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J . Am . Chem. SO C. 984, 106 3319-3328 3319nor PO PC undergo a p hase transition, since there are no dis-continuities in In k vs. pressure plots.I6 Pressure, however, doescompress the host lipid matrix (PO PC ), and in part th e positiveA v of transfer reflects the work necessary to o vercome this effect.Finally, MPNPC is an amphiphilic molecule and changes involume can arise from electrostriction effects near the charged

amphiphiles is governed by hydrophobic interaction^",'^ wepostulate a change in the packing of water around MPNPC(hydratio n density) in the activated state . Futu re studies to testthis hypothesis will focus on the use of neutral salts in a lyotropicseries, in conjunction with high-pressure perturbation, to varylipophile hydration.*choline moiety or by hydrophobic hydration of the fatty acidchains. The transfer rates of pyrene conjugated hydrocarbons4(uncharged and nonpolar molecules) indicate a AV similar tothat for MP NP C, correcting for differences in molecular weight(W. W. M antulin , unpublished d ata). Therefore, by comparisonit appears that the zwitterionic polar head group of M PN PC isnot as important a factor as the aliphatic region in establishingthe size and mag nitude of A v for transfer.17 Sinc e tran sfer of(16) Heremans, K.; DeSmedt, H.; Wuytack, F. Biophys . J . 1982, 37,(17) Massey, J. B.; Gotto, A. M., Jr.; Pownall, H. J . J . B i d . Ch em . 1982,74-75.257, 5444-5448.

Acknowledgment. W e acknowledge stimulating discussions withDrs. G. Weber and D. Jameson. The authors are indebted toDottie Tullos for preparing the manuscript, Susan Kelly forproviding the line drawing, and F. W. C. Fu for technical as-sistance. This research was supported by the Specialized Cente rof Research in Atherosclerosis HL-27341 (H.J.P. W.W .M.)and Grant HL-27104 (W.W.M.) and a gI,ant from the RobertA. Welch Foundation, 49 06 (H.J .P . ) .

Registry No. POPC, 6753-55-5; MPNPC, 79821-58-2.(18) Greaney, G. S.;Somero, G. . Biochemistry 1979, 18 5322-5332.

Stereoisomerism and Local ChiralityKurt Mislow* and Jay Siegel*Contribution fr om the Department of Ch emistr y, Princeton University,Princeton, New Jersey 085 44. Received Septemb er 19, 1983.Revised Manuscript Received February 4, 1984

Abstract: The traditional linkage between stereoisomerism and local chirality that is expressed in terms such as asymmetriccarbon atom or element of chirality represents a source of conceptual confusion in modern Stereochemistry. Molecularsegments must be viewed from two separate and d istinct aspects: their charac ter as stereogenic units and th eir local symmetry.The first is dependent on bonding co nnectivity (constitution) and is rooted in graph and p ermutation group theory, whereasthe second is indepe nden t of constitu tion and is rooted in the theory of symm etry groups. Althou gh these two aspects arein principle distinct and serve different purposes, they happen to overlap in the case of the regular tetrahed ral permutationcenter. It is for this reason that the concepts of chirality and stereog enicity are most closely associated in organic stereochemistrywhere this center plays a domin ant role. The present analysis clarifies stereochemical concepts, sheds new light on the m eaningof stereochemical terminology, and ipso facto disposes of a number of notions introduced into stereochemistry since van tHof fs day. To complete our analysis of stereochemical theory, a new treatment of prochirality is proposed. A theoreticalframew ork is construc ted that assigns membership in one of three classes of prochirality to any ach iral molecular model accordingto symmetry.

According to van t Hoff, a carbon atom that is combined withfour different univalent groups and whose affinities are directedtoward the vertices (or, equivalently, faces) of a tetrahedron isasymmetric.* This term refers to the environment of the carbonatom at the center of the tetrahedron, rather than to the atomi t ~ e l f . ~ owever, asymmetric could obviously ust as well referto the environment of the ligands tha t ar e attached to th e carbonatom . Wh y then should this term be reserved for the ligatingcenter? To resolve this question, we must first address the m oregeneral problem of symmetry and chirality at the local level.Local SymmetryW e recently discussed th e dissection of geometric objects intoisometric segments, with emphasis on objects that represent rigidmodels of m o le c~ le s. ~ t was shown that when such an objectis partitioned into an ensemble of segments by a cut, the rela-tionship among the segments is dictated by the symmetry of theensemble, Le., the object, the cut, and the segm ents in situ. In-trinsic to this analysis is the restriction that no segment maycontain a symmetry element that does not also belong to themolecular model. Two importa nt corollaries from this are th atall segments of a chiral model are chiral, and that the segmentsof an achiral model may be achiral or chiral. Thu s, if G and H

+Dedicated o the memory of George W. Wheland.0002-7863 /84/1506-3319$01.50/0

ar e the point groups of the model a nd of any one of its segments,respectively, then H , the local symmetry group, must be a subgroupof G . This condition expresses the fact tha t every segment must(1) van t Hoff, J. H. Voorstel tot uitbreiding der tegenwoordig in descheikunde gebruikte structuur-formules in de ruimte; benevens een daarmeesamenha ngende opmerking omtrent het verband tusschen optisch actief ver-mogen en chemische constitutie van organische verbindingen; J. Greven:Utrecht, 1874. van t Hoff, J. H. Arch. NZerl. Sci. Exacfes Nut. 1874, 9, 445.van t Hoff, J. H ., A Suggestion Looking to the Extension into Space of theStructural Formulas at Present Used in Chemistry and a Note upon theRelation between the Optical Activity and the Chemical Constitution ofOrganic Compounds; Benfey, 0. T., Ed.; Dover Publications: N Y , 1963;Classics of Science (Classics in the Theory of Chemical Combinations), Vol.1. See also: van t Hoff, J. H. Bull. Sot. Chim. Fr. 1875, 23 (2), 295.(2) For a historical overview, see: (a) Riddell, F. G.; obinson, M . J. T.Tetrahedron 1974, 30, 2001. (b) Mason , S. F. Top. Stereochem. 1976, 9, 1.(c) Ramsay, 0.B., Ed. =van t Hoff - Le Bel Centennia l; American ChemicalSociety: Washington, DC, 1975; AC S Symp. Ser. No. 12. (d) Ramsay, 0.B. Stereochemistry; Heyden: London, 198 1.(3) Wir bezeichnen deshalb ein solches Kohlenstoffatom als ein asym-metrisches, wobei in Erinnerung gebracht werden moge, dass diese Bezeich-nung sich nicht auf die Gestalt des Kohlenstoffatoms, sondern auf dessenraumliche Lage im Moleki i l be~ieht .~(4) van t Hoff, J. H . Die Lagerung der Atome im Rau me; Herrmann,F., Transl. and Ed.; F. Vieweg und Sohn: Braunschweig, 1877.(5) Anet, F. A. L.; Miura, S. S.;Siegel, J.; Mislow, K. J . Am . Ch em . S o t .1983, 105, 1419. It must be emphasized that this segmentation is an abstractand purely geometric operation and not a chemical fragmentation.

