D. Tavemler State University of Gent, Krijgslaan 281 (S4bis), 8-9000 Gent, Belgium The definition and nomenclature of the two diastereomers of acyclic compounds having two asymmetric carbon atoms has been the subject of discussion and controversy (for review and comment, see refs 1and 2). Threo and erythro are usually defined by reference to the spatial arrangement of like groups in an eclipsed conformation, hut in compounds as simple as cbaCCafd an ambiguity as to proper definition may aiise. Proposals have heenmide to repl&e threo and erythro by new, unambiguousnames. Based on the sequence rule, Seehach and Prelog ( 1 ) have introduced the 11u and Carey and Kuebne ( 2 ) the parflpref descriptors. In the present paper i t is pointed out that Gielen's definition (3) of threo and erythro provides alogical basis for conserving and at the same time restrictine these traditional names to compounds of the type c b a ~ ~ f f and b c cbaCCabd. As a corollary, a real or "hidden" twofold rotational axis emerges as the characteristic feature of the threo isomer. The relevant part of rhe llu nomenclature will be briefly reviewed. Symmetric cbaCCabc In constitutionally symmetric clhlalCICzazbzcz the asymmetric carbon atoms of the threo isomer have the same
' IUPAC (Nomenclatureof Organic Chemistry, Section E: Stereo-
chemistry. 1976) sates. "a compound whose individual molecules contain equal numbers of enantiomerlc groups, ident~callylinked, but no other chiral group, is termed a meso-compound". Thus eryihrcbaCCabc is properly called meso. The term dlis not defined by the cited IUPACdocument, but must refer to the isomer containing homomorphous groups. The term dl is a specialized relic of the formerly much used "dl" designation (and its variations d.1; DL; D.L) for any equimolecular mixture of enantiomers. The modern way of denoting an equimolecular mixture of enantiomers is by use of the prefix (i). The domain of the d1,mesodesignation encompasses far more than threo,erythroin cbaCCabc. Galactaric acid is one of the two meso forms of 2,3,4.5-tetrahydroxyhexanedioic acid (four asymmetric carbon atoms), but it is not an erythro isomer: d1,meso is also used to describe some conforrnational isomers. e.g., certaln derivatives of bis(9-triptycy1)methane(5. 6).
absolute configuration (the tetrahedra c1hlalCz and Clazbzcz are homomorphous), while asymmetric carbon atoms of the erythro isomer have the opposite absolute configuration (the tetrahedra clblalCz and Clazbzcz are enantiomornbous). No reference to an unrealistic eclinsed conformation is needed. Frequently the threo and Gythro isomers of cbaCCabc are called dl and meso, respectively.1 Consider now the possible symmetry elements in cbaCCabc. An assemblv of two enantiomornhous moieties either is devoid of symmetry or has two possibilities: amirrorplane or an inversion center. For example, a pair of shoes has no symmetry if casually dropped on the floor; but as usually
b aC $ b threo
I$:&:
+: b
b
b
b
erythro
threo
erythro
dl
meso
Figure 1. Tradltlonal fhreo.ewUwdefining Flscher projections.
In eclipsed conformations the GI Figure 2. The CI axis of fhre~~bBCCabc. axis lies in the plane containingthe two ldentlcal eclipsing ligands (cshown):in Staggered eonfwmations the C2axis IS ~. ~erwndlcularto the plane containing metwo ldentlcal antiligands.mi CI axis ofthe Flscher projection lies "skew' to the plane of the paper (see footnote 2).
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placed on a shelf, i t has a plane of symmetry and, as usually packed in a shoe box, i t has an inversion center. By contrast, an assembly of two chiral homomorphous moieties, if not devoid of symmetry, has a twofold rotation axis. In threochaCCabc it so happens that any conformation generated by rotation around the C-C bond has a twofold axis. I t can easily he spotted in almost any stereodrawing, he it sidewise, saw-horse, Newman, or Fischer2 (Fig. 2). As a mnemonic, remember that threo can he turned to an equivalent position. In erythro-chaCCabc, however, the general conformation has no symmetry, but there are two special forms, as shown in the upper half of Figure 3: a staggered conforma-
Figure 3. Above, the two symmelric or special conformations of erymre CbaCCabc: C. = mirror plane, C, = inversion cemer. Below. various stereodrawings of a general asymmetric conformation.
