French chemist Louis Pasteur, who had made a critical observation in 1848 while working on the problem of tartaric and racemic acids. In the form of tartaric acid this natural product was known to be optically active; in the form of racemic acid, it was known to be optically inactive. What Pasteur observed was that when a dilute solution of sodium ammonium racemate was allowed to evaporate, the crystals deposited were hemihedral—the
*Corresponding author. Address correspondence to: Department of Chemistry, University of Wisconsin–Eau Claire, Eau Claire, WI 54702.
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Figure 1. Both enantiomorphic forms of the hemihedral crystals of ammonium hydrogen malate. The plane of the paper must not serve as a mirror plane of symmetry.
crystals developed faces such that each crystal was prevented from having mirror symmetry. The hemihedral crystals of another compound, ammonium hydrogen malate, are shown in Figure 1. Hemihedral crystals are not identical to their mirror images, and the hemihedral crystals that Pasteur obtained were large enough to be separated manually into two groups each containing crystals of one form only. The crystals from one of these groups were identical to those of sodium ammonium tartrate, and they rotated plane polarized light the same amount and in the same direction as sodium ammonium tartrate; the crystals from the other group rotated the plane of polarized light exactly the same amount, but in the opposite direction (2). The different isomers were identified by the direction in which their solutions rotated plane polarized light. The isomer whose solution rotated the plane counterclockwise was designated as the levorotatory (l or {) isomer from the Latin laevo, to the left, and the isomer whose solution rotated the plane clockwise was designated as the dextrorotatory (d or +) isomer from the Latin dextro, to the right. The optical isomers of a chiral compound were characterized by their specific rotations, [α]. Based on his observations, Pasteur also suggested (quite a radical suggestion for the time) that the properties of the two crystalline forms might also reflect the symmetry of the molecules themselves, and that racemic acid was an equal mixture of the two molecular forms of tartaric acid (3). With the loss of its status as the name of a distinct organic compound, the term racemic then acquired its modern meaning—indicating an equal mixture of two mirror-image forms. At that time Louis Pasteur was a young scientist with little national reputation, and his results were called into question by an incredulous Biot. As a senior member of the French Academy of Sciences, Biot was in a position to insist that Pasteur prove his assertions by repeating his experiments under Biot’s personal supervision using samples of sodium ammonium racemate that Biot himself supplied. It is worthwhile pointing out that Biot had previously crystallized sodium ammonium racemate and found it to be neither hemihedral nor optically active. In a dramatic encounter, Pasteur convinced his skeptic, who exclaimed on witnessing the verification of Pasteur’s observation, “Mon cher enfant, j’ai tant aimé les sciences dans ma vie que cela me fait battre le coeur!” [“My dear child, so much have I loved science during my lifetime that this sets my heart aflutter!”]
Journal of Chemical Education • Vol. 74 No. 7 July 1997
Research: Science & Education It was not until years later that the reason for Biot’s failure to obtain hemihedral crystals from sodium ammonium racemate was discovered. It turns out that racemic sodium ammonium tartrate separates into right- and lefthanded forms only when the crystallization is initiated below 28 °C. Below this critical temperature, racemic sodium ammonium tartrate crystallizes in hemihedral prisms of the (+)- and ({)-tetrahydrates, each individual crystal containing only one of the two enantiomorphic forms of the molecule. Above this temperature, the same salt crystallizes as symmetrical prisms of a racemic monohydrate, each individual crystal containing equal numbers of the two enantiomorphic forms. Pasteur had prepared his crystals by slow evaporation of a dilute solution, so that crystallization occurred at low temperature; Biot, on the other hand, had prepared his crystals by the more usual method of cooling a hot solution, whereupon the racemate crystallized. Although racemates that crystallize in hemihedral forms large enough to permit them to be sorted by physical means are extremely rare, crystallization can be used as a method for resolving racemic compounds in suitable cases by the method of inoculating supersaturated solutions. The Haarman & Reimer (l)-Menthol Process (4) provides one excellent example of the use of this technique for resolving a racemate. The starting material for the Haarman & Reimer process is thymol, which is hydrogenated to a mixture of all eight possible stereoisomeric 2-isopropyl-5methylcyclohexanols; the (±)-menthol is separated and the remaining isomers are recycled. The critical step of the resolution is the enantioselective crystallization of (+) and ({)menthol benzoate carried out continuously in two separate vessels, by inoculating one supersaturated solution of (±)menthol benzoate with crystals of the (+) form and the other with crystals of the ({) form. The overall yield of the process, based on thymol, is more than 90%. Chirality in Individual Molecules: Absolute