0 1984 American Chemical Societv, , I -


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3320 J . Am . Chem. Soc., Vol. 106 No. 11, 1984be symmetry-adapted to G,6 regardless of the nature of the mo-lecular model.7Local symmetry is a general concept, and refers to every pointand segment of the molecular model, whether such space is oc-cupied by an atom or not. Wh ere local symmetry is used withreference to a single atom , it is customa ry to spea k of H as thesite symme try group,* which may be defined as th e subgrou p ofG that is composed of all symmetry operations that leave thenucleus unmoved. No te that molecular models built from atomsets properly represent molecular symmetry but generally induceincorrect assessment of local or site symmetry. For example, thesymmetry of hydrogen atoms in such sets LE )orresponds tothe local symm etry of H in H z and HC l, but not to that of H inH 2 0 C,),H in CH, Q, or H in CH Br ClF (C]). Of course,a given type of atom m ay exhibit more than one local symm etryin certain molecules; for example, the carbon atoms in D,A-

Mislow and Siege1The site symmetries of atoms in molecules fall into two classes,chiral and achiral.12 It would be useful to have terms to denotememb ership in these two classes. Such terms should have noconno tations of bonding type or connectivity, because chiralityand achirality are pure ly geometric attributes that are in no waydependent onmodels of bonding.13 In the words of Cahn, Ingold,and Prelog,I4 Thus, the main framework for th e classificationof chirality has to be geome trical. To introd uce theories ofchemical bonding, or structural energetics, at this fundamentallevel would create great difficulties.In a natural extension of previous and generally accepted

t e r m i n ~ l o g y , ~e therefore propose to characte rize as chirotopicany atom, and, by extension, any point or segm ent of the molecularmodel, whether occupied by an atomic nucleus or not, th at resideswithin a chiral environment, and as achirotopic any one that doesnot. We may speak of chirotopic and achirotopic centers, atoms,groups, faces, etc. and collectively of chirotopic and achirotopicunits or segments. Thu s, for example, a chirotopic atom is onewith chiral site symmetry, a chirotopic set of atoms is one withchiral local symmetry, and so forth.Chirotopic and Achirotopic Segments. Chirotopic atoms mayoccup y sites of C,,,D,, , 0 or I symmetry. An atom with cyclicsite symmetry (C,,) may be located in a molecule whose pointsymm etry is not C,. A chirotopic atom whose site symm etry ishigher than C, must be located a t the center of a molecule withthe same point symmetry.I6 An atom with Cl site symmetryoccupies a general position in the mode l. The above applies withequal force to any chirotopic segment in the model.All segments of a chiral model are chirotopic, for It [i.e.,chirality] is an all-pervasive property, as it affects all parts of achiral structure.17 While it is also possible to segment a n achiralmodel into exclusively chirotopic atoms, there will necessarilyalways be a t least one point in such a model tha t is achirotopic,even though it may not correspond to a site occupied by a nucleus.Mo re generally, all points in a model that remain invariant undera rotation-reflection operation are achirotopic. For example, inmeso-1,2-dichloro-l,2-dibromoethane,here are two achiralconformations, with Ci and C, symmetry. In the former 2), he

tetramethylallene 1) have DZd,Cz,, and IC, s it e s y r n m e t r i e ~ . ~

1In discussing the local symmetry in a molecular model, accountmust also be taken of the molecular environm ent. For mostchemical purposes, the symmetry of the model in isolation ap-proximates the symmetry of the system, and this approximatio nwill be adopted in all subsequent discussion. W e note, however,that under certain circumstances (e.g., interactions among mol-ecules in the solid state, solute-solvent interaction s, gas-phaseaggregatio ns) the intersection of th e symmetry of the model inisolation with the symm etry of the molecular environment ma yresult in desymmetrization.I0(6) In this sense, a segment has no identity o utside of its identity as a partof the molecular model. Th at is, the symm etry of such a segment is inse-parable from th at of its environment. An analogy might here be drawn to theconcep t of atom-in-molecule: the properties of such a bonded atom (a

segment) are distinct from those of the corresponding atom in the unboundstate (a fragment). From the perspective of symmetry, what a segment istherefore depends on where it is.7 ) T he general model of the molecule is a linear combination of thedistribution fun ctions of the three elementary part icles (the electron, theproton, the neutron). The nuclear point model retains only the 6 nucleardistribution. Degenerate permutations in the general model require the sym-metry equivalence of the permu ted parts, whereas degenerate permutationsin the point model ar e based on nuclear labels and d o not require symm etryequivalence of th e perm uted parts. A further approximation idealizes thenuclear positions to the vertices of regular co ordinatio n polyhedra or permu-tation frames. This model allows all the permutation s of the first two modelsas well as permutations yielding enantiomorphous structures; such permuta-tions ar e infeasible on he first two models without the addition of an inversionoperation. Along with this polyhedral model come stronger restrictions onthe systems to which the model is applicable. While the model may correctlyaccoun t for possible stereoisomers it may inco rrectly or ambigu ously predicttheir internal or external symmetry relations. To exemplify the relation amongthese three models, consider the results of permu tations on C H 3 C H 2 C H B r C Iwith respect to each model. Th e exchan ge of Br and CI distributions in generaland point models yields a new structure that is not symmetry-related to theparent struc ture. Th e polyhedral model, however, yields the mirror imagefrom the same permutation. On he other hand, while transposition of thetwo hydrogens in the methylene group is a degenerate permutation in thepolyhedral as well as in the point model, it creates a new structure in thegeneral model.(8) Flurry, R. L., J r . J . A m . C h em . SOC. 981, 103, 2901 and referencestherein. Th e term site sym metry is also used in solid-state chemistry withreference to the location of a n atom or group of atoms in the crystal .( 9 ) In 1, the three carbon atoms tha t differ in si te symmetry also happento differ in connectivity, but there is no essential connection between these twocharacteristics. For examp le, in C,- 1,1 dichloroallene the three car bon atom sdiffer in connectivity but h ave the sam e si te symmetry C2G), hereas in theC conformations of methan ol the three methyl hydrogens ar e constitutionallyequivalent but differ in si te symmetry C, and CJ,IO) This is an expression of Curies principle of superposition of symmetrygroups: in a composite system, only those symme try elements remain tha t ar ecommon to the component subsystems.

2 3only achirotopic point is the center of symmetry, whereas in thelatter 3), he achirotopic points constitute the plane of symmetry.In both conformations, all atom s ar e chirotopic.Chirotopic atom s located in chiral molecules are enantiotopicby external comparison between enantiomers. Chirotopic atomslocated in achiral molecules are enantiotopic by internal and

(1 1) Curie, P. J . Phys. Paris) 1894, 3 393. See also: Shubnikov, A. V.;Koptsik, V. A . Symmetry in Science and Art; Plenum Press: New York,(12) The site symmetry of molecules in crystals has been similarly clas-sified. See: Zorki, P. M.; Razumaeva, A. E.; Belsky, V. K. Acta Crystallogr.,Sect. A 1977, ,433, 1001.(13) Where the local symmetry refers to sets of atoms whose relatioeposition in space remains invariant under the given conditions, there is no needfor recourse to the directed valence bond model. For example, for the purposeof describing its local symmetry, CH, is treated as a set of four atoms,distributed tetrahed rally in space, whose neighborhood relationships rem ainfixed, and without reference to the question of which atom is bonded to which.(14) Cahn, R . S.; ngold, C. K.; Prelog, V . Angew. Chem., In?.Ed. Engl.1966, 5, 385.1 5 ) Mislow, K.; Raban, M. Top. Stereochem. 1967, I 1 . See also:Kaloustian, S. A,; Kaloustian, M . K. J . Chem. Educ. 1975, 52, 56. Eliel, E.L. Ibid. 1980, 57, 5 2 .(16) For a survey of high-symm etry chiral molecules, see: Farin a, M . ;Morandi , C. Tetrahedron 1974, 30, 819. Nakazaki, M. Top. tereochem.1984, 15 199.(17) Hirschmann, H.; Hanson, K. R . Top. tereochem., 1983, 14, 83.

