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Chirality Forum Pseudoasymmetry: A Final Twist? SOSALE CHANDRASEKHAR* Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey ABSTRACT The original definition of ‘‘pseudoasymmetry’’ conveyed the apparent paradox that a tetrahedral center with four different groups did not result in overall chirality. However, there are problems in applying the concept to cyclic systems that do not contain chirotopic centers. Pseudoasymmetry appears most appropriate to acyclic systems with chirotopic carbon centers, e.g. the meso trihydroxyglutaric acids. Analogous cyclic cases, e.g. the isomeric 1,4-dimethylcyclobutanes, are best treated as diastereomers, and may indeed be described by an interesting extension of the like–unlike notation. Remarkably, in several tri- and tetramethylcyclohexanes, CIP descriptors cannot be applied even to chirotopic centers, which can only be described by the modified l–u notation. Chirality 20:771–774, 2008. VC 2008 Wiley-Liss, Inc. KEY WORDS: chirotopic; CIP; hyoscyamine; like–unlike; stereogenic; trihydroxyglutaric acid INTRODUCTION ‘‘Pseudoasymmetry’’ is an intriguing stereochemical concept the origins of which apparently date back to the 1890’s. As the term implies, it refers to cases in which a molecule is achiral although it apparently possesses an asymmetric center.1–3 The classic example of the concept is the case of the trihydroxyglutaric acids 1 (Scheme 1). Of the four possible stereoisomers, the two meso derivatives 1a and 1b are deemed to possess a pseudoasymmetric carbon atom at C3. Although this center is connected to four different groups, the presence of the plane of symmetry passing through C3 ensures that the molecule is achiral. Thus, inverting the configuration at C3 only interconverts the diastereomers 1a and 1b, neither of which is chiral. ‘‘Pseudoasymmetry’’ has also been the subject of considerable debate and controversy in recent years (vide infra.) It is important to note that in a molecule possessing several stereogenic centers, the inversion of one of them in a particular diastereomer would—in general—have one of three possible consequences for the overall chirality of the molecule: (i) retention of chirality, i.e. one chiral diastereomer is converted to another (e.g. D-glucose ? D-mannose, a-D-glucose ? b-D-glucose); (ii) creation of chirality, e.g. the conversion of meso tartaric acid to the optically active form; (iii) destruction of chirality, e.g. the conversion of optically active tartaric acid to the meso form. A pseudoasymmetric center, however, submits to none of these consequences. Thus, inversion at a pseudoasymmetric center leads from one achiral form to another. This unique consequence—despite its linkage to four different groups—derives from the fact that the pseudoasymmetric center lies on a mirror plane as described earlier. It is further intriguing that configurational descriptors can be assigned to a pseudoasymmetric center, despite the fact that it does not lead to enantiomerism as discussed earlier. Thus, the CIP nomenclature can be interestingly extended to the case of a pseudoasymmetric center to assign either the r or s descriptor as appropriate. (This is based on the assumed higher priority for the R configured center over the S, attached to the pseudoasymmetric atom.) Thus, ‘‘pseudoasymmetry’’ appears to define a conceptual middle ground between chirality and achirality.y Recent decades have also witnessed a spirited debate on the precise definition of pseudoasymmetry.2–5 The controversy essentially centers around the question of whether the molecule containing the pseudoasymmetric center can be chiral or not.2 The currently accepted definition extends the pseudoasymmetry concept to (say) the case of the l-menthyl ether derivative 1c, which is chiral by virtue of the menthyl moiety. Although this seems to nullify the original definition of pseudoasymmetry (vide supra), it should be noted that even in cases such as 1c, the overall chirality is not due to the pseudoasymmetric center. Thus, inversion at the pseudoasymmetric center still leads to a diastereomer (not Sosale Chandrasekhar while on Sabbatical leave from Department of Organic Chemistry, Indian Institute of Science, Bangalore 560012, India. *Correspondence to: Sosale Chandrasekhar, Department of