Configuration More than three decades would pass before a molecular rationalization of optical activity would be developed. In part, this delay was a result of the lack of a tenable theory of organic structure, which was developed only in the late 1850s and early 1860s as a result of the work of Archibald Scott Couper, Friedrich August Kekulé, and Aleksandr Mikhailovich Butlerov. By the mid 1860s, the structural theory of organic chemistry had won wide acceptance, setting the stage for the next major development in stereochemistry. This occurred in 1874, when Jacobus Henricus van’t Hoff (5) and Joseph-Achille Le Bel (6) independently proposed that carbon with four tetrahedrally disposed bonds could display handedness at the molecular level if the four bonds were to different atoms. Of the two theories, Le Bel’s also proposed that this concept could be extended to other atoms, and the formation of chiral compounds based on nitrogen, silicon, sulfur, and phosphorus has verified his predictions. This new form of isomerism brought with it the problem of unambiguously designating the absolute configuration of the stereoisomer that one is dealing with. A simple model for this process might be to try to define a left hand without using the words “left” or “right”. In Pasteur’s experiment the different isomers were identified by the direction in which they rotated plane polarized light, but modern chemistry requires a more fundamental definition of configuration, especially as compounds have been discovered whose stereoisomerism is due to structural features other than chiral centers (such “stereogenic sites” include allene moieties and double bonds).
Two chiral molecules that are related to each other as object and mirror image, but which are not superimposable, are termed enantiomers, from the Greek εναντιος, (enantios, a mirror), and when not in the form of their racemates they share the common property of optical activity. Traditionally this phenomenon has been discussed in terms of asymmetry or dissymmetry in the molecule being discussed. Compounds in which there are four different groups attached to the same tetrahedral atom (e.g. CHBrClF) do not have any mirror planes or centers of symmetry, so they can exist in two different forms related to each other as object and nonsuperimposable mirror image, analogous to holding your right hand in front of a mirror and observing, in the mirror, the features of your left hand. The problem of unambiguously specifying the absolute configuration of a chiral center devolves into two separate tasks: (i) a standard orientation for the chiral center must first be defined; and (ii) the spatial relationship between the groups must be described when the molecule is placed in the standard orientation. Using the problem of defining a left hand alluded to above as our model, one solution showing how this problem might be solved is: “With the palm facing away from the viewer [the standard orientation is defined], the digits from the thumb to the little finger are encountered in order in a counterclockwise direction [the spatial relationship between the groups is defined].” One of the first successful methods for designating the absolute configuration of chiral molecules was developed by the great German chemist Emil Fischer, who won the Nobel Prize in 1902 for his work in organic chemistry, including unraveling the stereochemistry of carbohydrates. To construct a Fischer projection, the molecule must be oriented according to the following rules: 1. The structure is written with the main chain oriented vertically, with the carbon atom bearing the lowest locant number in the IUPAC name written uppermost. 2. The chiral atom lies in the plane of the paper, the groups on the vertical bonds project away from the viewer, and the groups on the horizontal bonds project toward the viewer.
The Fischer projection allowed the absolute configuration of many important molecules to be specified for the first time. Even today, it is still used extensively in specifying the absolute configurations of monosaccharides (if the OH group of the bottom chiral center is to the left of the main chain in the Fischer projection it is an L isomer, and if to the right it is a D isomer) and α-amino acids (if the amino group is on the left, the amino acid is an L isomer, and if it is on the right, it is a D isomer). The Fischer projections of the two enantiomers of the α-amino acid phenylalanine are given below as the right-hand structure of each pair; the form on the left of each pair is a version that has been used to indicate the relationship of the Fischer projection to the tetrahedron centered on the chiral center. CO2H
CO2H H2N
H
H2N
CH2C6H5
H CH2C6H5
L-
CO2H
CO2H H
NH2
H
CH2C6H5
NH2 CH2C6H5
D-
The Fischer projection was the first successful two-dimensional representation of a three-dimensional chiral center. Nevertheless, the Fischer projection suffers from one
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1. The substituents at the stereogenic center are ranked in order of decreasing precedence. The atomic number of the atom bonded to the stereocenter is used as the first discriminator (e.g., Cl takes precedence over F), then (if necessary) the mass number (e.g., D takes precedence over H); if these two rules do not distinguish between the two substituents, one then moves outward along the chain from the chiral center one atom at a time until the two groups are distinguished.
