M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 11
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The acetanilide molecules appear in pairs and the twomolecules in each pair are related by an inversion center. On the otherhand, the p-chloroacetanilide molecules are all aligned in one direction. The molecular arrangements in the two crystals are shown inFigure 2-33.Even very simple structures may form polar crystals. For example,in a polar crystal composed of diatomic molecules AB, the molecularaxis will be oriented more along the polar direction of the crystal thanperpendicular to it. Furthermore, as there is an ABAB. .
. array in thecrystal, it is required that the spacing between the atom A and the twoadjacent atoms B be unequal in order to have a polar axis present,ABABAB...Curtin and Paul characterize this situation from the point of viewof a submicroscopic traveler proceeding along this array of atoms.The observer is able to determine the direction of travel thanks to thedifference in spacing. The distance is always longer from atom B toatom A and shorter from atom A to the next atom B in one directionwhereas the reverse is true in the opposite direction.602 Simple and Combined SymmetriesFigure 2-33. Left: The centrosymmetric arrangement of acetanilide moleculesof the crystal resulting in centrosymmetric crystal habit; Right: The p-acetanilidemolecules are aligned in a head-tail orientation resulting in the occurrence of acpolar axis of the crystal habit [39]. Both are reprinted with permission from 1981 American Chemical Society and D.
Y. Curtin and I. C. Paul.Crystal polarity may have important consequences in the chemicalbehavior. In solid/gas reactions, for example, crystal polarity may bea source of considerable anisotropy. There are also important physical properties characterizing polar crystals, such as pyroelectricityand piezoelectricity and others [40]. The primitive cell of a pyroelectric crystal possesses a dipole moment. The separation of the centersof the positive and negative charges changes upon heating. In thisprocess the two charges migrate to the two ends of the polar axis.Piezoelectricity is the separation of the positive and negative chargesupon expansion/compression of the crystal. Both pyroelectricity andpiezoelectricity have practical uses.2.7. ChiralityThere are many objects, both animate and inanimate, which have nosymmetry planes but which occur in pairs related by a symmetry planeand whose mirror images cannot be superposed. W. H.
Thompson,Lord Kelvin, wrote: “I call any geometrical figure or group of points2.7. Chirality61‘chiral’, and say it has chirality, if its image in a plane mirror, ideallyrealized, cannot be brought into coincidence with itself” [41]. Hecalled forms of the same sense homochiral and forms of the opposite sense heterochiral. The most common example of a heterochiralform is hands. Indeed, the word chirality itself comes from the Greekword for hand, cheir. Figures 2-34 and 2-35 show heterochiral andhomochiral pairs of hands.
Illustrations, however, may be foundin the most diverse examples and Figure 2-36 presents a sampler.The simplest chiral molecules are those in which a carbon atom issurrounded by four different ligands—atoms or groups of atoms atthe vertices of a tetrahedron. All the naturally occurring amino acidsare chiral, except glycine.A chiral object and its mirror image are enantiomorphous, and theyare each other’s enantiomorphs. Louis Pasteur (Figure 2-37) was thefirst who suggested that molecules can be chiral. In his famous experiment in 1848, he recrystallized a salt of tartaric acid and obtainedtwo kinds of small crystals which were mirror images of each otheras seen by Pasteur’s models in Figure 2-38 preserved at InstitutPasteur at Paris.
Originally Pasteur may have been motivated to makethese large-scale models because Jean Baptiste Biot, the discoverer ofoptical activity had very poor vision by the time of Pasteur’s discovery[42]. Pasteur demonstrated chirality to Biot, who was visibly affected(a)(b)Figure 2-34. Heterochiral pairs of hands. (a) Tombstone in the Jewish cemetery inPrague; (b) Sculpture Park in Budapest (photographs by the authors).622 Simple and Combined Symmetries(a)(b)(c)Figure 2-35.
Homochiral pairs of hands. (a) Aguste Rodin, The Cathedral in theRodin Museum, Paris (reproduced by permission, photograph by the authors); (b)U.S. stamp; (c) Logo with SOS distress sign at a Swiss railway station (photographby the authors).by what he saw and told Pasteur: “My dear child, I have loved scienceso much throughout my life that this makes my heart throb” [43].The two kinds of chiral crystals have the same chemical composition, but differ in their optical activity.
One is laevo-active (L) andthe other dextro-active (D). According to the Nobel laureate biologistGeorge Wald, “No other chemical characteristic is as distinctive ofliving organisms as is optical activity” [44].The true absolute configuration of molecules could not be determined at Pasteur’s time, so the organic chemist Emil Fischer had arbitrarily assigned an absolute configuration to sugars that had a 50%chance of being correct [45]. It was a great achievement of crystallography when Bijvoet and his associates determined the sense ofchirality of molecules [46]. Luckily, Fischer’s guess proved to becorrect. By now the absolute configuration has been established forrelatively simple molecules as well as for large biological molecules.2.7. Chirality63(a)(b)(d)(c)(e)Figure 2-36.