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Stereoisomerism and Local Chiralitytherefore also by external comparison, since internal heterotopismis a sufficient condition for external heterotopism, but n ot the otherway around.18 Conversely, all enantiotopic atoms are chirotopic.On he Nature of the Asymmetric Carbon Atom

In the model conceived by van t Hoff, the differences amongthe ligands attached to a tetravalent carbon atom may be expressedby appropriate labeling (e.g., nume rical indexing or color coding)of the vertices or faces of a regular tetrahedro n. Th e symm etryof the labeled tetrahed ron is a subgrou p of Td. Accordingly, theregular tetrahedron functions as a permutation center or skeletonwith four equivalent sites, and models of stereoisomers are gen-erated by permutation of the ligands among these sites.Ig In thisformula tion, stereoisomers a re recognized as prototypes of per-mutational isomers,23 and the asymmetric carbon atom as theprototype of a stereogenic atom.24 Indeed, the classical chemicalpurposes served by the concept of the asymmetric carbon atom,Le., enumeration, classification, a nd description of stereoisomers,are those that express its cha racte r as a stereogenic element. This

J . Am . Chem. SO C . , o l . 106, N o . 11, 1984 3321identity as a stereoc enter depends on m odels of bonding since, bydefinition, stereoisomers have the same bonding connectivity(constitu tion). The cha racter of such an atom as a chirotopicentity is, however, separate and distinct from its character as astereocenter, as evidenced by the fact that the ligands in, forexample, CHBrClF are also chirotopic but are obviously notstereogenic. Thus, returning to the qu estion raised at the beginningof this paper, the re is no reason whatsoever to reserve th e termasymmetric or chiral26for the ligating center in such amolecule.The crux of the matter is that chirotopicity and stereogenicityare conceptually distinct; consider, for example, the halogen atomsin CH Br Cl F (chirotopic but nonstereogenic) and the carbon ato msin the CH Cl groups of 1,2-dichloroethene (achirotopic but ster-eogenic). Nevertheless, stereogenicity and local chirality app earto be inseparably linked in the pra ctice of organic chemistry, asepitomized by the very expression asymmetric carbon at om . Anexplanation of this linkage requires a more general discussion ofthe relation between ligand permutations and symmetry operations.If a perm utation is to effect the same changes as a geom etricsymmetry operation, all unpermuted points must be invariantunder this operation. It follows tha t in order to convert a chiralassembly constructed from an achiral skeleton and achiral ligandsinto the enantiomorph by a single ligand transposition, th e siteson the skeleton that are occupied by the transposed ligands mustbe related by a mirror plane in the skeleton and all the remain ingsites must be located on the same mirror plane.29 If all the mirrorplanes in a skeleton share this property, the skeleton is said tobelong to class a; otherwise it belongs to class b.29 All skeletonsbelonging to class b allow for at least one ligand transposition tha tis not equivalent to a reflection. As an example, consider ligandtranspositions in a chiral hexacoordinate complex with a regularoctahedral skeleton oh).Here, although all sites are pairwiserelated by mirror planes of the skeleton, only transposition ofligands in the trans sites leads to the enantiomorph, because thesesites are related by one of three mirror planes ( u h ) hat containthe remainin g four sites (e.g., 4 - ); transposition of one pairof ligands between cis sites does not necessarily afford the en-antiom orph because these sites are related by one of six mirrorplanes c r d ) that contain only two sites (e.g., 4 - ).

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(18) Reisse, J.; Ottinger, R.; Bickart, P.; Mislow, K. J . Am . Ch em . S O C.1978, 100, 911.(1.9) As van t Hoff recognized,20 nd as furth er discussed in H errmannsrendition of van t Hof fs work4 and in later editions,21 here exists an alter-native mode of modeling the desymmetrization of a regular tetrahedron. Inthis mode, the differences among the ligands are expressed in the shape of thetetrahedron itself ( La form e du tBtaMre [sic] mCme indique Iesptce de lacombinationnzh) in such a way t hat the lowered symmetry of the tetrahedronconforms to the substitution pattern. Thus, only C HI and th e like may berepresented by a regular tetrahedron in this mode, and the asymmetric atommust be represented by an irregular tetrah edromZ 2 This mode of represent-ation was regarded by van t Hoff as the physically more realistic of the two,since the interplay of forces among the li and a toms was expected to have anby the central ligating atom are constrained to remain tetrahedral so thatchanges in the shape of the tetrahedron are solely the result of changes in bondlengths, the two modes of representation become equ ivalent in the sense thatonly five point symmetries ( T d ,C,,, C C,, and C,) are representable by eithermode. In what is to follow, all references are to the permutational mode. Wenote in this connection th at the conditions entailed in a reversal in sense ofchirality depend not only on the model of the molecule but also on the natureof the parameters chosen to define that sense. For example, if the asymmetriccarbon atom* is represented by an array of four differently labeled pointslocated at the vertices of a regular tetrahedron, any deformation of the modelthat leads to a reversal in sense of chirality requires the intermediacy of anarray in which all four vertices are constrained to lie in a single plane. Onthe other hand , if the asymm etric carbon atom is modeled by an irregula rtetrahedron, deformation of the model through an achiral but nonplanar shape(e.g., C,, r C,J into its mirror image suffices to effect a reversal in sense ofchirality.(20) (a ) van t Hoff, J. H. La Chimie dans IEspace; P. M. Bazendi jkRotterdam, 1875. (b) van t Hoff, J . H . Dix AnnCes dans 1istoire duneTheorie; P. M. Bazendijk: Rotterda m, 1887. Marsh, J . E., Transl. and Ed.Chem istry in Space; Clarendon Press: Oxford, 1891.(21) van t Hoff, J. H. Die Lagerung der Atome in Raume ; F. Viewegund Sohn: Braunschweig, 1894, 1908. van t Hoff, J. H . The Arrangementof Atoms in Space; Eiloart, A,, Transl. and Ed.; Longmans, Green and Co.:London, 1898. See also: van t Hoff, J. H.; Meyerhoffer, W. Stereochemie;F.Deuticke: Leipzig and Vienna, 1892.(22) Detailed directions for the construction of tetrahedra of symmetrylower than Td are given in the Appendix (pp 46-53) of ref 4.(23) Ugi, I.; Marquarding, D.; Klusacek, H .; Gokel, G.; Gillespie, P. An-gew. Chem., Int . Ed. En g l. 1970, 9, 703. See also: Dugun dji, J.; Kopp, R.;Marquarding, D.; Ugi, I. Perspectives in Theoretical Stereochemistry - aComputer Or iented Representat ion of the Logical S t ructure ofStereochemistry; Lecture N ote Series; Springer Verlag: Heidelberg, in press.(24) McCasland, G. E. A New General System for the Naming ofStereoisomers; Chemical Abstracts: Columbus, OH , 1953; p 2. The termwas defined as (a) An atom (usually carbon) of such nature and bearinggroups of such nature that it can have two non-equivalent configurations. (b)An atom bearing several groups of such nature that an interchange of any twogroups will produce an isomer (stereoisomer). Although definition b refersto maximally labeled permutation centers, e.g., C in Cabc d and P in Pabcde,we believe that the usefulness of the term can be expanded (in the spirit ofdefinition a) by deletion of the conditional any. Submaxim ally labeledpermu tation centers then also qualify as stereogenic at o m , e.g., P in trigonallybipyramidal Pa4b.2s By extension, any mono- or polyatomic permutationcenter or skeleton may be referred to as a stereogenic element or unit, or asa stereocenter, if ligand permutation produces stereoisomers. Note, however,that these terms are not necessarily limited to permutational isomers.(25) I t is worth noting that the apical isomer of Pa4b is a representativeof a frequently overlooked class of nonp lana r stereois omers : models ofmolecules in this class do not contain any chiral arrangements of four dis-tinguishable points (atoms).

effect on the shape of the te t rah edr ~n. ~.* ~*However, if the angles subtended

2 2

5 4 6Membership in class a is not, however, sufficient to establishequivalence between ligand transposition and formation of theenantio morp h. For example, in a regular trigonal-bipy ramidalskeleton ( ,), apical and equatorial sites are not related by amirror plane, and transposition of a pair of ligands between thesepositions in a chiral complex will not lead to the enantiomorphb ut t o a n a n i ~ o m e t r i c ~ ~tructu re (e.g., 7- ). Indeed, for anyskeleton except the regular tetra hedron , there exists at least one

transposition of ligands tha t does not lead to the enantiom orph.(26) The essential feature of interest is the chiral environment of the atom,and the present discussion fully applies to all chiroto ic stereocenters.27 Thisincludes the central carbon a tom in th e vespirenes,28)whosesite symme try isD,. The s ite symmetry of asymmetric carbon ato msn must by definition be(27) Whether a stereocenter is chirotopic or not may depend on the dis-tribution of ligands, as, for example, in Pa2b2c.(28) Haas, G.; Prelog, V. Helu. Chim. Acta 1969, 5 2 , 1202. See also:Haas, G.; Hulbert, P. B.; Klyne, W.; Prelog, V.; Snatzke, G . Ibid. 1971, 5 4 ,491. Mills, 0.S., et al., unpublished results cited in: Prelog, V.; BedekoviE,D. Ibid. 1979, 6 2 , 2285.(29) (a) Ruch, E. Angew. Chem.,In?.Ed. Engl. 1977, 16, 65; (b) Theor .Chim. Acta (Berlin) 1968, 11 183. (c) Ruch, E.; Schonhofer, A. Ibid. 1968,10, 91. S ee also: Ruc h, E. Acc. Chem. Res . 1972, 5 , 49.(30) Mislow, K. Bull . S O C.Chim. Belg. 1977, 86, 595.