ing the lowest precedence (an atomic number of zero). O S
Not all chiral molecules possess chiral centers, and the fact that the only requirement for chirality is that the molecule not be superimposable on its mirror image it is often overlooked. This property can be translated into a molecular symmetry requirement: chiral molecules cannot contain rotary-reflection axes (improper rotation axes). The S 1 improper axis of rotation corresponds to a mirror plane of symmetry and the S 2 improper axis of rotation corresponds to a center of inversion; thus, chiral molecules may not contain a mirror plane of symmetry or an inversion center. There are several examples of chiral molecules for which the requirements for chirality are met without the presence of a chiral center. The molecules below will be achiral if R = H as a mirror plane bisects the molecule. However, if R is not hydrogen, each of the molecules is chiral because the mirror symmetry of the molecule is broken. H R
R
R
H
H2N
H CH2C6H5
H2N
H H
C6H5CH2
NH2
Although chiral centers based on tetrahedral carbon are the dominant source of chirality in chemistry, any tetrahedral atom with four different substituent groups will exhibit chirality, as was proposed by Le Bel himself. Examples of chiral centers based on tetrahedral silicon and nitrogen are well known. In principle, trigonal pyramidal nitrogen should be capable of existing in enantiomeric forms, but the rate of inversion of nitrogen in simple amines is such that these compounds actually exist as unresolvable racemates. When the atom at the center of the trigonal pyramid is from the third row of the periodic table, however, the rate of inversion is slow enough to permit the optical resolution of the racemate [e.g., optically active sulfoxides based on chiral sulfur have been used as intermediates in asymmetric synthesis (8)]. The chirality about such chiral centers is almost always designated using the Cahn– Ingold–Prelog system, with the lone pair of electrons hav-
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R R
R
a e
M f
c d
d
M f
3+
N
b c
a e
N N
M
N N
N
3+
N N N
M
N N
N
CO2H
CO2H C6H5CH2
R
H Me
H
As was mentioned previously, chirality is not restricted to organic systems. A number of inorganic compounds are chiral also. The coordination compound M(abcdef), where a– f are 6 different octahedrally distributed ligands, contains a chiral center. Bidentate ligand coordination can also yield compounds that are stereogenic. The complex ion tris(ethylenediamine)cobalt(III), for example, has two enantiomeric forms.
Applying these sequence rules to L-phenylalanine, shown below in Fischer projection, one determines that the absolute configuration is S.
CH2C6H5
R
H
b
H2N
R
HO
3. If the precedence of the three highest-ranked substituents in this standard orientation decreases in a clockwise direction, the absolute configuration is R (Latin rectus, right); if the precedence of the three is counterclockwise, the absolute configuration is S (Latin sinister, left).
CO2H
O
H3C
OH
2. The molecule is oriented so that the lowest-ranked substituent projects away from the viewer.
CO2H
••
important shortcoming that is a direct result of the way in which the standard orientation is defined: by definition, the groups on the horizontal bonds project toward the viewer and those on the vertical bonds project away from the viewer. This restricts the way in which comparisons between Fischer projections may be made—for purposes of comparison, a Fischer projection may be rotated through 180° in the plane of the paper or an even number of pairs of substituents may be interchanged, but no other manipulation is permitted. As the examples of chiral molecules whose absolute configurations needed to be specified became more complex, the limitations of the Fischer system of designating absolute configuration became more apparent. The solution to the problem of specifying the absolute configuration of more complex molecules was developed by R. S. Cahn of the Royal Society of Chemistry, Sir Christopher Ingold, and Nobel laureate Vladimir Prelog (7). Under the Cahn–Ingold–Prelog system, the absolute configuration of a chiral molecule is defined by applying a series of sequence rules to the structure. As applied to a chiral center, these rules are as follows.