Organic Chemistry, Indian Institute of Science, Bangalore 560012, India. E-mail: sosale@orgchem.iisc.ernet.in Received for publication 9 April 2007; Accepted 26 October 2007 DOI: 10.1002/chir.20515 Published online 19 February 2008 in Wiley InterScience (www.interscience.wiley.com). y The case of a carbon atom bearing two different sets of enantiomeric ligands, C(R)(S)(R0 )(S0 ), is noteworthy. If R and S, as also R0 and S0 , are enantiomeric but otherwise identical, the carbon centre would be ‘‘doubly-pseudoasymmetric,’’ and it is easily verified that it would be chiral. ‘‘Double-pseudoasymmetry’’ would thus represent a transition from pseudoasymmetry to chirality. On the other hand, a carbon atom bearing two identical sets of enantiomeric ligands, C(R)2(S)2, would be achiral. Apparently, pseudoasymmetry depends on a delicate balance of symmetry, and occurs when a tetrahedral centre is bonded to two, and only two, enantiomerically related ligands. CHIRALITY 20:771–774 (2008) VC 2008 Wiley-Liss, Inc

shown) but not an enantiomer (of the other diastereomer). Also, the expanded definition can be accommodated into the spirit of the earlier—more fundamentalist—view that pseudoasymmetry is the ‘‘duality arising out of the combination of two enantiomeric ligands with two enantiotopic half-spaces.’’2,4 Thus, the enantiotopic half-spaces could be considered to exclude the additional chiral ligand (the chiral menthyl moiety in 1c). This author is largely in sympathy with the original formulation, which aptly conveyed the sense of paradox inherent in the pseudoasymmetry concept. However, to reiterate, a chiral moiety extraneous to the main framework bearing the pseudoasymmetric center, does not seriously affect the spirit of the classical definitions, and can be accommodated as discussed earlier.{ Thus, the key requirement of pseudoasymmetry should be that despite the presence of chirotopic centers, the molecule as a whole is achiral by virtue of a plane of symmetry that also bears the pseudoasymmetric center. In the acyclic cases, this implies that pseudoasymmetry only occurs in certain meso isomers.6 (Not all meso isomers, of course, bear a pseudoasymmetric center; cyclic systems can bear a pseudoasymmetric center without being strictly termed as meso, as discussed further below.) The extension of the concept of pseudoasymmetry to cyclic systems, however, is not straightforward, as exemplified by the case of the symmetrically 1,3-disubstituted cyclobutanes 2 (Scheme 2).1 These possess two stereogenic centers, but again by virtue of a plane of symmetry, are incapable of enantiomerism. However, there are important differences between the acyclic exemplars of pseudoasymmetry such as 1 and the cyclic analogs 2, as discussed in the following section. DISCUSSION The 1,3-disubstituted cyclobutane system 2 possesses two stereogenic but achirotopic centers, C1 and C3. Indeed, the term ‘‘stereogenic’’ was introduced to describe such centers, as they cannot be termed ‘‘chiral centers,’’ the molecule as a whole being achiral.1,6 Thus, configurational inversion at these centers leads to diastereomers but not enantiomers. On the basis of this criterion, these centers have been considered to be pseudoasymmetric, and the pseudoasymmetric notation has been extended to them in an ingenious manner. This involves the tactic of ‘‘ligand complementation,’’1 originally employed to determine the priority order in the case of cyclic ligands at a chiral center.7 Thus, the new descriptors rn and sn were proposed for systems such as 2. A problem with this approach is that the term ‘‘pseudoasymmetric’’ was (presumably) originally meant to convey the sense that even though such a center was bonded to four different groups, it did not lead to overall molecular chirality. This clearly does not apply to the case of 2, in which the stereogenic centers are not bonded to four different groups. Indeed, there are no chirotopic carbon atoms in 2 at all. One could, however, argue that in the case of the ‘‘trans’’ isomer 2a the two ‘‘arms’’ of the cyclobutane ring that lead from one stereogenic center to the other, i.e. the two methylene groups, are enantiomorphic. Thus, although these two arms lead from (say) C1 to the same stereogenic center C3, one of them approaches C3 from the left hand side and the other from the