M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 13
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It was also given to pregnant women sufferingfrom morning sickness. The drug was marketed as a racemate and bythe early 1960s, many birth defects in Western Europe were associated with thalidomide. When thalidomide was administered to pregnant women in the first trimester of their pregnancy, it acted as ateratogen, causing stunted or deformed arms and legs in the infants.In the wake of the many tragedies, the drug was withdrawn fromthe market. The tragedies occurred worldwide except in the Sovietblock where it was not available and the United States where the Food2.7.
Chirality73Figure 2-44. Thalidomide images (Computer drawing by Ilya Yanov, Jackson,Mississippi).and Drug Administration (FDA) had never approved it. The lack ofapproval originated from the mistaken belief by an FDA agent whosuspected incidences of peripheral neuropathy, which, as it turned out,was unconnected with the teratogenic effect of thalidomide.Research on thalidomide did not stop with its removal from themarket.
For a while, it was used as an excellent example of oneversion being beneficial and the other harmful. Accordingly, it wassuggested that had the beneficial isomer been resolved and administered selectively, the tragedies could have been avoided. Later studies,however, reported that thalidomide undergoes rapid interconversionbetween the enantiomers in the human organism, so resolvation couldnot have eliminated the dangers.
Thalidomide research continues dueto its potentials for beneficial uses as, for example, in treating inflammatory and autoimmune diseases [67]. The thalidomide tragediesfacilitated the introduction of stringent regulations about the approvalof chiral drugs especially in the European Union and the UnitedStates.There are a few examples on the next page in which twinenantiomers have different properties.742 Simple and Combined SymmetriesRight-hand versionLeft-hand versionEthambutolTreats tuberculosisCauses blindnessPenicillamineTreats jointsVery toxicNaproxenReduces pain, fever, inflammationToxic for the liver(however, carries the risk of heart disease)Propoxyphene∗Pain relieverCough medicineNorgestrelNegligible contraceptive activity,Contraceptivebut no harmful effectAsparaginBitterSweetCarvonCaraway smellSpearmint smellLimoneneLemon smellOrange smellIn the light of the above set of examples, it is obvious why it isso important to produce chirally “pure” substances [68].
Three scientists from among those who worked out reliable and efficient techniques for this purpose were awarded the Nobel Prize for Chemistryin 2001, K. Barry Sharpless, William S. Knowles, and Ryoji Noyori.The Swedish academician who introduced the three scientists at theaward ceremony stressed that they “have developed chiral catalysts inorder to produce only one of the [chiral] forms” [69]. Chiral production and separation continue to be among the most practical problemsin the application of chemical advances [70].2.7.3. La coupe du roiAmong the many chemical processes in which chirality/achiralityrelationships may be important is the fragmentation of somemolecules and the reverse process of the association of molecular fragments.
Such fragmentation and association can be considered generally and not just for molecules. The usual cases are those in which anachiral object is bisected into achiral or heterochiral halves. On the∗Note that the names of the respective medications are each other’s mirror images,RRversus Novrad.Darvon2.7. Chirality(a)75(b)(c)Figure 2-45. Dissection of an equilateral triangle into (a) Achiral; (b) Homochiral;and (c) Heterochiral segments after Shubnikov and Koptsik [72].
Used with permission from Nauka Publishers, Moscow.other hand, if an achiral object can be bisected into two homochiralhalves, it cannot be bisected into two heterochiral ones. A relativelysimple case is the tessellation of planar achiral figures into achiral,heterochiral, and homochiral segments. Such tessellations are illustrated for the equilateral triangle in Figure 2-45 [71].Anet et al. [73] have cited a French parlor trick called la coupedu roi—the royal section—in which an apple is bisected into twohomochiral halves, as shown in Figure 2-46. An apple can be easilybisected into two achiral halves. On the other hand, it is impossible to bisect an apple into two heterochiral halves.
Two heterochiralhalves, however, can be obtained from two apples, both cut into twohomochiral halves in the opposite sense. According to la coupe du roitwo vertical half cuts are made through the apple. One cut goes fromthe top to the equator, and another, perpendicularly, from the bottom tothe equator. In addition, two nonadjacent quarter cuts are made alongthe equator. If all this is properly done, the apple should separate intotwo homochiral halves.The first chemical analog of la coup du roi was demonstrated by Cinquini et al. [74] by bisecting the achiral moleculeof cis-3,7-dimethyl-1,5-cyclooctanedione into homochiral halves,viz.
2-methyl-1,4-butandiol. The reaction sequence is depicted in762 Simple and Combined SymmetriesFigure 2-46. The French parlor trick la coupe du roi: An apple can be cut into twohomochiral halves in two ways which are enantiomorphous to each other. (An applecannot be cut into two heterochiral halves. Two heterochiral halves originating fromtwo different apples cannot be combined into one apple).Figure 2-47 after Cinquini et al. [75] who painstakingly documentedthe analogy with the pomaceous model. Only examples of thereverse coupe du roi had been known prior to their work.