Chirality and Crystallography Most chemists are reasonably conversant with the symmetry elements of compounds when dealing with an individual molecule, but much less so when addressing the problem of symmetry in the crystal lattice. In a crystal, one is dealing not only with the symmetry of the individual molecule, but also with symmetry that arises owing to the translational component of the crystal lattice. There are two important symmetry operations that combine a translation with the simple symmetry elements applied to an individual molecule: the glide plane and the screw axis. A glide plane corresponds to a reflection in a plane combined with a translation of one-half the unit cell dimension along an axis parallel to the plane. A screw axis is designated by a subscripted term, nm, where n is the order of the axis. In a screw axis, m < n and n must be 2, 3, 4, or 6. Thus, an nm axis corresponds to rotation about an axis of (360/n)° combined with a translation along the axis of the fraction (m/ n) of the unit cell dimension. For example, a 31 screw axis results from a combination of a (360/3)° rotation and a (1/3)
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Research: Science & Education unit cell translation along the rotation axis, while a 32 screw axis results from a combination of a (360/3)° rotation and a 2/3 unit cell translation along the rotation axis. Because of the periodicity of the crystal, translation of the fraction m/ n of the unit cell along the axis also corresponds to translation of the fraction (n – m)/ n along the axis in the opposite direction, so a 32 screw axis is the mirror image of a 31 screw axis.
HO HO
OH OH
HO HO translation
OH
reflection
translation
OH rotation
glide plane
2 1 screw axis
The permissible combinations of rotation, reflection, and inversion symmetry with translation symmetry are restricted by the repetitive nature of a crystal to 230 combinations, known as space groups. Of the 230 space groups, 165 have reflection symmetry (mirror or glide planes) or inversion symmetry (a center of inversion, rotatory reflection axis or rotating inversion axis). Since these symmetry operations convert a chiral molecule into its enantiomer, chiral molecules can crystallize in these space groups if and only if they co-crystallize with an equal number of molecules of the opposite enantiomeric form—as racemates. If the chiral compound is not racemic, however, the number of space groups in which it may crystallize is reduced from 230 to the 65 space groups in Table 1. Twenty-two space groups (which are actually eleven pairs of enantiomeric space groups) have the property of being unable to accommodate anything but optically active forms of chiral molecules. Table 2 (9) lists these symmetry groups. Although they are not strictly synonymous, the terms “scattering”, “diffraction”, and “reflection” have often been used as though they are, a practice which sometimes leads to confusion. On the advice of a referee, we have chosen to avoid the terms “reflected” and “reflection” and to replace them by “scattered” and “scattering point”, respectively, throughout this manuscript. The experimental basis for X-ray crystal structure analysis is the scattering of X-rays by electrons in a crystal. The repetitive nature of the crystal lattice results in the production of an interference pattern known as a diffraction pattern: where the scattered X-ray beams are in phase, they reinforce each other, and the intensity of the beam increases; where the scattered X-ray beams are out of phase
Like its counterpart for individual molecules, the mirror plane, a glide plane is incompatible with chirality except in the case of racemic compounds, to relate one chiral molecule to its enantiomer. Similarly, like its counterpart for individual molecules, the simple axis of rotation, a screw axis is compatible with chirality. Table 1. The 65 Space Groups Possible for Chiral Molecules (11 ) The combination of translational symmeSpace Group Space Group Space Group try with rotation axes and mirror planes can Crystal Class S y m b o l S y m b o l N o . S ymbol No. N o . lead to new symmetry constraints on a system T r i c l i n i c P 1 1 imposed by the crystal lattice that may not be present in the isolated molecule. For example, Monoclinic P2 3 P21 4 C2 5 only twofold, threefold, fourfold, or sixfold roOrthorhombic P222 16 P2221 17 P21212 18 tational symmetry is compatible with the reP212121 19 C2221 20 C222 21 petitive nature of the crystal lattice; fivefold F222 22 I222 23 I212121 24 symmetry is not. Thus, it is possible that a molecule may possess molecular symmetry incom76 P42 77 Tetragonal P4 75 P41 patible with crystal symmetry A good example P43 78 I4 79 I41 80 of a compound where the molecular and crys90 P4122 91 P422 89 P4212 tal symmetry must differ is ferrocene: the molP41212 92 P4222 93 P42212 94 ecule possesses fivefold rotational symmetry, P4322 95 P43212 96 I422 97 but the crystal cannot have this order of symmetry and cannot impose it on the molecule. I4122 98 The advent of X-ray crystallography as a Trigonal P3 143 P31 144 P32 145 relatively routine tool for determining the R 3 1 4 6 P 3 1 2 1 4 9 P 3 2 1 150 structure of chemical compounds has made it P 3 1 2 1 5 1 P 3 2 1 1 5 2 P 3 1 2 153 more important for chemists to understand the 1 1 2 relationship between molecular symmetry and P3221 154 R32 155 crystal symmetry. In its simplest form, a crysHexagonal P6 168 P61 169 P65 170 tal is a three-dimensional structure generated P6 2 171 P64 172 P63 173 by translation of simple units known as unit P622 177 P6122 178 P6522 179 cells along each of three principal axes of the crystal. A unit cell contains one or more molP6222 180 P6422 181 P6322 182 ecules. In unit cells containing more than one Cubic P23 195 F23 196 I23 197 molecule, the spatial orientations of the molP213 198 I213 199 P432 207 ecules within the unit cell are usually (but not P 4 3 2 2 0 8 F 4 3 2 2 0 9 F 4 3 2 210 2 1 always) related to each other by simple transI432 211 P4332 212 P4132 213 lational or rotational operations or combinations of both. I4132 214