Illustrations of chiral pairs. (a) Decorations (in Bern, Switzerland,photograph by the authors) whose motifs of fourfold rotational symmetry are eachother’s mirror images; (b) Quartz crystals; (c) J. S. Bach, Die Kunst der Fuge,Contrapunctus XVIII, detail; (d) Legs (detail of Kay Worden’s sculpture, Wave, inNewport, Rhode Island), (photograph by the authors); (e) A molecule and its mirrorimage in which a carbon atom is surrounded by four different atoms, for example,CHFClBr.If a molecule or a crystal is chiral, it is necessarily optically active.The converse is, however, not true. There are non-enantiomorphoussymmetry classes of crystals that may exhibit optical activity.L.
L. Whyte extended the definition of chirality: “Threedimensional forms (point arrangements, structures, displacements,and other processes) which possess non-superposable mirror images642 Simple and Combined SymmetriesFigure 2-37. Louis Pasteur’s bust in front of the Institut Pasteur, Paris (photographby the authors).are called ‘chiral’” [47].
A chiral process consists of successive statesall of which are chiral. The two main classes of chiral forms are screwsand skews. Screws may be conical or cylindrical and are orderedwith respect to a line. Examples for the latter are the left-handed andright-handed helices in Figure 2-39.Figure 2-38.
Pasteur’s models at the Institut Pasteur (photographs by the authors).2.7. Chirality65Figure 2-39. Left: Left-handed and right-handed helices at the Monastery inZagorsk, Russia; and Right: in an Italian monastery (photographs by the authors).Vladimir Prelog offered yet another definition of chirality thatcontains only subtle differences from previous definitions: “An objectis chiral if it cannot be brought into congruence with its mirror imageby translation and rotation. Such objects are devoid of symmetryelements which include reflexion: mirror planes, inversion centersor improper rotational axes” [48].
Prelog had a beautiful ex librisbookplate by the Swiss graphic artis, Hans Erni (Figure 2-40). Prelogmaintained that the drawing represented all three basic paraphernalianecessary for dealing with chirality, viz., human intelligence, a leftand a right hand, and two enantiomorphous tetrahedra. These twotetrahedra are not regular because regular tetrahedra could not bechiral due to their symmetry planes.An interesting overview of the left/right problem in science is givenby Martin Gardner [50]. Distinguishing between left and right hasalso considerable social, political, psychological connotations.
Forexample, left-handedness in children is viewed with varying degreesof tolerance in different parts of the world. Figure 2-41 shows different(homochiral and heterochiral) chairs a quarter of a century ago at the662 Simple and Combined SymmetriesFigure 2-40. Hans Erni’s ex libris bookplate for Vladimir Prelog with a dedicationto one of the authors (courtesy of Vladimir Prelog, Zurich). A peculiar feature ofthis drawing is that the two hands appear to be inverted and can be imagined as aresult of the two arms being crossed [49]. Erni made other versions of this drawingin which the two hands appear to be non-inverted.University of Connecticut. Older classrooms used to have chairs forthe right-handed students only whereas newer chairs were made forboth right-handed and left-handed students.2.7.1. Asymmetry and DissymmetrySometimes the terms asymmetry, dissymmetry, and antisymmetry areconfused in the literature although the scientific meaning of theseFigure 2-41.
Classrooms with homochiral and heterochiral chairs in the 1980s atthe University of Connecticut (photographs by the authors).2.7. Chirality67terms is in complete conformity with the grammar of these words.Asymmetry means the complete absence of symmetry, dissymmetrymeans the absence of certain symmetry and antisymmetry means thesymmetry of opposites (see Section 4.6). Pasteur used “dissymmetry”for the first time as he designated the absence of a symmetry planein a figure. Accordingly, dissymmetry did not exclude all elementsof symmetry, only the absence of certain symmetries.
Chirality is aconspicuous example of dissymmetry.Pierre Curie suggested a broad application of the term dissymmetry. He called a crystal dissymmetric in case of the absence ofthose elements of symmetry upon which depends the existence ofone or another physical property in that crystal. In Pierre Curie’soriginal words: “Dissymmetry creates the phenomenon” (“C’est ladissymétrie qui crée le phénomène”) [51]. Namely, a phenomenonexists and is observable due to dissymmetry, i.e., due to the absence ofsome symmetry elements from the system. Finally, Shubnikov calleddissymmetry the falling out of one or another element of symmetryfrom a given group [52]. He argued that to speak of the absenceof elements of symmetry makes sense only when these symmetryelements are present in some other structures.Thus, from the point of view of chirality any asymmetric figureis chiral, but asymmetry is not a necessary condition for chirality.
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