Alternating axis

A molecule is chiral if it cannot be superimposed on its mirror image (or if it does not possess an alternating axis of symmetry) and would exhibit optical activity, i.e. lead to the rotation of the plane of polarization of polarized light. Lactic acid, which has the structure (2 mirror images) shown exhibits molecular chirality. In this the central carbon atom is said to be chiral but strictly it is the environment which is chiral. 

Although the ultimate criterion is, of course, nonsuperimposability on the mirror image (chirality), other tests may be used that are simpler to apply but not always accurate. One such test is the presence of a plane of symmetry A plane of symmetry (also called a mirror plane) is a plane passing through an object such that the part on one side of the plane is the exact reflection of the part on the other side (the plane acting as a mirror). Compounds possessing such a plane are always optically inactive, but there are a few cases known in which compounds lack a plane of symmetry and are nevertheless inactive. Such compounds possess a center of symmetry, such as in a-truxillic acid, or an alternating axis of symmetry as in 1. A... 

This molecule has no chiral carbons, nor does it have a rigid shape, but it too has neither a plane nor an alternating axis of symmetry. Compound 32 has been synthesized and has, in fact, been shown to be chiral. Rings containing 50 or more members should be able to exist as knots (33, and see 37 on p. 114 in Chapter 3). Such a knot would be nonsuperimposable on its mirror image. Calixarenes, ° crown ethers, catenanes, and rotaxanes (see p. 113) can also be chiral if suitably substituted. For example, A and B are nonsuperimposable mirror images. 

Dissymmetric Compounds lacking an alternating axis of symmetry and usually existing as enantiomers. Some people prefer this to the term asymmetric. 

We have already seen that mesotartaric acid is optically inactive because of internal compensation, although, it contains two asymmetric carbon atoms. We have also seen that the molecule as a whole must be asymmetric for being optically active. Therefore, the best criterion to judge optical activity would be whether molecule is superimposable on its mirror image or not. Now superimposability would lead to optical activity and vice-versa and non-symmetrical molecules are non superimposable. To decide whether a molecule is symmetrical or not, we should first try to know whether it has a plane of symmetry, a centre of symmetry or an alternating axis of symmetry. The presence of any one of these would lead the molecule to be symmetrical and hence to optical inactivity. 

In 1956 McCasland and Proskow prepared the p.toluenesulphonate of the compound X and found that it has neither a plane nor an centre of symmetry and yet the molecule was superimposable on its mirror image and hence inactive. The molecule owes its symmetry due to the presence of what has been called an alternating axis of symmetry. Rotation of the molecule through 90° along the axis shown produces XI. Observing the latter through a central plane perpendicular to the axis shows that it is identical with X and also coincides with it. 

Therefore a molecule will be said to have an n fold alternating axis of symmetry if rotation through 360° n along an axis produces a structure, observing which in a plane perpendicular to the axis, which is identical with and coincides with the original. 

For information about point groups and symmetry elements, see Jaffd, H. H. Orchin, M. Symmetry in Chemistry Wiley New York, 1965 pp. 8-56. The following symmetry elements and their standard symbols will be used in this chapter An object has a twofold or threefold axis of symmetry (C2 or C3) if it can be superposed upon itself by a rotation through 180° or 120° it has a fourfold or sixfold alternating axis (S4 or Sh) if the superposition is achieved by a rotation through 90° or 60° followed by a reflection in a plane that is perpendicular to the axis of the rotation a point (center) of symmetry (i) is present if every line from a point of the object to the center when prolonged for an equal distance reaches an equivalent point the familiar symmetry plane is indicated by the symbol a. 

The photoproduct derived from 3, the new tricyclic [4,4]cyclophane 4, has 5-type cyclobutane rings and has no alternating axis of symmetry, showing it chiral, and the oligomers are considered to have a zig-zag shaped rigid chain structure of alternative (IS, 2S, 3R, 4R ) and (1R, 2R, 3S, 4S ). 

The definitions of plane. center, and alternating axis of symmetry arc taken from Elicl Elements of Stereochemistry-. Ref. I. pp. 6,7. Sec also Lcmitrc Aldcrwcireldt J. Org. Chem. 1980, 45. 4175. 

This is the operation of clockwise rotation by 2w/ about an axis followed by reflection in a plane perpendicular to that axis (or vice versa, the order is not important). If this brings the molecule into coincidence with itself, the molecule is said to have a n-fold alternating axis of symmetry (or improper axis, or rotation-reflection axis) as a symmetry element. It is the knight s move of symmetry. It is symbolized by Sn and illustrated for a tetrahedral molecule in Fig. 2-3.3.f... 

Whether a molecule is or is not superimposable on its mirror image is a question of symmetry. A molecule which contains a n-fold alternating axis of symmetry (Sn) is always superimposable on its mirror... 

One simple practical method of assessing the possibility of the existence of non-superimposable mirror images, particularly with complex structures, is to construct models of the two molecules. The property of chirality may alternatively be described in terms of the symmetry elements of the molecule. If there is a lack of all elements of symmetry (i.e. a simple axis, a centre, a plane, or an n-fold alternating axis) the chiral molecule is asymmetric, and will possess two non-superimposable mirror image structures (e.g. 2a and 2b). If, however, the molecule possesses a simple axis of symmetry (usually a C2 axis) but no other symmetry elements, the chiral molecule is dissymmetric. Thus 4a and 4b are dissymmetric and the simple C2 axis of symmetry, of for example 4a, is shown below. If the molecule possesses a centre of symmetry (C.) or a plane of symmetry (mirror images of the molecule are superimposable and the molecule is optically inactive. These latter three symmetry elements are illustrated in the case of the molecule 4c. 

Enantiotopic ligands and faces are not interchangeable by operation of a symmetry element of the first kind (Cn, simple axis of symmetry) but must be interchangeable by operation of a symmetry element of the second kind (cr, plane of symmetry i, center of symmetry or S , alternating axis of symmetry). (It follows that, since chiral molecules cannot contain a symmetry element of the second kind, there can be no enantiotopic ligands or faces in chiral molecules. Nor, for different reasons, can such ligands or faces occur in linear molecules, QJV or Aoh )... 

Fig. 16. Enantiotopic ligands in molecules with center or alternating axis of symmetry...

Most chemists would accept the general statement that optically active molecules are those without an alternating axis of symmetry, as adequate. This is perhaps a reliable diagnostic of natural optical activity, but it offers no explanation of the Faraday effect, which shows that achiral molecules become optically active in an applied magnetic held. 

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