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Research: Science & Education Table 2. Chiral Space Groupsa Space Group
Space Group
Space Group
P31 (P32)
P3112 (P3212)
P3121 (P3221)
P41 (P43)
P4122 (P4322)
P41212 (P43212)
P61 (P65)
P62 (P64)
P6122 (P6522)
P6222 (P6422)
P4132 (P4332)
aThe space group in parentheses gives the reverse spiral form of the group preceding it.
the interference is destructive, and the intensity of the scattered beam is reduced (ultimately to zero). Ultimately this interference pattern contains all the structural information for both the crystal lattice and the molecules or ions in the crystal. The first step in an X-ray crystal structure analysis is to measure the intensities of the scattered X-rays. As measured, these intensities are a function of several variables, including the distribution of the electron density within the unit cell of the crystal, the dimensions of the crystal, the diffractometer geometry, and several other experimental variables. In a typical X-ray structure analysis, therefore, the intensities of the scattered X-rays are first converted into structure amplitudes, |F(hkl)| (10), where h, k, and l are called the Miller indices of the scattering points. Each scattering point is defined by a unique set of three Miller indices. The structure amplitude of a particular scattering point is related to the experimentally observed intensity, but since it is corrected for geometric, instrumental and other experimental factors, it is much more generally useful and much more amenable to the mathematics of the structure analysis. A fundamental quantity in the scattering of X-rays by crystals is the structure factor (11). Unlike beam intensities, structure factors can be calculated from atomic positions and they can be used directly to calculate electron densities. The structure factor is a vector that can be written in the form of a complex number: F(hkl) = A′ (hkl) + iB′ (hkl)
—
where i is √ {1 . A′ and B′ are parameters related to a key quantity known as the phase angle, φ, through the equations: A′ (hkl) = |F(hkl)|cos φ (hkl) B′ (hkl) = |F(hkl)|sin φ (hkl) If one knows the phase angles, φ (hkl), of the reflected X-rays, the solution of the structure becomes straightforward, since Fourier transformation of the experimental structure amplitudes along with the appropriate phase angles gives an electron density map from which the positions of atoms within the unit cell may be extracted. Unfortunately, these phases cannot be measured directly, so a key part of the process of extracting structural information from a diffraction pattern involves determining the phase angles, φ (hkl), of the scattered X-rays to reproduce the diffraction pattern—solving the phase problem (12). There are several methods for solving the phase problem. One of the simplest is to ensure that the compound whose structure is being determined contains a heavy atom (i.e., one with many electrons). When a molecule contains a heavy atom, that atom contributes disproportionately to the scattering of the Xrays, and one can often locate its position in the unit cell by
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a process known as a Patterson synthesis (13). While the Patterson synthesis is still used in certain cases, many modern crystallography programs use symbolic logic to develop a set of phase angles that serve as the basis for generating the first electron density map. When this set of phase angles is used, the solution of the problem is said to be accomplished by direct methods (14). Regardless of how the initial set of phase angles is obtained, the next step of the Xray structure analysis is the Fourier transformation of the experimental structure amplitudes along with the appropriate phase angles to give an electron density map. From this electron density map, the positional coordinates of some or all of the atoms of the molecule may be obtained. In Xray crystallography, these positional coordinates are expressed relative to the dimensions of the unit cell rather than as Cartesian coordinates. If the positional coordinates of the atoms of a compound are known, a set of structure factors may be calculated1 and used to compare with the observed structure amplitudes (i.e., those derived from the experimental data). The relationship for calculating the structure factors from atomic positional coordinates is: F(hkl) = ∑ficos2π(hxi + kyi + lzi) + i[∑ficos2π(hxi + kyi + lzi)] where the positions of individual atoms relative to the unit cell are given by the xi, yi, and zi coordinates, and the element type of individual atoms (the number of electrons available to scatter X-rays) is given by the individual fi factors, also known as atomic scattering factors. It is important to reiterate that the positional parameters for atoms are not Cartesian coordinates. The atomic scattering factor, which is expressed