Improper axis of rotation

Note that the cis isomer lacks an improper axis of rotation and is therefore chiral, but that the trans isomer has a plane of symmetry and will be achiral in the absence of an asymmetric carbon in the phosphine ligand-28 As in the case of the previously encountered cyclopentadienyl complex (page 476), it can be argued whether the coordination number is 5 or 9. In either semantic interpretation these compounds are of considerable interest since isomerism in nine-coordinate complexes Is even less well documented than in those with coordination number 5. 

It was mentioned above that tris(chelate) complexes of the type (Co(en) ],+ lack an improper axis of rotation. As a result, such complexes can exist in either of two enantiomeric forms (or a racemic mixtire of the two). Figure 12.20 illustrates the complex ions (Co(en)j]3+ and (Crfoxy3-. each of which ts chiral with Di symmetry. 

Thus Sj is equivalent to L Confirm this to your satisfaction with tnuLs-N2F2. which contains a center of symmetry and thus must have a two-fold improper axis of rotation. Note that the SiF4 molecule, although it possesses true C2 axes, does not have a center of symmetry, and thus cannot have an S2 axis. Furthermore S, is equivalent to c because, as we have seen, C, = E and therefore the second step, reflection, yields... 

B As we have. seen. Hie formal definition of optical activity is bused upon the absence of an improper axis of rotation. The Iwo definitions arc equivalent. 

The Cahn-Ingold-Prelog rules work for inorganic compounds too but coordination complexes often have coordination numbers greater then four and may exhibit helical chirality, for example, denoted A and A (or Pand Min the Cahn-Ingold-Prelog system). The formal condition for chirality is that the molecule should not have an improper axis of rotation (i.e. a rotation + reflection axis, 5n =... 

It was mentioned above that tris(chelate) complexes of the type (Co(en) ] lack an improper axis of rotation. As a result, such complexes can exist in either of two enantiomeric forms (or a racemic mixtire the two). Figure 12.20 illustrates the complex iems (Colen),] and (Cr(ox)3p". each of which is chiral irifh >, symmetry. It is not necessary to have three chelate rings present. The cation dichloro-bis(ethylenediamine)coball(I () exists as two geometric isomers, cis and trans The trans isomer has approximate D f, symmetry (Hg. 12.21b). Because it has three internal miiror planes, it is achiral. The cis isomer has symmetry and is chiral (Fig. I2.2la>. Since the two chlmde ions rq)Jace two nitrogen atoms from an eth-... 

One definition of chirality is that the molecule be nonsuperimposablc on its mirror image. An equivalent criterion is that it not possess an improper axis of rotation (page 52). The absence of a mirror plane does not insure optical activity because a molecule may have no mirror plane, yet may possess an improper rotational axis. We can, hpv/ever, be sure that the molecule with a mirror plane will be optically inactive. 

As we have seen, the formal definition or optical activity is based upon the absence off an improper axis of rotation. The two definitions are equivalent. 

A molecule is chiral or handed if it is not superposable on its mirror image. The general criterion for chirality is that a molecule must not possess an improper axis of rotation In particular it must not possess either a centre of inversion (improper rotation axis with zero angle) or a plane of symmetry (improper rotation by 7t). 

Similar statements can be written to show the combined effects of successive operations. For example, in planar BCI3, the 5 3 improper axis of rotation corresponds to rotation about the C3 axis followed by reflection through the crj, plane. This can be written in the form of equation 3.4. 

FIGURE 13.4 The scroll pictured has an S2 symmetry element It is the combination of a Q rotation and a reflection through a plane that is perpendicular to the Cj axis. The C2 operation switches the curls on the scroll, and the resulting reflection returns the curls positions back to their original orientation. The improper axis of rotation does this as a single symmetry element. Note that although the scroll has an 2 symmetry element, neither the Q axis nor a a plane as indicated are, by themselves, symmetry elements of the object... 

These observations also imply that, if an improper axis of even order is found, there must be a rotation axis with half its order and an inversion centre. Also, for a molecule with an inversion centre, there must be an improper axis of rotation. In the case of a molecule with an inversion centre but without any simple rotation axes, the improper rotation is an S2 axis. However, this S2 axis is not usually quoted, since 5 2 = i and 82 = E, so there are no unique operations associated with an S2 axis. 

A more rigorous symmetry-based definition is that a chiral molecule does not have an improper axis of rotation (S ). There are several ligands... 

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