Enantiomorphs chiral point groups

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. ... 

We will first derive the four types of point group that are composed uniquely of rotations (operations of the first type). These groups describe chiral objects or enantiomorphs. An enantiomorph and its mirror image are not superimposable. 

Definition (Chirality, enantiomorph, self-enantiomorph) The determinant det is a sign map for each point group P of a molecule in space, P c O3. The point group is the stabilizer of the molecule considered, in the orthogonal group, and we distinguish two cases ... 

The possibility of applying an approach such as the above to the synthesis of asymmetric polymers was pointed out by Morawetz et al [31,32] who also described a system (para-benzamidostryrene) in which, they argued, there are probably formed polymer chains which are individually chiral. However, since the space group of the reactant crystal is of the second type, equal numbers of chains of opposite chiralities would be formed. Morawetz pointed out that if such a process could be conducted in a crystal of enantiomorphic structure, then all the chains formed would be of the same chirality. 

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