right hand side. (Thus, the molecule possesses a left-hand side and a righthand side, despite being achiral overall. Note that 2a possesses, in addition to the plane of symmetry passing through C1 and C3, a C2 axis of symmetry passing though C2 and C4.) On this basis, an extension of the concept of pseudoasymmetry is perhaps admissible. However, similar arguments cannot be made in the case of the ‘‘cis’’ isomer 2b, which now possesses an additional plane of symmetry passing through C2 and C4 (orthogonal to the one passing through C1 and C3, and in lieu of the C2 axis in the case of 2a.) Accordingly, the two ‘‘methylene arms’’ of the cyclobutane ring (vide supra) are identical in the case of 2b, so the stereogenic centers cannot be termed ‘‘pseudoasymmetric’’ in the true sense. Therefore, the validity of ‘‘pseudoasymmetry’’ is apparently dubious in the case of 2a and clearly inadmissible in the case of 2b. In any case, and decidedly, the concept of pseudoasymmetry cannot be applied uniformly to the two diastereomeric pair 2a and 2b, and thus loses much of its meaning and significance. Thus, originally, ‘‘pseudoasymmetry’’ defined a phenomenon in which configurational change interconverted one ‘‘pseudoasymmetric form’’ to another. This clearly applies Scheme 1. The trihydroxyglutaric acid diastereomers 1a–1c, with the appropriate pseudoasymmetry descriptors (both r-s and l-u). Scheme 2. The 1,3-dimethylcyclobutane diastereomers 2a and 2b, with the appropriate diastereomer (l-u) descriptors, derived as indicated in 2c and 2d. { Mislow and Siegel have severely criticized the pseudoasymmetry concept as not being particularly meaningful.5 They argue that a pseudoasymmetric centre can be classified satisfactorily on the basis of either its stereogenicity or its symmetry, and is thus neither novel nor useful. An alternative view, however, would be that pseudoasymmetry exemplifies the disconnect between stereogenicity and symmetry. (A pseudoasymmetric centre is rare in being stereogenic but achirotopic.) 772 CHANDRASEKHAR Chirality DOI 10.1002/chir

to the case of 1a and 1b, but is tenuous at best in the case of 2a and 2b. Because of these ambiguities, it seems desirable to limit the use of the term pseudoasymmetric to refer only to the case of systems possessing chirotopic atoms. The case of 2a and 2b may perhaps be termed ‘‘quasi-asymmetry’’ to distinguish it from ‘‘pseudoasymmetry,’’ but it appears best to treat it as a case of diastereomerism. Therefore, ‘‘pseudoasymmetry’’ would generally appear to apply only to acyclic systems, as the additional symmetry elements that occur in cyclic systems complicate its application. Thus, the C2 axis in 2a and the mirror planes in 2b, mentioned earlier, are absent in 1a and 1b. These symmetry elements relate to the absence of chirotopic atoms in the cyclic frameworks, and apparently conspire to invalidate the concept of pseudoasymmetry in them. Diastereomer Descriptors (‘ l-u’) for 2 In fact, the configurational descriptors employed for diastereomers8,9 may be extended in an interesting way to the case of 2a and 2b. Firstly, the ring methylene centers are arbitrarily labeled as a and b (say, C2 and C4, respectively), thus (temporarily) converting C1 and C3 into chiral centers. Then, assuming a higher priority for the group labeled ‘‘a,’’ the CIP chiral descriptors for C1 and C3 are determined (cf. 2c and 2d). The isomers are termed ‘‘like’’ (l) or ‘‘unlike’’ (u) depending on whether the descriptors are the same or different, respectively. Thus, the ‘‘trans’’ isomer 2a would be l and the ‘‘cis’’ isomer 2b would be u. Note that this is a general result independent of the nature of the substituent: thus, (say) the ‘‘trans’’ and ‘‘cis’’ 1,3-dihydroxycyclobutanes would also be l and u, respectively. The configurations at C1 and C3 depend only on the order of C2 and C4, regardless of whether the substituent precedes or succeeds these. Note also that the configurations at the ‘‘temporary’’ chiral centers are not relevant to the final outcome: thus, the arbitrarily higher priority assigned to methylene group ‘‘a’’ implies the R configuration for C1 and C3 in the case of 2a; the configurations would be S were methylene group ‘‘b’’ to be assigned the higher priority; however, the final outcome would be ‘‘l’’ in both the cases. Similar arguments can