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3322 J . A m . C h e m . S O C . ,Vol. 106, No. 11. 1984 Mislow and Siege1significance of this isotopic labeling (as in chiral acetic acid(CHDTCOOH)34s35)ies primarily in the transformation of CH,into a stereogen ic center; local chirality, Le., chirotopicity, playsat most a secondary role. Indeed, methyl groups that are chirotopicwithout being stereogenic are ubiquitous in chemistry and inbiochemistry; thus all CH, groups in chiral molecules are ipsof ac to c h i r o t ~ p i c . ~ ~e provide two particularly instructive ex-amples.In 1,2,3,4-tetrachloro-5,8,9-trimethyltriptycene9 ) , threechemical shifts are observable for the 9-methyl protons at -90T3 nder these conditions the three hydrogen atoms a re clearly

I 3

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7 8It follows th at among chiral assemblies constructed from achiralpermutation frames and achiral ligands, the regular tetrahedronis the only skeleton in which every transposition of ligands isequivalent to a reversal in the sense of chirality of the ligatedEven so, this relation obtains only un der specialcondition^.^^We a re therefore faced with a remark able coincidence. First,the building block of organic chemistry, the tetravalent carbonatom, is also representable as a regular tetrahedral ligating center.Second, when such a center is appropriately complemented withfour different achiral ligands, chirotopicity and stereogenicity areuniquely linked.32 It is this coincidence tha t accounts for theenormous practical success of the concept of the asymmetriccarbon atom.The preceding discussion demonstrates the need to maintaina strict distinction between chirotopicity and stereogenicity in thetreatment of stereochem ical problems. Th e next two sectionsillustrate the way in which this distinction serves to throw newlight on some notions that are prevalent in stereochemistry.On Chiral Methyl Groups. From the beginning,34 he des-ignation of a methyl group as chiral or asymmetric has beenexclusively restricted to CH DT.35* 36However, the biochemical

31) This special feature of the regular tetrahedro n may be demonstratedby construction. Choose two points (A,B) in one dimension (El) . Each ismirror-related to the other through the midpoint between them. (There areno figures in El of more than two points such that each point is mirror-relatedto all others.) To generate the analog ue in E2, mirror lines (Y and p are passedthrough A and B. Two new points are created, CAby reflection of A through,8 a nd C B by reflection of B through a see i); neither CAand B nor CBand

A are related by a mirror element. CA nd CB an be brought into coincidenceby rotation of a and ,8 abo ut A and B, respectively. All three points (A, B,C A B ) re now pairwise related through mirrors, and the figure in E 2 istherefore an equilateral triangle (i i). Similarly, the step from E2 to E3 isaccomplished by passing mirror planes through the edges of the equilateraltriangle. Three new points are created. Rotation of the mirror elements, thistime about the edges, brings the three new points into coincidence. As before,all points are pairwise related through mirrors. The new figure is the regulartetrahedron. Because all symmetry operations can be expressed as permu-tations, it follows that all transpositions (pairwise relations) have the sameeffect as reflection for two points in E, the vertices of the equilateral trianglein E2, and the vertices of the regular tetrahedron in E).32)This equivalence relation, unqualified, is valid only in the simplestcases, e.g., with l igands such as H, the halogens, CN , etc. In general, it alsorequires that there be no restriction on the freedom of orientation of the ligandsrelative to the ligating center and that the internal motion be uncorrelated aswell a s ~nre s t r i c t e d . ~ )33) In bis(9-triptycy1)methane the 9-triptycyl groups undergo unrestrictedrotation, but this motion is tightly coupled (ge ar effect) and the isomer countin appropriately substituted d erivatives is therefore high er than would be thecase in the absence of correlated rotation. See: Guen zi, A.; Johnson, C. A,;Cozzi, F.; Mislow, K. J . Am . Ch em . S O C. 983, 105, 1438. Thus, derivativeswith substitution pattern 16 (Table I, loc. it.) form three racem ic pairs whichare not intercon verted in the absence of gear slippage; in two of these, trans-position of the substituents a and b on the central carbon atom does not yieldthe enantiomeric form. Similarly, transposition of H a nd O H on the centralcarbon atom in bis 2,3-dimethyl-9-triptycyl)carbinol substitution pattern 12)does not interconvert D and L isomers (cf. Figure 5, loc. cit .).34)Cornforth, J . W.; Redmond, J . W.; Eggerer, H . ; Buckel , W.; Gut -schow, C. Narure (London) 1969, 221, 1212. Liithy, J ; Rt tey, J . ; Arigoni,D. Ibid. 1969, 221, 1213.

9 10distinguishable (diastereotopic) and th e 9-me thyl group is chi-rotopic, but obviously it is not stereogenic. Althoug h at roomtemperature this distinguishability is lost du e to rapid site exchangeon the N M R time scale, the CH, group remains chirotopic.Similarly, CH3s in the 5 and 8-positions are also chirotopic.These groups remain chirotopic under all conceivable time scalesof o b ~ e r v a t i o n . ~ ~The local symmetry of the C H, group in lo4 s C on any timescale, barring inversion a t sulfur or bond-breaking processes. T hehydrogen atoms are therefore always indistinguishable (homotopic)even though the CH 3 gr oup mus t r emain ch i r ~ t o p ic .~ ~On Pseudoasymmetric Carbon Atoms. The central carbonatom ((2-3) in the two achiral diastereomers 11, 12) of 2,3,4-

COOH COOH C O O H C O O HIH O C C ~ HIH C C OH

H C C - O H

IH r C - O HIIH DC 4 O H

H C C OH H O C C - HH C 4 O H H r C 4 O H H 0 r C - H H C C OH

I I H O C C 4 HI I I II I I ICOOH COOH COOH COOH

I I 12 I 3 14trihydroxyglutaric acid has been dubbed pseudoasymmetric.This atom is attach ed to four ligands that differ in structure, andalthoug h C -3 is therefore according to definition, undoubtedlyan asymm etric carbon atom ,43 plane of symmetry passesthrough C -3 in the model. The designation of C-3 as asymmetrictherefore seems to be inappropriate, if not actually co ntradictory.Small wonder th at this molecule was troublesome to van t Hoff.

35)Floss, H. G.; Tsai , M.-D. Ado. Enzymol. 1979, 50, 243. Floss,H. .;Tsa i, M.-D.; Woodard, R. W . Top. Stereochem. 1984, 15 , 253.36)Simi la r ly, by chi ra l phospho group i s meant P6017080.See:Knowles, J. R . Fed. Proc., Fed. Am. SOC. xp. Biol . 1982, 41, 2424 andreferences therein. Lowe, G. Acc. Chem. Res. 1983, 16, 244 nd referencestherein.37)Of course, the presence of chirotopic methyl groups need not berestricted to chiral molecules. For example, the CH,s in achiral 2-chloro-propane are chirotopic.38)Nakamura , M.; Ob, . ; Nakanishi , H.; Yamamoto, 0 .Bul l . Chem.S O C. pn. 1974, 47, 2415. Similar observations have been made for chirotopicCF, groups: K han, M. A.; Tavares, D. .; Rauk, A. Can. J . Chem. 1982,60,2451 and references therein.(39) Chirality and achirality are properties of the model and must bea ppropri at e t o the t im e s ca le of ob se r~ a t i o n . ~~40)Mislow, K.; ickart , P. Isr. J . Chem. 1976/1977, 15, 141) ranzen, G . ; Binsch, G. J . Am . Ch em . S O C. 973, 95, 175.42)The C ymmetry of such a CH, group cannot be represented by the6 distribution of th e four nuclei7 but is clearly shown by the electron distri-bution (Guti trrez, A.; Jackson, J . E.; Mislow, K., unpublished results).43) aeger, F. M. Spatial Arrangements of Atomic Systems and OpticalActivity; McGraw-Hill : New York, 1930; p 41-42.


