Structural Differentiation in Asymmetric Reactions 161 



or point of symmetry is replaced by an isotopic atom, the molecule 

 becomes asymmetric with respect to the labelled atom. In any reaction 

 with an asymmetric reagent, this labelled atom (or group) may react 

 at a rate which is different from that of its counterpart through the 

 plane or point of symmetry, and the difference in rates will be expressed 

 in the distribution of the isotope in the products. This asymmetric 

 behaviour would be superimposed on any difference in the rates of 

 reaction which would result from the different masses of the isotopic 

 atoms." 



2. Racusen and Aronoff: 3 "Discrimination of identical groups or 

 atoms by an asymmetric agent (enzyme, optical antipode, etc.) is 

 possible only in molecules which do not possess a twofold (or greater) 

 axis of symmetry." * 



3. Schwartz and Carter: 4 "In any molecule containing one (or more) 

 meso-carbon atoms, reaction of the two (a) groups with an asymmetric 

 reagent will proceed at different rates, yielding unequal amounts of 

 diastereoisomeric products." 



4. We should like to propose the following criterion: A three-dimen- 

 sional representation of a molecule containing two (or more) identical 

 groups or atoms a designated as a' and a" is moved so that the position 

 of a" will coincide with the original position of a'. If this can be done 



* Two kinds of axes of symmetry are being distinguished. An object is said 

 to possess an n-fold simple axis of symmetry if a rotation around this axis 

 through an angle of 360°/n yields an arrangement indistinguishable from the 

 original. An object is said to possess an w-fold alternating axis of symmetry 

 if rotation around this axis through an angle of 360°/n followed by a reflection 

 in a plane perpendicular to this axis produces an arrangement indistinguishable 

 from the original. It can readily be seen that a onefold alternating axis is 

 equivalent to a plane of symmetry and that a twofold alternating axis is equivalent 

 to a center (point) of symmetry. A compound which possesses no alternating 

 axis cannot be superimposed on its mirror image and is termed asymmetric in 

 the usual language of organic chemistry. However, such a compound may still 

 possess a simple axis greater than one, and if it does it is often designated as 

 dyssymmetric. A compound which has only onefold simple axes is not considered 

 to possess symmetry of any kind and is termed asymmetric, since every object, 

 no matter how irregular, has an infinite number of such axes. Numerous synonyms 

 are in use. An alternating axis is also called a "rotation-reflection axis," "mirror 

 axis," "improper axis," "axis of the second order," etc., whereas a simple axis has 

 also been called a "rotation axis," "axis of the first order," or merely an "axis of 

 symmetry." The last term, however, unless defined is ambiguous. 8 A few ex- 

 amples of axes of both kinds and a brief discussion of their significance will be 

 given below, but for further information reference is made to the classical treatise 

 by Schoenflies 9 and to accounts given by others. 10-12 Reference 12 discusses 

 the subject without the aid of mathematics. 



