Two-Dimensional Chirality in Three-Dimensional Chemistry Claude E. Wintner Haverford College, Haverford, PA 19041 I wish to point out a valuable way to enhance students' understanding of 3-dimensional stereochemistry: through the concept of 2-dimensional chirality. The ideas below are largely due to Prelog and form just a small part of his comprehensive work on stereochemistrv ( I ) . It will be demonstrated that 2-dimensional chirality can be used as a key to teaching and understandine concents such as enantioto~ism. . . diastereotopism, pseudoasymmetry, retention and inversion of configuration, and the stereochemical results of addition to double bonds. In 2-dimensional space a triangle with three differing identified vertices (I) is chiral, that is, it is not congruent, either by translation or rotation in its plane, with its mirror image. In other words, in 2-dimensional space such a triangle is enantiomorphous with its mirror image. (In this discussion the terms enantiomorphous and diastereomorphous will he applied to models and spaces, the terms enantiomeric and diastereomeric to molecules.)
in 3-dimensional space where the 2-dimensional enantiom o r p h ~become a single object with two different faces which can be given specifying descriptors. The descriptor Re is used for the face and can also be used for the 2-dimensional chirality if the order of the vertices is clockwise. The descriptor Si is used if it is counterclockwise (11) (2-4). It should be noted that re and si in this context, seen in many older and some contemporary publications, are properly Re and Si (36,4).
Two-dimensionally chiral objects, for example 2-dimensionally chiral triangles, divide 3-dimensional space into two enantiomorphous half-spaces (IV) which can also be specified by RP and Si. A
Re half - space
SI half - space
c' I'b IV
Where the fourth ligand A (V) of a tetrahedron which contains a 2-dimensionally chiral triangle is the same as one of the ligands comprising the triangle, and all of the ligands are achiral, the two ligands A lie in two enantiomorphous half-spaces and are called, as proposed by Mislow and Raban (51, enantiotopic.
v In accordance with Hanson ( 2 ) the central atom in such a case may be called prochiral. The classical example of such a prochiral atom is C-1 of ethanol. In the presence of the enzyme alcohol dehydrogenase hydrogen is transferred by NADH to Lhe Re face of acetaldehyde (6-8). The transferred hydrogen in the resulting ethanol lies in the Re half-space and is called in this discussion H,lc, (VI) (4). In the nomenclature of Hanson and Hirschmann ( 2 , 3 ) this hydrogen is called pro-R, but the two nomenclatures are not equivalent in the sense that apro-R group does not necessarily fall in the Re half-space as defined by the triangle of the remaining groups.
space.) Thus, the two faces of acetaldehyde can he laheled Re and Si. VI
If one ligand of a prochiral atom is (3-dimensionally) chiral (VII: the 2-dimensionally c h i d letter F is used to symbolize such a ligand), then the two half-spaces are diastereomorphous: Re half-space or Si half-space relatwe to the same chiral ligand F. Here the two ligands A are called, again as proposed by Mislow and Rahan (5). diastereotopic. 550
Journal of Chemical Education
A A s,-
The ideas outlined above also allow a discussion of "retention of configuration" and "inversion of configuration," concepts which are difficult to delineate unambiguously (9). In order to do this it is necessary to define what we mean when we say that two molecules have the same configuration or differ in configuration. On the basis of the previous discussion one may say that two molecules have the same configuration when they have in common an identical 2-dimensionally chiral triangle of ligands and when the fourth ligands of each differ hut lie in the same half-space defined by the chiral triangle. If the fourth ligands lie in opposite half-spaces defined by the chiral triangle, the molecules differ in their configuration (XI).
A
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/L
F / ~
FAB
bA
A
A
Re
B,.. F
~ S i d . 0 F
\\\
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Such diastereotopic ligands are, for example, the two methyl groups in L-valine (VIII).
A
some configuration retention
-
A
-
A
different configuration inversion -< Esi-
-/LDRe
clB
XI
k
For examole, since all of the "natural" a-amino acids have
VIII
Finally, if two ligands are achiral A and B andtwo are (3dimensionally) chiral F and its enantiomorph F, then the half-spaces Re and Si of the enantiomorphous triangles ABF and ABF can he combined with theremaking fourth ligand F or F in the two different ways F R ~Fsi , or FR- FSI which lead to two achiral diastereomorphous models (IX).