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Stereoisomerism and Local ChiralityFischer, Landolt, Mohr, and Pope, and has been a source ofcontention ever since.44However, it is easily shown tha t th e difficulty stems from th esame unwarranted linkage of stereoisomerism and chirality thatwe have already discussed for the traditional asymmetric carbonatom. In compounds such as CHB rC lF the carbon atom isstereogenic and chirotopic, but there is no reason to excludestructural types with elements in which stereogenicity is unac-companied by chirotopicity or vice versa. Com poun ds such as11 2nd 12 contain a tetrahedral coordination center ((2-3) thatis stereogenic and achiroto pic, whereas t he chiral stereoisomersof 2,3,4-trihydroxyglutaric cid 13, 14) contain a tetrahedralcoordination center (C -3) th at is nonstereogenic and chirotopic.According to Jaeger,3 h e latter fails to qualify as an asymmetriccarbon atom-a striking illustration of our contention that theclassical chemical purposes served by this concept are those th atexpress its character as a stereocenter independent of local sym-m e t r ~ . ~ ~The relationship between the central carbon atoms in com-pounds exemplified by CHBrClF, 11, and 13can now be mean-ingfully analyzed und er the separate an d distinct aspects of ligandpermutability (relating to stereoisomerism) an d symmetry. Withrespect to permutability, CHB rCl F resembles 11 since transpo-sition of two ligands yields a new structure . With respect tosymmetry, CHBrClF resembles 13 since both molecules areasymmetric and th e four ligated groups ar e all nonequivalent (thetwo CH OH CO OH groups in 13or 14 are diastereotopic and areexpected to differ spectroscopically and in reactivity).With respect to stereogenicity, the central carbon atom inachiral molecules of type 11 hus differs in no way from tha t ina molecule like CHBrC lF, even though the latter is asymmetric .With respect to local and molecular symmetry, molecules of type11differ in no way from m olecules like meso-2,4-dihydroxyglutaricacid or 2-propanol, even though the central carbon atom in thelast two molecules is nonstereogenic: in their most symm etricconformation, all three molecules have C, symmetry, with twoenantiotopic groups (C HO HC OO H or C H3) at tached to thecentral carbon atom . The stereochemical description of moleculesof type 11 thus presents no difficulties so long as the traditionallinkage between stereogenicity and local symmetry is broken.The term pseudoasymmetric therefore lacks any meaningfulreference to symmetry and geometry. It is seen to be an artifactof an unwarranted superposition of stereogenicity onto localchirality. Nothin g illustrates mo re strikingly the historical con-fusion engendered by the enforced lin kage between stereoisom-erism and chirality than this infelicitous term. Th e same applies,of course, to derived and allied terminology, such aspropseudoasymmetric center, etc.Stereochemistry without Stereoisomerism

Since the day s of van t Hoff and Le Bel, stereochemistry hasbeen firmly wedded to the concept of a molecule as an assemblyof atoms connected by localized valence bonds. From this ariseall classification schemes and theoretical constructs tha t deal withthe question of stereoisomerism. Indeed, the very conceptstereoisomer owes its existence to a classification scheme th atassigns first priority to bonding connectivity (co nstitution ) andthat defines as stereoisomers those molecular states th at havethe same constitution but that differ with respect to certainmeasurable properties because of differences in the spatial ar-rangements of the constituent atoms. Tha t has been the meaningand content of stereochemistry ever since the term was firstemployed in 1890 by Victor Meyer.2It is well to remem ber, however, that stereo chem istry had itsbeginnings before the advent of structural theory: Pasteursrecognition that the optical activity of tartaric acid is a mani-festation of molecular dissymmetry (Le., chirality) owed nothing

J . Am . Chem. Soc . . Vol. 106 No. 11 1984 3323to tha t t h e ~ r y . ~ . ~ ~hus, an analysis of molecular models thatgives primacy to sy mme try and chirality instead of constitutionfollows in the tradition of Pasteur, the founder ofstereochemistry,4 even though it represents a radical departurefrom tradition al stereochemistry as practiced since van t Hoff.As we have seen, stereogenicity and local symmetry areconceptually distinct. Th e former is grounded in the theory ofgraphs and permutation groups, whereas the latter is based onthe theory of symmetry groups; the former refers to a model thatrequires specification of constitution, of permutation frames, andof structural energetics, whereas the latter requires no specificationother than a distribution of atoms that is consonant with the timesca le of ~b se r va t io n .~ ~his section, whose seemingly paradoxicaltitle is meant to serve as a re minde r of our disassociation fromthe traditional meaning of stereochemistry as a subject solelyconcerned with stereoisomerism,8 deals with some aspects of th echirality/achirality dichotomy apart from stereoisomerism andwith the problem of chiral descriptors.Chirotopicity and Optical Activity. Chirotopicity is appropriateto the analysis of physical or chemical properties that depend onchirality. In this section we discuss one such property, opticalactivity.Though the molecule as a whole acts as the chromophore inany chiroptical measurement (as is obviously the case in, say,hexahelicene), it is often found convenient to dissect the modelinto a local, achiral chromophore and a chirally perturbingenvironment. Sector rules (e.g., the oct ant rule for the carbonyln- * ransition) can then be developed that relate the sign andamplitu de of the Cotton effects to the spa tial distribution of theperturbing atoms about the chromopho re, regardless of consti-tuti0n.4~ All that matters is the chiral distribution of atoms amongthe sectors. However, althoug h the sectors are formally con-structed on the basis of local achirality in the chromophore, theactual site symmetry of the chromo phoric atoms in the achiralmolecule must be chiral. For example, the octant rule is basedon local C,, symmetry of the unperturbed carbonyl chromophorein, say, formaldehyde, but the same group in, say, (+)-3-methylcyclohexanone has local C1symmetry, and the carbonylgroup is therefore chirotopic.By the same token, chirotopic CH3groups should be capableof acting as optically active chromophores. This is indeed wh atis experimentally observed by Ram an circular intensity differentials p e c t r o s ~ o p y . ~ ~ethyl groups can thus be used as probes ofmolecular chirality in molecules such as (+)-a-pheny lethylamin e.Similarly, optical activity of octahedral transition-metal( We rn er ) com plex es of t h e t yp e C ~ ( e n ) ~ ~ +rises from chiralperturba tion of d-d or charge-transfer transitions on the metalatom or on the meta l plus its ligating atom s.51 This chromophore

44)OLoane, J. K. Chem. Reu. 1980, 80, 41.45)Thus, for example, 3R,5R)-3,5-dimethylheptan-4-01hould functionlike R,R 2R 3C OH n an asymm etric atrolactic acid synthesis, even though C-4is not an asymmetric ca rbon atom. For a related reaction, see: Mislow,K.; Prelog, V.; Scherrer, H. Helo. Chim. Acta 1958, 41, 1410.

