Point groups chiral molecules

Chiral molecules need not be asymmetric. Asymmetric is defined as the complete absence of symmetry. However, many chiral molecules have one or more proper rotation axes —just no improper axes are present. These compounds can be referred to as dissymmetric, essentially a synonym for chiral. Thus, while all asymmetric (point group Ci) molecules are... 

All have pyramidal molecules (Cj point group for OSX2), and OSFCl is chiral though stereochemically labile. Dimensions are in Table 15.14 the short O-S distance is notable. The unstable compound OSI2 was mentioned on p. 692. 

Molecules that belong to Cn or Dn point groups are also chiral. For instance, tra i-2,5-dimethylpyrrolidine (Fig. 1-9), containing a twofold rotation axis, belongs to the point group C2 and is chiral.5 7... 

An introduction to point groups containing chiral molecules can be found in any of the leading text books. For example, in Eliel, E. L Wilen, S. H. Mander, L. N. Stereochemistry of Organic Compounds, John Wiley Sons, Inc., New York, 1994. 

Enantiomers The same in all scalar properties and distinguishable only under chiral conditions. Only molecules of which the point groups are Cn (n> 1), Dn (n> 1), T, O, or / are chiral and can exist in enantiomeric forms. 

Homotopic Groups Not distinguishable under any conditions, chiral or achiral. To have homotopic groups, a molecule must have a finite axis of rotation. Thus the only molecules which cannot have homotopic groups are those whose point groups are Ci, CS) Q, and CCXJV. 

In order to ascertain which symmetry elements are present in raeso-tartaric acid, it is necessary to look at the various conformations of the molecule. The symmetrical highest energy conformer, i.e. the synperiplanar conformer (sp), has a plane of symmetry in which both enantiomorphic halves of the molecule are reflections of each other. No other symmetry elements are present in this conformation (point group Cs). In the ap conformation of raeso-tartaric acid the only symmetry element present is a centre of symmetry (disregarding the fact that the centre of symmetry is equivalent to any of the infinite number of S2 axes). The symmetry point group is therefore Cj. All other conformations, e.g. the +synclinal conformation (+sc) of raeso-tartaric acid shown below, are chiral and do not possess any symmetry elements and therefore belong to the point group C. ... 

The compound has two chirality centres and three pseudo chirality centres. There is however, only one (achiral) diastereomer of the compound shown in the question. The two isomers can be distinguished from one another solely on the relative position of the chlorine or bromine atoms which lie in a plane which also happens to be the plane of symmetry of the molecule (this is the only symmetry element present, therefore the symmetry point group is Cs). It is possible in this instance to specify the configuration unequivocally using the descriptors E and Z. However, in systematic nomenclature the complete configuration of all the stereogenic centres is specified. Thus the (so-called) Z isomer is (ls,3r,5 ,6r,7S)-l,6-dibromo-3,6-dichloroadamantane and the isomer is (ls,3r,5 ,6s,7S)-l,6-dibromo-3,6-dichloroadamantane, i.e. the two isomers can be distinguished simply by the descriptor used for position 6. 

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