Permutation Descriptors

Figure 2-74. Basic stages for describing a stereoisomer by a permutation descriptor. At the stereocenter, the molecule is separated into the skeleton and its ligands. Both are then numbered independently, with the indices of the skeleton in italics, the indices of the ligands in bold.

Figure 2-75. Determination of a permutation descriptor of a stereoisomer after reflection at the stereocenter...

Determination of the Permutation Descriptor after Rotation of the Molecule... 

The two structures in our example are identical and are rotated by only 1 20 h Clearly, rotation of a molecule docs not change its stereochemistry, Thus, the permutation descriptor of both representations should be (+ I). On this basis, we can define an equation where the number of transpositions is correlated with the permutation descriptors in an exponential term (Eq. (9)). 

Figure 2-83. EKample of the process to decide whether two structures are enantiomers by determining the permutation descriptor.

The same reference unit of Figure 2-86 is also used here for the determination of the permutation descriptor of the trans isomer. In the same manner as above, wc write down the permutation matrices of the two structures, and then determine the transpositions (Figure 2-87),... 

In this case, two transpositions have to be performed, resulting in a permutation descriptor of (+ 1) for the right-hand subunit. 

Stereochemistry can be represented graphically in 2D structures, but also by (permutations) descriptors. It is included in all line notations and exchange formats. 

The permutational descriptor of the given chemical constitution is then a permutation of atom indices (or the inverse permutation of graph indices) which transforms the reference constitution into the considered constitution. 

Pi upon the ligand indices. Thus, Pi and Ps are equivalent as permutation descriptor of configurations. 

It is a particular advantage of the permutation descriptors that they do not only represent configurations, but provide also a basis for the representation of configuration interconversions. The permutational isomerization (PI) of a configuration A into a configuration B is described by the isomerizer Iab = Pb Pa 1, with Pa and Pb being the permutation descriptors of A and B. 

Configurations of Ruch s class A occur pairwise, e.g., asymmetric C-atoms. The parities of their permutation descriptors can be used as their -parity descriptors. A permutation containing an even number of transpositionsP has a parity of +1, conversely, odd permutations have parities of — 1. Since a-atom RASI (see Section 5.4.1) correspond in most casses to the CIP sequences, an assignment of +1 to an asymmetric C-atom is equivalent to an R-configuration, and — 1 to the S, if the skeleton is indexed as shown in 25. 

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