Symmetry Elements and Molecular Achirality Guo-Oiang Chen Biochemistry Section, Basic Department, Zhejiang Agricultural, University, Hangzhou 310029 PRChina Molecular chirality has been discussed in new terminoloow " and classification svstems in the last few years ( I ) . Molecular achirality is us;ally predicted by inspecting a symmetrv element such a s a d a n e . a center, or an alternating axis of symmetry (2). he' operation of i n alternating ax& of svmmetrv includes chanzine the orirrinal molecule to its mirror image, which is theoperation that defines achiralitv. I n contrast. the overation of a symmetry plane or symk e t r y center is based on analyzing the s t r & u a l character of the molecule (3). However, a symmetry plane or symmetry center is not necessary forachirality (4). We tried to fmd a general rule for the prediction of achirality by analyzing the structural character of a molecule. Rule: Suppose a molecule is divided by an imaginary plane into two parts, if one of the parts undergoes imaginary rotation through angles of both +a and * (clockwise and anticlockwise, 0 < a < 180") about an axis perpendicular to the plane and gives the mirror image of the other part, then the molecule is achiral.
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I t is orooosed . that the plane described above be named the "rotating plane of symmetry ( 0 3 . For example, mesotartaric acid (with a symmetry plane), 1,3-difluoro-2,4dichlorocyclobutane (with a symmetry center) a n d 3.43.4'-tetramethvlspiro ,. . . . (1,1')3-dipyrrolidinium ion (without any plane or center of symmktry) all possess ro~ am ~ respectively , tating planes of symmetry: ao, o ~ and (see f w r e ) . A molecule without optical activity may give innumerable plausable chiral chemical conformations. But if it is easy to go from a chemical conformation to its mirror image by rotation of chemical bonds in the molecule, the molecule is actually achiral, and i t is easy to find a chemical conformation that possess a rotating plane of symmetry. Sometimes, a chemical conformation with chirality is rigid hrcausc of steric hndrance or bond tension for rotation of chemical bonds in the molecule, such as in the case of ansa compounds ( l o ) where the mol~culeis actually chir d and it docs nor possess any rotatingplane of symmetry. Consider W ~ l l ~ athree-rung 's Mobius ladder, which was experimentally proved to be chiral (51.This ladder does not possess any rotating plane of symmetry. Though the ladder is topologically achiral, it is impossible to go from the chiral confi~rmationto it* mirror image in reality, and it is in
The rotating plane of symmetry of meso-tartaric acid (uo),1 , 3 d ' i luoro-2,4-dichlorocyclobutane (a,, ), and 3,4.3',4'-tetramethylspiro (1,1')3-dipyrrolidiniumion (a9,,).
reality impossible to find a conformation that possess arotating plane of symmetry. The reliability of a prediction of achirality of a molecule by inspecting a rotating plane of symmetry is ensured by the following demonstration: Suppose the mirror image of molecule A B is B'A' and A B is divided bv a d a n e into two parts, A and B. The mirror image of Ais k;the image B is B'. Now consider rotation about the axis oeroendicular to the if A rotates by -a giving B' then B rotated by +awill give A', and if A rotates by +aalso giving B', then AB as a whole mtated by + a will be identical with B'A' and, hence, AB is achiral. We usually find that the absence of a rotating plane of symmetry is suffkient for chirality I n fact, it is shown that a symmetry plane and a symmetry center are special cases of a rotating plane of symmetry (a= W and a = 180', respectively). Literature Cited
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2. J e w M.Aduaned 0r.qanle Chsmlsfry, 3rd ed.; Wiley: New York,1985;p 84
Volume 69 Number 2 February 1992
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