in units of electrons, is a measure of the effective electron density of an atom. As such, the atomic scattering factor is related to the atomic number of the atom (in fact, its maximum value is the atomic number of the atom), although the relationship is not simple; the value also depends on the scattering angle. The ability to distinguish between atoms of different elements is associated with this part of the structure factor term; a relatively electron-rich atom like copper has a larger fi value than does carbon. Once a completed structure has been obtained, the structural model is refined by least squares methods that minimize the sum of the squares of differences between the observed structure amplitudes and the structure amplitudes calculated on the basis of the structural model. One measure of the confidence in a structural model is defined in terms of a reliability index, R, that compares the |F(hkl)| values derived from the intensities with those calculated from the structural model. X-ray Crystallography and Absolute Configuration Many molecules whose structures are determined by X-ray crystallography are chiral, and they can exist as one of two enantiomeric forms. It is frequently important to be able to assign not only the relative configuration to a molecule (a process for which X-ray crystal structure analysis is unrivaled for crystalline compounds), but also its absolute configuration, as well. Unfortunately, in most cases Xray crystal structure analysis is limited in the amount of information it can provide about the absolute configuration of a molecule. In practice, this limitation is often circumvented by using a chiral adjunct of known absolute configuration (e.g., crystallizing an amine as its (1 S)-(+)camphorsulfonic acid salt prior to X-ray crystal structure analysis), but this is often impractical.
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Research: Science & Education The reasons for the lack of information about the absolute configuration of a molecule provided by X-ray structure analysis are summarized by a generalization known as Friedel’s law (15), which states that the intensities of the hkl scattering points are usually the same as those of thehkl (or {h,{k,{l) scattering points. In other words, the X-ray diffraction pattern produced by scattering from a crystal is normally centrosymmetric regardless of whether the molecules within the unit cell of the crystal are chiral or not. Friedel’s Law makes the point that while X-ray scattering is highly sensitive to the magnitude of the scattering angle, θ, for most atoms it is not sensitive to measurement at +θ or { θ. Friedel’s law has two major practical consequences. The first relates to the actual diffraction experiment—the centrosymmetry of the diffraction pattern means that only a fraction of the entire volume around the crystal need be sampled for X-rays, even though the scattering of X-rays occurs throughout the entire spherical volume surrounding the crystal. The second consequence is that either enantiomer of the molecule may be chosen as the structure model, since they give the same results in terms of statistical measures of agreement between the model and the measured data. This means that it is normally not possible to determine the absolute configuration of small molecules by Xray diffraction analysis alone. Like many generalizations, Friedel’s law is not absolute. Certain atoms (rubidium is a good example) give what is known as anomalous scattering, where scattering of the X-ray through +θ degrees gives a beam whose intensity differs significantly from that obtained when the X-ray is scattered through { θ degrees, in violation of Friedel’s law (16). In 1951 Bijvoet (17) demonstrated how the chirality information can be retained and extracted when the molecule contains atoms that participate in anomalous scattering. He determined the absolute configuration of potassium rubidium tartrate. This feat, the first experimental assignment of the absolute configuration of a chiral organic molecule, showed that Fischer’s arbitrary assignment of D-glucose had, in fact, been correct (perhaps to the chagrin of textbook publishers, who would have had a windfall if all the structures in organic chemistry books had to be redrawn as their mirror images). In practice, when anomalous scattering is appreciable, a number of intensity values from the two hemispheres of the region about the crystal may be different enough that their comparison reveals which chiral species is present. In these cases, absolute configuration assignment is possible. In conclusion, chirality is a molecular property that is well understood by most chemists, but transferring the concept of chirality to the same molecule within a crystal lattice is a much less common part of the training of a chemist. However, as X-ray crystal structure analysis assumes a
position where it is considered routine for analyzing a new compound, it becomes more important that chemists understand the scope and limitations of the technique, including the relationship between molecular and crystal symmetry. Note 1. The atoms within a molecule and the molecules within a crystal are constantly in motion due to molecular and crystal vibrations. Atomic positions revealed in the structure solution correspond to the time-averaged positions of the atoms. Calculated structure factors are usually modified by thermal correction parameters that model the time-averaged motions of real atoms in the crystal.