unlike
tion that has an invenioncenter and aneclinsedone that has a mirror plane (and is the basis of the traditional erythro definition). Thus, when confronted with a stereodrawing of cbaCCabc, i t suffices to look for the presence (absence) of o twofold axis to directly decide on the threo (erythro) designation. Surely this recipe, which goes directly t o the characteristic twofold axis of the threo isomer, is to be preferred to the tortuous reorganization of the stereodrawing to the traditional defining Fischer projection. In the traditional erythro definition one has the mirror symmetric eclipsed conformation a t hand, and i t is tempting hut erroneous to explain by reference to it the nonresolvability into enantiomers of erythro-chaCCahc, hut this ought not to be explained to students as the result of the chance occurrence of a mirror plane in a particular Fischer projection. The present approach leads naturally to a correct explanation. Erythro-cbaCCahc has either achiral (mirrorsymmetric or centro-symmetric) or asymmetric conformations, t h e e n a n t i o i e r s of which a r e formed by an appropriate rotation around theC-C bond. This is in general a fast process, and rhe nonresolvability at room temperature is due to the accidental circt~mstanreof low interconversion barriers. Compounds cbaCCabd Wintner has expounded in THIS JOURNAL on the term configuration (4). Two asymmetric carbon atoms Cahcd and Cabcf, having in common three distinct ligands abc partitioning space into two distinguishable half-spaces Re and Si. are saidio have thesame configuration if thifourthligand of each lies in the same half-space; they have the opposite configuration if the fourth ligands lie in opposite half-spaces (Fig. 4). The strength of this definition is that i t neglects the dissimilar ligands d and f and turns the attention to the three-dimensional moiety common to the two asymmetric carbon atoms. that is. to the two tetrahedra Cahc. If Cabcd and Cabcf have the s&ne (opposite) configuration then the two tetrahedra defined bv Cabc are homomornhous lenantiomorphous). In ch1a~C1C9agb.d . . . ... the tetrahedra common to the two asymmetric carbon atoms are (a~blCn)C~ and (azhzC1)Cz. Following Gielen and Wintner threo(erythro)-cbaCCabd is defined as having chiral centra with the same (opposite) c~nfiguration.~ This description includes as a special case the threo, erythro definition for symmetric cbaCCahc. An extension of the practical "if twofold axis, then threo"
like configuration
Figure 4. Same and opposite configurationfor Cabcd and Cabcf. The Re,.% parliiioning followsfroman assumed sequence order a > b > c.
a
C21threol
Figure 5 Neglect in cbaCCaod 01 ma conf~gwationally lnelevsnt iigandr c.d reduces the lhreo ,somer to a smrnure met has a wdold rotation axe. The general evihho conformerremalns a5ymmetric.
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Journal of Chemical Education
Due to the conventional and stylized nature of the Fischer projection, it is easy to spot me twofold axis if perpendicularto the plane of the paper. It exchanges the two "down" groups on the vertical line and the two pairs of diagonal "up" groups from the horizontal lines, see Figure 1 for example. In contrast, a twofold axis "skew" to the plane of the paper is not readily perceived by the unprepared mind. It lies in a plane defined by two horizontal eclipsing ligands and the two asymmetric carbon atoms, and exchanges vicinal "up" and "down" ligands. The Fischer projection shown in Figure 2 has a "skew" twofold axis lying in the plane cCCc and exchanging the iigand pairs aa and bb. For molecules with noncontiguous asymmetric carbon atoms, such as cbaC-X-Cabcand cbaC-X-Cabd, where X is some nonstereogenic fragment,say -CH2CHr, threo,eWhroconespondsto the same (opposite)configuration of the chiral centers, but arbitrary conformationsof the threo isomer will not have the twofold rotational symmetry characteristic of the more simple cbaCCabc series. However, for both isomers special symmetric geometries, which emphasize the homomorphic (enantiomorphic)relationship of the moieties, can be found.These special geometries need not be based on the horseshoe Fischer projection but may also be based on more realistic conformers.