46) Are the atoms of the right [tartaric] acid grouped on the spirals ofa dextrogyrate helix, or placed at the summits of an irregular tetrahedron, ordisposed according to some particular asymmetric grouping or other? W ecanno t answer these questions. But it canno t be a subject of doubt that thereexists an arrange ment of the atoms in an asymmetric order, having a nonsu-perposable image. It is not less certain tha t the atom s of the left acid realizeprecisely the asymm etric grouping which is the inverse of this [Pasteur, L .Researches on Molecular Asymmetry of Natural Organic Products; AlembicClub Reprint No. 14, ivingstone: Edinburgh, 19641,Pasteurs dissymttrieand dissymttrique were mistranslated as asymmetry and asymme tric.MSee ref 20b, p 29-30, or the original version.47)Robinson, R. Tetrahedron 1974, 30 1477.48)This is in the spirit of Jaegers exhortation: Retournons I Pasteur See: Jaeger, F. M. Bull. SOC. him. r. 1923, 33, 853.49) ee, for example: Cr ab bt, P. Optical Rotatory Dispersion andCircular Dichroism in Organic Chem istry; Holden-Da y: San Francisco,1965. Caldwell, D. J ; Eyring, H . The Theory of Optical Activity; Wiley-Interscience: New York, 1971. Charney, E. The M olecular Basis of OpticalActivity; Wiley-Interscience: New York, 1979. Barron, L. D. MolecularLight Scattering and Optical Activity; Cambridg e University Press: Cam -bridge, 1982. Mason, S. F. Molecular Optical Activity and the ChiralDiscriminations; Cambridge University Press: C ambridge, 1982.50)Barron, D. Nature (London) 1975, 255, 458. Hug, W.; Kint, S.;Bailey, G. F.; Scherer , J . R . J . A m . Chem. SOC. 975, 97, 5589.51) Schipper, P. E. n Stereochemistry of Optically Active TransitionMetal Compounds; Douglas, B. E., Saito, Y., Eds.; American ChemicalSociety: Washington, DC, 1980; CS Symp. Ser. 119, p 73-90. Saito, Y.Inorganic Molecular Dissymmetry; Springer-Verlag: New York, 1979;Chapter 6.


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3324 J . A m . C hem. SOC.,Vol. 106, No. 11 1984 Mislow and Siege1perm utational a p p r o a ~ h ~ ~ ~r requiring prior specification ofchemical b ~ n d i n g , ~ ~ ~ ~ ~ ~ ~ ~ ~e., schemes tied to the concept ofstereoisomerism.For example, the center of mass in a chiral molecule might betaken as the origin of a coordinate system.s7 Three mutu allyperpendicular vectors intersecting at that origin will then definethe handedness of th e coordinate system and thus serve to specifymolecular chirality. The three vectors could be chosen by somealgorithm based on the distribution of electrons and/or nuclei inthe molecule an d independen t of connectivity,s8 but be cause thechoice of this alg orithm is entirely arbitra ry, it follows th at th esame enantiom er could be right-h anded or left-hande d, de-pending on the choice. Th at is, sense of chirality is not absolute.59Furthermore, a set of vectors in a given chiral structure is en-antiomorphously related only to the corresponding set in theenantiomer, and not to that in any other structure. Accordinglythere must be as many distinct chiral descriptors as there aresymmetry-unrelated ch iral structures, since each set of descriptorsis limited to one particular structure and its enantiomer.Similarly, it is possible in principle to assign symmetry-adap teddescriptors to all chirotopic segments in a mo lecular model. Suchdescriptors must be different for all symmetry-nonequivalentsegments. An infinity of such descriptors is required becau sechirality is sampled continuously, and where there is one chirotopicpoint in a model there is an infinite number. Where, for chemicalreasons, th e analysis is limited to a finite numb er of chirotopicsegments, each segment requires a separate d escriptor. For ex-ample, each of the five atom s in CH BrC lF mu st be given its ownchirotopic descriptor, one that indexes the sense of chirality definedby the environment of th at atom (e.g., a or H, p for C, y for F,etc.).60 In the enan tiomer, the corresponding descriptors indicatethe oppo site handedness for the corresponding environments (e.g.,h for H, for C, 9 for F, etc.).60 Because there a re only twosymmetry-relatable molecular environments, Le., those of the twoenantiomers, and because the chiral environments (and hence thechirotop ic descriptors) of the individu al atoms ar e interdependent:it follows that each descriptor (e.g., a an only be used in con-junction with others from the same molecular environment (e.g.,@, not 6 . It further follows that enantiomeric relationships maybe expressed by reference to any chirotopic point in the model;in the example above, a and fully express the relationshipsbetween the enantiomers of CHBrCIF, even though reference ismade to the environment of a nonstereogenic atom (H) ratherthan to that of a stereogenic one (C).Chirality Descriptors and the Labeling of Stereoisomers andStereogenic Elements. The chirotopic descriptors discussed in th epreceding section are obviously unsuitable for the purpose ofestablishing a systematic nomenclature for stereoisomers. On theother hand, because such systems of nome nclature must deal withmolecules that are not related by symmetry (e.g., diastereomers),their unquestioned u sefulness in the enumeration and description

Equivalent) EquivalentlFigure 1. Flow c ha r t for the classification of topic re la tionships . Th edecisions in response to questions ar e given by heavy (yes) and l ight (no)lines. T h e que st ions a r e a s follows: (1) Are t he a t om s re l a t e d by asym m e t ry ope ra t ion of the molecule? (2) Are t he y r e l a t e d by a sym -m e t ry ope ra t ion of the f i rs t kind (proper rota t ion)? (3 ) DO they havethe same bonding connec t ivi ty (const i tut ion)?is also formally considered a chiral, but since the site symm etryis D 3 , he metal atom is chirotopic.Enantio topic chromophores have a n equ al but opposite effecton optical activity. For example, since the C H3 groups in 2-chloropropane are enantiotopic, their effect on Rama n opticalactivity is nullified through mutual cancellation in the C , con-formation.Symmetry and Sp ectral Anisochrony. We recently proposed30a classification of pairwise relations between isomeric structuresbased primarily on symmetry an d only secondarily (if at all) onconstitution. We argued tha t in many ways such an approachis preferable to the traditional one, which is based primarily onconstitutio n. This new classification was also applied to topicrelationship^,'^ Le., to the description of segments in relation toothers within the model. Let us define atoms or sets of atomsthat are related by a symmetry operation in G as symmetryequivalent and those that are not as symmetry nonequivalent. Alltopic relationships may then be classified as shown in Figure 1 s2Bonding connectivity plays no role in analyses based solely onconsiderations of sym metry, and su ch analyses are therefore blindto the distinction between diastereomers and constitutional isomersor between diastereotopic and constitutionally heterotopic atoms:all that needs to coyern us in such a case is that the models aresymmetr y nonequi~a len t .~~hen no distinction is made betweendiastereomer and constitutional isomer, there is no need forthe term stereoisomer, since the relationship between enan-tiomers (object an d nonsuperposable mirror imag e) does not re-quire any knowledge of constitution or structural energetics: thegeometric attri bute of chirality alone requires the existence of twomirror-image-related struc tures . Stereoisomerism andstereoheterotopisms4 thus fall by the wayside under the novelclassification, since these terms have no meaning unless constitutionis specified.The new classification of topic relationships is especially wellsuited for the analys is of problems in spectroscopy: resonancesdue to symmetry equivalent and nonequivalent atoms are iso-chronous and anisochronous, respectively. These distinctions areparticularly significant in N M R spectroscopy. Differences inscreening constants between diastereotop ic an d constitutionallyheterotop ic groups are dealt with by precisely t he sam e theory;Le., the anisochronies observed in both cases stem from a singlesource: the symm etry nonequivalence of nuclei.*Specification of Chirality and Chirotopicity. Models of enan-tiomers have the opposite handedness; i.e., they differ in their senseof chirality. Since chirality is a geometric property tha t is in-depend ent of constitution , it should be possible to specify senseof chirality without having to resort to schemes based on the

~ ~~

52) The terms properly and improperly equivalent (Figure 1) weresuggested by R . A. Davidson (private communication).53) It is well to remember that diastereomers may differ more in physicalor even in chemical properties than constitutional isomers. A classic examplez1is the conversion of maleic, but not fumaric, acid to a cyclic anhydride.54) Hirschmann, H.; Hanson, K . R. Eur. J . Biochem. 1971, 22, 301.