Literature Cited 1. Biot, J. B. Mem. Acad. Sci. Inst. 1819, 2, 41. 2. Pasteur, L. Ann. Chim. Phys. 1848, 24(3), 442; Compt. Rend. 1849, 28, 477; 29, 297. 3. Pasteur, L. “Molecular Asymmetry”; Alembic Club Reprint No. 14. 4. Recent Developments in Flavor and Fragrance Chemistry; Hopp, R.; Mori, K., Eds.; Proceedings of the 3rd International Haarman & Reimer Symposium; VCH: Weinheim, 1993; p 20. 5. van’t Hoff, J. Voorstel tot uitbreiding der tegenwoordig in die scheikunde gebruikte structuur-formules in die ruimte: benevens een daarmeê samenhangende opmerking omtrent het verband tuschen optisch actief vermogen en chemische constituie van organische verbindingen; Utrecht, 1874; this work was revised, expanded and reprinted in French as La Chimie dans l’Espace; Paris, 1875. 6. Le Bel, J. A. Bull. Soc. Chim. Paris 1874, 22, 333. 7. Cahn, R. S.; Ingold, C. K.; Prelog, V. Experientia 1956, 12, 81. 8. Posner, G. H.; Miura, K.; Mallamo, J. P.; Hulce, M.; Kogan, T. P. In Current Trends in Organic Synthesis; Nozaki, H., Ed.; Pergamon: London, 1984; p 177; Posner, G. H.; Mallamo, J. P.; Miura, K.; Hulce, M. In Asymmetric Reactions and Processes in Chemistry; Eliel, E.; Otsuka, S., Eds.; ACS Symposium Series 185; American Chemical Society: Washington, DC, 1982; p 139. 9. Cotton, F. A. Chemical Applications of Group Theory, 3rd ed.; Wiley: New York, 1990; p 410; Ladd, M. F. C. Symmetry in Molecules and Crystals; Halstead: New York, 1989. 10. Buerger, M. J. Crystal Structure Analysis; Wiley: New York, 1960; pp 259–282; Lonsdale, K. Simplified Structure Factor and Electron Density Formulae for the 230 Space Groups of Mathematical Crystallography; G. Bell & Sons: London, 1935; Ladd, M. F. C.; Palmer, R. A. Structure Determination by X-Ray Crystallography, 2nd ed.; Plenum: New York, 1985; p 168. 11. International Tables for Crystallography, 4th rev. ed.; Hahn, T., Ed.; International Union for Crystallography; Kluwer Academic: Norwell, MA, 1995; Vol. 1. 12. Ladd, M. F. C.; Palmer, R. A. Structure Determination by X-Ray Crystallography, 2nd ed.; Plenum: New York, 1985; pp 230–286. 13. Patterson, A. L. Z. Krystal. 1935, A90, 517. 14. Hauptmann, H.; Karle, J. Solutions of the Phase Problem, I. The Centrosymmetric Crystal; American Crystallographic Association Monograph No. 3, 1953; Germain, G.; Main, P.; Woolfson, M. M. Acta Crystallogr. B 1970, B26, 274. 15. Ladd, M. F. C.; Palmer, R. A. Structure Determination by X-Ray Crystallography, 2nd ed.; Plenum: New York, 1985; p 168. 16. Ibid; p 283. 17. Bijvoet, J. M.; Peerdeman, A. F.; van Bornmell, A. J. Nature 1951, 168, 271.
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