rule is also possible. Threo- and erythro-cblalC1C~a~bzd are actually asymmetric, but we can neglect the dissimilar substituents c and d and restrict our attention to the partial structure defined by b1a1C1C2apbp(Fig. 5). In the threo, but not in the erythro isomer a rotation over 180' is possible which simultaneouslv exchanees a, with a? and b, with bn ("hidden" Cp axis). ~ ~ a it hne,feasibility or this rotation is readilv visualized from most stereodrawinas, allowina areater ease of determination of the stereochem&& identiGof the comnound under consideration. ~ h o s ~ h o r uchemistry s provides an excellent illustration of the views expressed above. Diphosphine has a high bbarrier . to pyramidal inversion a t phosphorus. As a consequence there are two diastereomers of a tetrasubstituted diphosphine baF'Pab, and of the monosulfide baP(=S)Pab and disulfide baP(=S)P(=S)ab derived therefrom. In baPPab and baP(=S)P(=S)ab . . . . one of the two isomers has a twofold axis, but in the monosulfide the two diastereomers are asymmetric. However. neelect of the sulfur atom reduces the stereochemistry t h k of the diphosphine baPPba. Compounds cbaCCafd and cbaCCgfd In cbaCCafd and cbaCCgfd the stereochemical nature of the asymmetric carbon atoms cannot be compared by the homomorphism or enantiomorphism of common partsthere simply are insufficient identical groups. Additional conventions are needed. The sequence rule and the thereby derived descriotors R/S allow a detailed desienation of stereochemical isbmers. For a compound havingiwo asymmetric carbon atoms numbered x.v the label (xR.vR) describes an enantiomer of known absoiute configurati%,'(xR*,yR*) an euantiomer of known relative configuration, and (xRS,yRS) an equimolecular mixture of (RR) and (SS) enantiomem4 Seebachand Prelog ( I ) propose that the (xR*,yR*) diastereomer be called 1 (like descriptors for atoms x,y) and the (xR*,vS*) diastereomer be called u (unlike descriptors for x,y). The llu nomenclature is operationally simple, easy to remember, and applicable to acyclics with noncontiguous chiral centers, to acyclics with more than two chiral centers, and to assemblies of rings and chains (Fig. 6). The llu nomenclature can be applied to cbaCCabc (where always 1 threo; u = erythro) and to cbaCCabd, but here there is no correspondence between llu and threo,erythro,
-
'Maehr has recently proposed (7)an elegant convention for the graphic representation of the three levels of information (R,R); (R*.R') and IRR,SS). ~ h.. & eisa 2D amloa. Alkena stereochemistrv can be described: ..-(1)forbaC-=Cabashomomorphous (enantiomordhous)lriangles baC (transand cis. respectively).(21for ba,C, = C*,c as homomorphous (enantiomorphous)triangles a,C,C2 and C,C,a,. For abC=Cdc additional conventions are necessary: the application of the sequence rule leads to well-known ZlEdescriptors. ~
~-
~~~~~~
~
I
2RS.3RS=
1
threo
2RS,4SR=U
Et erythro
Figure 0. Examples of lludssuiptors.In the hydroxyketone wllh Uwee a s p metric carbon atoms, me descriptors followthe numbering of the systematic name (3.5dimethyl4hydroxy-hepun-Z-ane).
e.g. threo-Me(OH)HCCH(OH)Et= (RS,RS) = 1; but threoHFClCCBrClH = (RS,SR)= u. Chemists will therefore probably continue to use the time-honored threo,erythro in these simple cases. The very constitution of cbaCCabc and cbaCCabd allows a quick and neat statement about the asvmmetric carbon atoms (same or o ~ o o s i t econfieuration) wGhout having to go through the rdutine of the sequence rule (ordering of ligands) and the chirality rule (RIS descriptor).5 Consider for instance the reaction of X X and an alkene baC=Cac to give baXCCXac. Suprafacial addition to the alkene isomer having trans(cis)-positioned a's yields threo(ervthr0)-baXCCXac, while antarafacial addition yieldsthk erythro(thre0) isomer. Such succinct statements are not possible using the 1/11 nomenclature. T o end this paper, a word on the simultaneous use of threo.ervthro and DL. Threo and erythro are relative statements i f same or opposite configuration. Obviously, if in addition the absolute configuration of one asymmetric carbon atom is given, then that of the other one is also known. For reasons of tradition, it is not the new RIS, but the older and much more restricted DL nomenclature that is used in conjunction with threo,erythro. Literature Clted (1) Seebaeh, D.: Pnlog, V. Angem. Chem. Int. Ed. Engl. 1982,21.654. (2) Carey, F.A,; Kuehne, M . E. J. Or& Chem. 1982,47,3811. (3) Gielen, M. J. Chrm. Edue. 1971.64.673. (4) Wintoor, C. E. J. Chpm E d u . 1983.60,550. (6) Johnson,C. A,: Guenzi. A,: Midow, K. J A m r . Cham. Sac. I981,103.6240 16) Ksvisda.Y.: Okamoto. Y.: Iluamurs. H. TefrohodronLoft. 1985.24.5359. (4 Maehr. ~ Chem. . i~ d & 1985.62.114. .
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