55) Cahn, R. S . ; Ingold, C. IC.; Prelog, V. Experientia 1956, I2 , 8 1 .56) Prelog, V.; Helmchen, G . Angew. Chem.,Znt. Ed. Engl. 1982, 21, 567.See also: Prelog, V.; Helmchen, G. Helu. Chim. Acta 1972, 55, 2581.57) Th e center of mass in chiral m olecules with D , or higher sym metrycoincides with the unique point whose site symmetry is equal to the molecularsymmetry. In molecules with C,,ymmetry the si te symmetry of the centerof mass is also C,, ut its position is not uniquely defined by th at sym metry.58 ) In principle an arbitrary algori thm based on through-space notthrough-bond) distances could be formalized to index a chiral moleculewithout reference to bonds. Taking the center of mass I ) as the point of firstpriority, three more po ints 2, 3, 4) are chosen in order of descending priority.Point 2 is the point furthest from I . Point 3 is the point of greatest perpen-dicular distance from the l ine 12. Finally, point 4 is the point of greatestnormal distance from the plane 123. The descriptor, say +) or (-), wouldthen be given by the sense of the helix 1234. Where two or more points sharethe characteristic of grea test distance, additional characteristics (e& greatestslope or curv ature) of these points would have to be considered. Th e aboveis intended only as an example of a possible algorithm and not as the basisfor a nomenclatural scheme.59) This statement should not be construed to negate the meaning ofabsolu te config uration, since that term is defined with respect to a given,say right-handed, coordinate system.60) The chirotopic descriptors a ,p. y etc.) could be established, forexample, by an algorithm similar to that developed for the center of mass.isW e are not, however, proposing a new system of nomenclature.


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Stereoisomerism and Local Chiralityof individual stereoisomers deman ds as a price the loss of relevanceto the sym metry relationships among m olecules and their segments.For example, in all such systems of nomenclature two de-scriptors suffice to label all enantio mers: one for th e right-handed and one for the left-hand ed molecule. This is the basisfor the familiar dichotomy of symbols such as D/L,R/S , A/A,etc. However, the sense of chirality of nonenantiomeric m oleculescanno t be properly co mpare d, and th e use of such symbols withreference to the chirality of two nonenantiomeric structures (e.g.,D-glucose and L-mannose, or (R) -alan ine and (S)-leucine)therefore clearly indicates that such symbols are incompatible withthe symm etry relationships among models of these structu res.In fact, except in the case of enantiomers, chirality labelsattached to stereoisomers or stereogenic units ar e not, and cannotbe, symmetry-adapted. They are not generally compatible withthe sense of molecular or local chirality because they serve adifferent purpose altogeth er: the identification an d naming ofstereoisomers. Typica lly, labels for stereoisomers refer to aconstruct, intended as a model for stereoisomerism, that consistsof a permutatio n fram e (the skeleton) representing th e ligatingunit and of a set of ligands that are permutable among the sitesof the skeleton. The labels are mea nt to describe the orientationof the ligands on the skeleton, and a re assigned by a set of arbitraryrules, e.g., the sequence and conversion rules of the CIP ~ y s t e m . ~ , ~ ~They solely serve to identify stereoisomers a nd have no be aringwhatever on sym metry relationships am ong or within molecularmodels.61 It is therefore inappropriate to refer to the m as chiraldescriptors.Tha t th e labels attached to stereogenic atoms are incompatiblewith the local chirality of these atom s may be illustrated by twoexamples. According to CI P rules, the configurations a t C-3 in11 and 12 are specified by chiral descriptors ( r and s), eventhoug h the atoms in question a re achirotopic. The labels usedto provide a distinction between 11 and 12 are therefore seen tobe merely nomenclatural devices that bear no relation to the localsymm etry of the atoms to which they refer. As a second example,consider the compound form ed by esterification of th e hydroxylgroup at C-3 in 11with (S)-lactic acid. According to CI P rules,the configuration at C -3 in this ester is R. According to the sam erules, the configu ration at C-3 in the mirror im age of this esteris also R , even though the ato ms in the two esters are enantiotopic.Once ag ain, we see that such labels bear no relation to t he localsense of chirality.We conclude this section with a general commentary on theC IP system of factorization. In their original paper on thespecification of asymmetric configuration^,^^ Cah n, Ingold, andPrelog stated th at three-dimensional space can in principle beoccupied asymmetrically about the zero-, one-, or two-dimensionalelements of symmetry , that is, the point (or centre), the line (oraxis), and th e plane. This notion was embodied in the CI P systemfor the specification of m olecular ch irality as ce nters, axes,and planes of chirality (collectively referred to as elements of~ h i r a l i t y ) . ~ . ~ ~ore recently, Prelog and Helmchen haveiden tified t hese e le me nts a s stereog enic ~ n i t s . ~ ~ , ~ ~Paradoxically, the selection of elements of chirality in amolecule does not depend on local or mo lecular chirality. Consider,for example, two classes of molecules with D 2 symmetry, thevespirenes 15, n = 6-8)28 and the doubly bridged biphenyls 16,X = 0 S, O , CH2).64 In both 15 and 16 the center of mass

J . A m . C h em . S O C . ,Vol. 106 No. 11 , 1984 3325

(61) According to R u c ~ , ~ ~hiral ligated assemb lies composed of an achiralskeleton and achiral ligands can be divided into two heterochiral classes (inthe m anner of shoes cr screws) only if the skeleton belongs to class a (e.g.,t he re gu la r t et ra he dr on ). H ow ev er , a s a ls o p oin ted o ut by R ~ c h , ~ ~ ~ven sothis division cannot be accomplished unless the ligands differ by no more thanone continuously varying parameter (likened to the didmeter of a sphere).(62) (a) Cahn, R. S . J . Chem. Educ. 1964, 41, 116. (b) Prelog, V. roc.K. ed . Akad . Wet . ,S er . E : Phys . Sci . 1968, 71, 108. (c) Chem. Er. 1968,4, 382. (d) Helmchen, G. ; Haas, G.; Prelog, V . Helu. Chim. Acta 1973, 56,2255. e) Prelog, V. cience (Washington, D.C.) 976, 193, 17.( 6 3 ) Hirschma nn and Hanson have advanced an alternative factorizationscheme based on elements of stereoisomerism; n their s cheme, primacy isexplicitly given to stereogenicity.Jr . J . A m . Chem. S O C . 964, 86, 1710.(64) Mislow, K ; lass, M . A . W.; Hopps, H. B.; Simon, E.; Wahl, G .,

15 16is the unique point with D2 ite ~y mm etr y. ~ his point coincideswith the central carbon ato m in 15, which is also a stereocenter,and with the center of the biphenyl bond in 16. Yet it is only thevespirenes that a re considered to possess a center of chirality,28w hi le the b iphenyls a re said to possess ax ia l ~ h i r a l i t y ~ ~ . ~ ~venthoug h, according to C IP convention, centers of chirality neednot coincide with atomic This example makesit abundantly clear that local or molecular chirality is not at issueand t hat elements of chirality are related purely to stereogenicity.Similarly , the cen tral atom in molecules with T symm etry (e.g.,tetra-tert-butylphosphonium ion6 and tetrakis(trimethylsily1)si-lane68) s located at th e uniqu e point with T site symm etry, yet,because it is not a stereocenter, that atom does not qualify as acente r of chirality under the C IP system.14 Conversely, inmolecules with C, symmetry there is no unique point whosesymmetry identifies it as the molecular center,57yet it is only thestereogenic units in such molecules that are described as elementsof chirality under the C IP system.Elements of chirality are not related to observable quantities.They cannot be identified or characterized by any physical orchemical measurements; for example, it is impossible to identifyelements of chirality by chiroptical or spectroscopic (e.g., N M R )observation^.^^ It cannot be emphasized too strongly that thepurely stereogenic character of elements of chirality in amolecule must not be confused with the chirality properties ofth at molecule. For example, a stereospecific rearrangem ent ofa chiral educt with a single stereocenter M to a chiral productwith a single stereocenter N is commonly referred t o as a transferof chirality from M to N (Le., from center of chirality M tocenter of chirality N). In fact, however, what is transferredin this process are stereocenters ( M - ): chirality is retainedthroug hout, not transferred. It is equally misleading to speak ofa m olecule as being chiral (or optically active) at M , where th eintent is to express Ms property as a stereocenter in a chiral