ThusAnet et al. [76] reported the synthesis of chiral 4-(bromomethyl)-6(mercaptomethyl)[2.2]metacyclophane. They then showed that twohomochiral molecules can be combined to form an achiral dimer asshown in and illustrated by Figure 2-48.2.8. Polyhedra“A convex polyhedron is said to be regular if its faces are regular andequal, while its vertices are all surrounded alike” [79].
A polyhedronis convex if every dihedral angle is smaller than 180◦ . The dihedralangle is the angle formed by two polygons joined along a commonedge.There are only five regular convex polyhedra, a very small numberindeed. The regular convex polyhedra are called Platonic solidsbecause they constituted an important part of Plato’s natural philosophy. They are: the tetrahedron, cube (hexahedron), octahedron,2.8.
Polyhedra77Figure 2-47. La coupe du roi and the reaction sequence transforming cis-3,7dimethyl-1,5-cyclooctanedione into 2-methyl-1,4-butanediol. After Cinquini et al.[77].dodecahedron, and the icosahedron. The faces are regular polygons;regular triangles, regular pentagons, or squares.A regular polygon has equal interior angles and equal sides.Figure 2-49 presents a regular triangle, a regular quadrangle, i.e.,square, a regular pentagon, and a few more. As the number of sidesapproaches infinity, the circle is the limit. The regular polygons havean n-fold rotational symmetry axis perpendicular to their plane andgoing through their midpoint. Here n is 1, 2, 3, . .
. up to infinity forthe circle.The five regular polyhedra and some of their characteristicsymmetry elements are shown in Figure 2-50 with their parameters782 Simple and Combined SymmetriesFigure 2-48. Reverse la coup du roi and the formation of dimer from twohomochiral 4-(bromomethyl)-6-(mercaptomethyl) [2.2]metacyclophane molecules.c 1983 American ChemicalAfter Anet et al. [78]. Reprinted with permission from Society and Kurt Mislow.compiled in Table 2-3. A commemorative stamp honoring LeonhardEuler and his equation, V − E + F = 2, where V, E, and F are thenumber of vertices, edges, and faces, are reproduced in Figure 2-51.The equation is valid for polyhedra having any kind of polygonalFigure 2-49.
Regular polygons.2.8. Polyhedra79Figure 2-50. The five Platonic solids with some of their characteristic symmetryelements.faces. According to Weyl [80], the existence of the tetrahedron, cube,and octahedron is a fairly trivial geometric fact, but the discovery ofthe regular dodecahedron and the regular icosahedron was “one of themost beautiful and singular discoveries made in the whole history ofmathematics.” However, according to Coxeter [81], to ask the question who first constructed the regular polyhedra is like asking thequestion who first used fire.Many primitive organisms have the shape of the pentagonal dodecahedron.
As will be seen later, pentagonal symmetry used to be considered forbidden in the world of crystal structures. Belov [82] suggestedthat the pentagonal symmetry of primitive organisms represents their80NameTetrahedronCubeOctahedronDodecahedronIcosahedron2 Simple and Combined SymmetriesTable 2-3. Characteristics of the Regular PolyhedraPolygonNumberVertex Numberof facesfigureof vertices343534681220334354862012Numberof edges612123030defense against crystallization.
Polyhedral-shaped radiolarians fromErnst Haeckel’s book [83] have been reproduced frequently in treatises on symmetry; in Figure 2-52, we show a few of them. Two artisticrepresentations of the regular pentagonal dodecahedron are shown inFigure 2-53.Figure 2-54 shows Kepler and his planetary model based on theregular solids [84]. According to this model the greatest distance ofone planet from the sun stands in a fixed ratio to the least distance ofthe next outer planet from the sun.
There are five ratios describing thedistances of the six planets which were known to Kepler. A regularsolid can be interposed between two adjacent planets so that the innerplanet, when at its greatest distance from the sun, lays on the inscribedsphere of the solid, while the outer planet, when at its least distance,lays on the circumscribed sphere.Arthur Koestler in The Sleepwalkers called this planetary model[86] “.
. . a false inspiration, a supreme hoax of the Socratic daimon,. . .” However, the planetary model which is also a densest packingmodel probably symbolizes Kepler’s best attempt at attaining a unifiedFigure 2-51. Euler and his equation, e − k + f = 2, corresponding to V − E + F =2, where the German e (Ecke), k (Kante), and f (Fläche) correspond to vertex (V),edge (E), and face (F) in English, respectively (East German postal stamp).2.8. Polyhedra81Figure 2-52. Radiolarians from Haeckel’s book [85].view of his work both in astronomy and in what we call today crystallography.Inorganic chemistry is especially rich in systems that can bedescribed by two or more polyhedra, nested into each another. Aninteresting case is the W6 S8 (PEt3 )6 crystal [88] in which there isa central octahedron formed by the tungsten atoms, surrounded bya sulfur cube that is enveloped by an octahedron formed by thephosphine ligands (Figure 2-55).
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