Permutational isomer notation

Permutational and Binary Notations for Isomers of P(1 2 3 4 5) with Five Different... 

Fig. 7. Itinerary for permutational isomerizations by single turnstile rotation, or by Berry pseudorotation, when the five ligands in trigonal bipyramidal phosphorus are different. Isomers are denoted by Permutational Notation.

The molecular structure of phosphetane (6) was elucidated by X-ray crystallographic analysis, as discussed in Section II.89 The preferred isomer is (6-(l 4) (2 6)), which is shown in two space orientations in order to illustrate the application of the Permutational Notation. The ligand indices are prescribed by the Sequence Rules.75 The ligand and skeletal indices must coincide in (6-E), which thus gives the orientation of the skeleton. The permutation (1 4) (2 5) gives isomer (6 -(l 4) (2 5)) as a... 

Two phosphoranes (71) and (72), which differ in the configuration of the ring-carbons, are isolated10 from the reaction of dimethyl phenyl-phosphonite (61) with pentafluorobenzaldehyde (46). Consider first isomer (71) with the ci,5-arrangement of the hydrogens in the ring. There are two energetically favorable TBP (71-(1 4) (3 5)) and (71-(1 4) (2 5)) these can be derived from the Reference (71-E), which is an unfavorable TBP, by the Permutational Notation, f Below —50° one observes... 

Hence the conjugacy class of these stabilizers, in short the stabilizer class, is a characteristic of the orbit. But it should be clear that several orbits can have the same stabilizer class and that different x e X can have the same stabilizer. For example, several permutational isomers may be asymmetric, i.e. G = 1, which means that the conjugacy class of the stabilizer consists of the identity subgroup only, G = 1. Therefore, we introduce the set of orbits with the conjugacy class L7 of a subgroup 17 of G as set of stabilizers for this particular set of orbits, using the following notation ... 

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