(65) The concept of axial chirality was introduced as axial asymm etryin the 1956 paper by Cahn, Ingold, and PrelogS5 nd illustrated with fourclasses of structures: allenes, alkylidenecycloalkanes, spirans, and biaryls. Intheir 1966 paper14 a fifth class was added, the adamantoids, and biaryls asa class were said to be conformational while the other four classes wereclear1 configurational. In the most recent (1982) revision of the CIPsystemY6 relog and Helmchen stated that stereoisomers with chirality planesand chirality axes are in fact atropisomeric conformers. Spirans, alkylide-necycloalkanes, and adamantoids thus no longer qualify for axial chirality.However, chiral biaryls and allenes seem to have survived the vicissitudes ofthis definition.(66) Tetrasubs tituted ad aman tanes (form ula 62 in ref 14) exemplifycenters of chirality that do not coincide with atomic centers.(67) Schmidbaur, H. ; Blaschke, G.; Zimmer-Gasser, B.; Schubert, U .Chem. Eer. 1980, 113, 1612.(68) Bartell, L. .; lippart, F. B., Jr.; Boates, T. L. Znorg. Chem. 1970,9 , 2436. See also: Iroff, L. D.; Mislow, K. J . A m . C h e m. S O C . 978, 100,2121.(69) Identification of a stereogenic element (e.g., a chirality element)requires prior definition of the molecular bonding grap h, which is based onthe localized valence bond mode l. This poses few difficulties in the case ofmost conventionally struc tured , Le., covalently bonded, molecules ( e . , organiccompounds) but may lead to problems in the domain of inorganic or or-ganometallic chemistry, where bonding relationships are more complex. Forexample, in l-fluoro-2-chloroferrocene,hich are th e stereogen ic elements:the C SH,FC1 ring, whose faces represent en antiotopic coordination sites, orthe carbon atoms in the ring, which, if viewed as formally bonded to Fe,function as tetraw ordinat e stereocenters? Such questions defy solutions basedon observations and must be settled arbitrarily (from the point of view ofbonding theory) on grounds of perceived convenience in stereochemical no-menclature.


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Stereoisomerism and Local Chirality J . Am . Chem. Soc. . Vol. 106, N o . 1 1 , 1984 3321

17

H

X I18

P

3

2

I

021 D 24 23

Figure 2. Partial desymmetrization lattice for tr iptycene 17). T h e index p is shown on he r ight for each row of (pro)P-chi ral s t ructures. Symm etr iesa r e D J h ,C,,, C a n d Cl for p = 3, 2, 1, an d 0, respectively. M represents a s -bond ed l igand, e .g . , a t ransi t ion-metal #-complex.chirality as an attr ibute related purely to symmetry.We define as (pro)P-chiral (p > 0 ) any finite, achiral objectthat can be desymmetrized into a chiral object by at most pstepwise replacements of a point by a differently labeled one andas (pro)'-chirality the corresponding property of an a chiral object.All such objects contain subspaces (points, lines, or planes) th atremain invariant under every improper rotation (rotation-re-flection) of the point group, an d the aforementioned replacementsare restricted to points lying outside these achirotopic subspaces.(Pro) -chirotopicitys defined in parallel for segments of achiralobjects. Use of the term "desymrnetrization" will hereafter berestricted to the point-replacement scheme described in the abovedefinitions.W e now list the charac teristics of the (pro)'-chiral classes (Tab leI) and illustrate each with chemical examples.79Models with p = 3 may belong to D d , Dnh,one of the achiralcubic groups, I),, or K h a n d a re ( p r ~ ) ~ - c h i r a l .ecause of theirhigh symm etry, mem bers of this class serve as good examples forthe desymmetrization procedure. Consider a model of (~ ro )~ -c hi ra ltr iptycene 17, Figure 2 ) . The achirotopic points in 17 aredistributed amo ng the following subspaces: central point D3,,sitesymm etry), rotation axes ( C 3 , r C2 site symm etry), and mirrorplanes C, site symm etry). The points in these three categoriesar e (pro)'-chirotopic, w ith p = 3 , 2 , and 1, respectively. All otherpoints lie in general positions and are ch irotopic (p = 0 . In Figure2 ar e shown various ways in which replacem ent of points in themodel yields structures with lower symmetry and p indices.Replacement of (pro)2-chirotopic H on C-9 or C-10 in 17 byanother atom (X) yields (pro)2-chiral 18, whereas replacement

(78) Where th e replacing p i n t is not new to the model, the symmetry ofthe object becomes the local symmetry of the ensemble of points that aresimilar to the replacing point. Thus, in the replacement of H on C-3 of(E)-2-chloro-2-butene by CI, the H has C, site symmetry but the symmetryof the product Z)-2,3-dichloro-2-butene) s the sam e as the local symmetryof the ensemble of Cl's, i s . , C,. Similarly, the sy mme tries of the five possibleproducts obtained upon replacement of H in chlorododecahedrane ( C 3 u ) yCI are D3d.C,, C,, C,, and C,, corresponding to t he local symmetries of thetwo Cl's, and not C,,, C,, ,, ,,and C,,corresponding to the site symmetriesof the replaced H's.(79) The construct of (pray-chirality is based on he desy mmetrization ofachiral symmetry groups. As such, the index p may appear to bear someresemblance to the chirality index n dis cussed by R ~ c h . 2 ~ ~owever, the indexp , as we define it, accounts for the desym metrization of the entire object, andnot merely of the permutation frame (skeleton). As a consequence, in ourscheme there is no class of objects that can not be desymmetrized to chiral ones.Th at is, we do not recognize intrinsically ac hiral objects; for example, n = 0but p = 3 for benzene (D6, , ) .

3

I

Figure 3. Desymmetr izat ion la t t ice for (pro)'-chiral ob jec ts. Se e tex tfor addi t ional comments.of (pro)'-chirotopic H on C-1 yields (pro)l-chiral 19. Replace-ments a re not necessarily restricted to ligand substitutions; thusa-complexation of 17 (corresponding t o replacem ent of a pointon the u ,plane) yields (pro)'-chiral 20 a known compound forM = Cr(C O)3.8 0 By the sam e token, cT-complexation of 17 byadditio n of Df o C-1 (corresponding t o replacement of a pointin a general position) yields chiral 21.Models with p = 2 may belong to C or c,), and are (pro)2-chiral. As before, desymrnetrization need not occur in a stepwisemanne r. For example, replacement of (pro)'-chirotopic H on C-1in 18 (Figure 2 ) by Y yields (pro)'-chiral22, whereas replacementof a chirotopic point by a-complexation yields chiral 23.Models with p = 1 may belong to S2 C,, o r C, nd are(pro)'-chiral. Unde r the operatio n of S2 or i, a single point inth e model remains invariant, and under the operation of u so doall the points in the plane. These are the achirotopic points. Allother points in the model are chirotopic and fall into enantiotopicpairs related by S2,,, , or u. Only a one-step desymmetrizationto a chiral object is possible, e.g., 22 o 24, and 19 or 20 to 25(Figure 2 ) .Models with p = 0 lack symmetry elements of the second kind.Therefo re, by definition, (pro)o-ch iral hiral." The re are no

(80) Pohl, R. L.; Willeford, B. R. J . Organomef . Chem. 1970, 23, C45.(81) Desymmetrization of achiral objects to chiral ones by the point-re-placement procedure can only lead to objects with C, symmetry. The otherchiral symmetries Dn, , 0 r ) are listed in Table I for completeness.


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questions on stereochemistry

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