Isometric molecules

The expression homochiral in its original meaning concerns isometric molecules of various kinds with the same configuration, for example, the (i,)-aminoacids. There were propositions to use this word in a narrow sense, as the equivalent of enantiopure. For a discussion, see Ref. 6, p. 215. 

Mislow [18] has proposed a classification of isomers based not on the bonding connectivity of atoms as above, but on the pairwise interactions of all atoms (bonded and nonbonded) in a molecule. The operation of comparison of all pairwise interactions is called isometry (for detailed explanations, see [19]). Isomers in which all corresponding pairwise interactions are identical are said to be isometric, and they are anisometric if this condition is not fulfilled. Isometric molecules may be superimposable, in which case they are identical (homomeric), or they may be nonsuperimposable, in which case they share an enantiomeric relationship. As regards anisometric molecules, they are categorized as diastereoisomers or constitutional isomers, depending on whether their constitution is identical or not. This discussion is schematically summarized in the lower half of Fig. 2. 

Name all of the isometric tripeptides which could be formed from one molecule each of tyrosine, alanine, and valine. 

For quasirigid molecules a symmetry concept has been used very early in some branches of molecular research, e.g. stereochemistry2,3 This symmetry concept was based on the concept of isometric mappings4) and formed the basis of extended applications to molecular dynamics since 1930, developed first by Wigner5). 

Since most of the nonrigid molecules treated so far may be described by a SRM whose covering group is the improper group C[, the internal isometric group is treated first. 

Relation Between the Isometric Group and the Permutation-Inversion Group (Longuet-Higgins Group) of Nonrigid Molecules... 

In this section a relation of the isometric group approach to the permutation-inversion group of nonrigid molecules, introduced by Longuet-Higgins7, will be established. Such an interrelation is obtained in a natural way, if the isometric transformations... 

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