-
IX
same configuration. During a chemical reaction in which one ligand is exchanged for another, the two ligands which are involved may either lie in the same or in opposite half-spaces. In the first case we speak of retention, in the second of inversion (XI). However, one must be aware that the concepts of retention and inversion can lead to contradiction if used in sequences with several individual steps. XI1 is a representation of one of a group of seemingly contradictory sets of cases where several reactions in sequence (101, all said to proceed with "retention of configuration" in fact do not lead to the same molecule, hut to an enantiomeric pair, the enantiomer ohtained being dependent on the path traversed. It is true that each reaction in XII, taken singly, proceeds with retention. However, the final result comes about because in this case two different ligands displace Asi from two models which do not have in common the same 2-dimensionallv chiral triangle in addition to As;. Retention of configuration is equivalent to preservation of configuration, and although cases of sequences with successive retentions of configuration may he rare, the same arguments are valid for cases where confieuration is oreserved because ligands are not exchanged hut instead converted without directly involving the chiral center. There are many examples in this category, such as the conversion of (+) glyceraldehyde to (+) or (-) lactic acid (XIII). XIV makes clear how in this case the CH20H group is replaced by two different ligands a t the Re faces of two different chiral triangles. Two identical and juxtaposed 2-dimensionally chiral triangles can be arranged in the plane in two different ways leading to two diastereomorphous models (XV).
This is the model of Werner's pseudoasymmetric atom, exemplified hy the classical case of C-3 in the 2,3,4-trihydroxy glutaric acids (X). C02H HO
toH
H O i H
F
~
F
. E
F
OH
C 02H
Volume 60
Fy HO
Number 7
Julv 1983
551
qfvCH3
CH3 H ~ O H C02H (+) iact~cacid
preservation
q\Id\o*H+OH
CH20H
CHO
In the first case (cis) the two iuxtauosed trianeles disulav faces of different 2-dimensional ihirality on one surface of the model as a whole. In the second case (trans) faces of the same 2-dimensional chirality are displayed on one surface. The cis case is 2-dimensionally achiral; the trans case is 2-dimensionally chiral (XVI). The 2-dimensional diastereomorphism does not get lost in 3-dimensional space as does the 2-dimensional enantiomorphism, and the models therefore correspond to two 3-dimensionally diastereomeric molecules. It is immediately recognized that these models represent the planar cis-trans stereoisomers around double bonds as in maleic and fumaric acids (XVII). Such stereoisomerism has been known for more than a century, but it has not been generally perceived as 2dimensional diastereomorphism. Students will readily understand from XVIII that, for example, cis-addition of hydroxyl groups to fumaric acid must lead to the two enantiomers of chiral tartaric acid, as a result of attack on the two surfaces, differing in their 2-dimensional chirality, of fumaric acid. Likewise, cis-addition of hydroxyl groups to maleic acid will give achiral tartaric acid, while trans-addition of hydroxyls to maleic acid will lead to the 552
XIV
Journal of Chemical Education
trans
CJ XVI
Si Re
aoZH ll C
IC
H
Re
Si
C
Re
Sl
Si
C,
Re
I;,
H03C
chiral tartaric acids and trans-addition to fumaric acid must yield achiral tartaric acid.
and of retention and inversion figuration among of configuration during the course of chemical reactions. Acknowledgment I wish to acknowledge many discussions with Professor Prelog over the period 1972-1981, including two rewarding leaves a t the Swiss Federal Institute of Technology, Ziirich, 1972-1973and 1976-1977. Literature Cited
XVIII
the 2-dimensional chirality In summary, a of molecular models allows a clear insight into the geometrical roots of 3-dimensional stereoisomerism, including enantiotopism, diastereotopism, and pseudoasymrnetry. Likewise, bonds both the basis of cis-trans isomerism around and the results of addition to douhle honds can be unamhiguously treated. In addition, consideration of the half-spaces defined 2-dimensionally c h i d triangles allows an informative discussion of the concepts of same and different con-
11) Prcloe,V..Sclm,F, 191, 17 lIY76!:l'relo~. V..andHelmchen.C.,Anglll. C I r ~ r n i r I r > t b.d, 21, 567 09821: se~hach,~ . m ~d r r l w v., A ~ Z C F Uc~h. i m i e hzr. ~d ,21,654 IIYH21. I?! Hansi,n, K R., J. Amvr l'hmr So' .XU, 2731 110661 {:U fa! Hir%'hmnn. H ,and Hanwn. K. H . J Oil: Chrm .X.:129:1119il!; Telrnh?dron, 30. :I649 119741lli!Hanson. K. R.. A n n Rev. Hiic1ii.m . 4 i , :ill7 11976) (41 P ~ ~ I U v., X. md H ~ I ~ ~ I : . .I H,~ ~ V c~ h, m Acin.ii.2iX1 110721 is! M ~ i l c wK.. and iishan, M.. "Ti,pzci in S l e r ~ o c h e m ~ s l r y .?Ilinwr, " N.1.. and Eliel. I