be made for the case of 2b: C1 and C3 (respectively) would be either R and S (‘‘a’’ higher priority) or S and R (‘‘b’’ higher priority), the final outcome being ‘‘u’’ in both cases. There are two main advantages of this notation over the current rn–sn notation.1 Firstly, the l–u notation would clearly indicate that the case under consideration is one of diastereomerism rather than pseudoasymmetry; thus, it would distinguish 2 from a case of genuine pseudoasymmetry, e.g. 1. Secondly, it is rather easier to apply, based on simple inspection (‘‘at a glance’’). This is because the the rn–sn notation is based on a rather elaborate disconnection scheme1 : although it is valid, a simpler and equally rigorous notation should be preferred in practice. In fact, the above disconnection scheme for the rn–sn notation depends on the tactic of ‘‘ligand complementation’’ of the CIP scheme, which leads to the priority order for multiply bonded and cyclic ligands. The disconnection ‘‘creates’’ chirality (where none existed), thus converting stereogenic centers into chiral centers, so the CIP system could be extended. In the present proposal, the arbitrary labeling of the ring methylene groups effectively raises the question ‘‘if the ring were to be chiral by virtue of substitution, what would be the configurations at C1 and C3’’? Thus, both the previous rn–sn and the proposed l–u notations ‘‘temporarily create chirality.’’ However, the latter approach is rather more straightforward as the rings need not be disconnected.§ Modified l-u Notation for 1 Interestingly, it is also possible to extend the l–u notation to systems bearing genuinely pseudoasymmetric centers such as 1, by employing the modified l–u notation which arbitrarily assigns ‘‘l’’ to the lowest numbered chiral center (cf. Scheme 1).8 This would be the R configured center attached to the pseudoasymmetric center. Furthermore, one may denote the analogous chiral and pseudoasymmetric descriptors as equivalent, i.e. R 5 r and S 5 s. In the case of a pseudoasymmetric system with three stereogenic centers (e.g. 1), the two possible stereoisomers would then be l,l,u and l,u,u. All this, of course, is possible because pseudoasymmetry results in diastereomers. The extension of the l–u notation to pseudoasymmetry is a natural consequence of this fact. While in acyclic cases of genuine pseudoasymmetry (e.g. 1) the l–u notation follows from the existing r–s one, in the ‘‘ambiguous’’ cyclic cases (e.g. 2) extension of the l–u notation requires a departure from the existing rn–sn one, as discussed at length above. Other Systems, Other Problems for the CIP System It is also interesting to consider more elaborately substituted ring systems, e.g. the 1,2,3,5-tetramethylcyclohexane isomers 3a and 3b (Scheme 3). While 3a is chiral, 3b (a meso isomer) is not, so C2 can be considered to be pseudoasymmetric in the case of 3b but not 3a, by the earlier definition. There is no problem in assigning pseudoasymmetric descriptors in the case of 3b, but 3a is rather simiScheme 3. The 1,2,3,5-tetramethylcyclohexane diastereomers 3a and 3b, with the appropriate diastereomer (l-u) descriptors. (The r-s system is applicable only to 3b, as indicated; however, in 3a the CIP system itself fails at C2 and C5, as indicated by the question marks.) § It is noteworthy that both the rn–sn and l–u notations were proposed around the same time (1982),1,8 so the suitability of the latter for cyclic cases (e.g. 2) was not apparent. PSEUDOASYMMETRY 773 Chirality DOI 10.1002/chir

lar to the case of 2b discussed at length above (pseudoasymmetry is inapplicable to both). In fact, the case of 3a is intriguing in that, despite its being chiral, the C2 and C5 centers cannot be assigned normal R or S configurations. Again, it would be inappropriate to consider them as pseudoasymmetric as the molecule is chiral, so the diastereomer notation described above needs to be employed, to arrive at ‘‘l.’’ (This involves the arbitrary labeling of, say, the 1S center as ‘‘a’’ and the 3S center as ‘‘b,’’ as described for the case of 2 above.) These examples again emphasize the problems of applying the pseudoasymmetry concept to ring systems, discussed above. Thus, even with chirotopic centers in a cyclic system (i.e. 3a), ‘‘pseudoasymmetry’’ cannot be applied in a straightforward manner. Note also the apparent breakdown of the CIP notation in the case of the C2 and C5 centers in 3a, which can only be stereochemically designated by the above-described extension of the l–u notation. This is indeed a remarkable example in which chirotopic centers cannot be assigned CIP descriptors, but need to be assigned diastereomer descriptors. (Note that the case of the 1,2,3-trimethyl analog of 3a would be similar.)} An Unambiguous Cyclic System A genuine case of pseudoasymmetry in a cyclic system is that of 3-hydroxy-8-azabicyclo[3.2.1]octane (cf. 4a–4c, Scheme 4). This is the hyoscyamine framework,2 and interestingly, it contains two pseudoasymmetric centers, C3 and N8. Thus, 4a–4c are diastereomers. The configurations at the C1 and C5 chirotopic centers, and the pseudoasymmetry descriptors at C3 and N8 have been indicated. In the earlier discussed cases of 2 and 3, the problem is that only one isomer of each pair possesses a pseudoasymmetric center, i.e. 2a (possibly) and 3b. This ambiguity is absent in the case of 4, in which C3 and N8 are genuinely pseudoasymmetric, as they are flanked by two chirotopic centers (C1 and C5) and also lie on a mirror plane. (Note that a meso compound is defined as one of a set of stereoisomers, at least one of which is chiral6 ; thus 4 is not a meso compound as it does not possess a chiral stereoisomer.) Thus, ‘‘pseudoasymmetry’’ may also be applied in the case of cyclic systems, but with due care and caution. CONCLUSIONS The concept of pseudoasymmetry, despite its rarity, challenges the normal notions of chirality: although a pseudoasymmetric center is bonded to four different groups, it does not lead to the chirality of the molecule as a whole. Furthermore, pseudoasymmetry has played a seminal role in the development of the general concept of stereogenicity. (Thus, a pseudoasymmetric center may be termed as stereogenic but not chiral.) Apparently, however, ‘‘pseudoasymmetry’’ cannot be applied to certain ring systems in a consistent manner, because of the additional symmetry elements present in them (and the consequent absence of chirotopic ring atoms). These cases, in fact, can be treated as cases of diastereomerism, and the ‘‘like– unlike’’ nomenclature extended to them in an interesting manner. Therefore, it would be better to limit the use of the term ‘‘pseudoasymmetric’’ to atoms linked to chirotopic centers: in these the pseudoasymmetric center would lie on a mirror plane, and the pseudoasymmetry descriptors (r and s) can be employed for the resulting isomers. In certain cyclic chiral systems the limitations of the classical CIP notation become apparent; the modified l–u notation can be applied to these, which is remarkable in that chirotopic centers need to be assigned diastereomer descriptors. LITERATURE CITED 1. Eliel EL, Wilen SH, Mander LN. Stereochemistry of organic compounds. New York: Wiley; 1994. p 67–69,667–668. 2. Mislow K. Stereochemical terminology and its discontents. Chirality 2002;14:126–134. 3. Fujita S. Pseudoasymmetry, stereogenicity, and the RS-nomenclature comprehended by the concepts of holantimers and stereoisograms. Tetrahedron 2004;60:11629–11638. 4. Prelog V, Helmchen G. Pseudoasymmetrie in der organischen Chemie. Helv Chim Acta 1972;55:2581–2598. 5. Mislow K, Siegel J. Stereoisomerism and local chirality. J Am Chem Soc 1984;106:3319–3328. 6. Eliel EL, Wilen SH, Mander LN. Stereochemistry of organic compounds. New York: Wiley; 1994. p 1202. 7. Eliel EL, Wilen SH, Mander LN. Stereochemistry of organic compounds. New York: Wiley; 1994. p 107–109. 8. Eliel EL, Wilen SH, Mander LN. Stereochemistry of organic compounds. New York: Wiley; 1994. p 119–120. 9. Seebach D, Prelog V. The unambiguous specification of the steric course of asymmetric syntheses. Angew Chem Int Ed Engl 1982; 21:654–660. Scheme 4. Three 3-hydroxy-8-methyl-8-azabicyclo[3.2.1]octane diastereomers, 4a–4c, with the appropriate pseudoasymmetry descriptors (r-s). } Interestingly, it may be argued that the case of 3a supports the contention that chiral systems may be termed pseudoasymmetric. However, such an inclusive definition of pseudoasymmetry would be a travesty. Such ambiguous systems, whether achiral (e.g. 2a and 2b) or chiral (e.g. 3a), can be described by the l–u notation, as discussed above. 774 CHANDRASEKHAR Chirality DOI 10.1002/chir