Isomerism permutational analysis

III. Formal Analysis of Permutational Isomerizations of Pentavalent Phosphorus... 

Prior to the conception of the TR-mechanism, the appearance of two methoxy-signals in the proton n.m.r. spectrum of (65) in the temperature range +70° to +100°, where isomers (65-(l 4) (2 5)) and (65-(l 4) (3 5)) are undergoing rapid regular permutational isomerization, was taken as an indication that TBP such as (65-(2 5), (3 5) and (2 4) (3 5)) with a diequatorial five-membered ring were excluded from the isomerization itinerary.10 The same conclusion was reached from an analysis of the n.m.r. signal-form.77 The new conception of the multiple TR process,65-89 applied in Fig. 17-1, avoids the involvement, not only of those TBP, but also of all the other isomers that violate the polarity rule. 

The theoretical investigation of these reactions requires quantum-mechanical methods, in particular, the study of chemical bonds in initial, final, and intermediate compounds, as well as the consideration of nuclear motions. Yet frequently the important information can be obtained without analysis of electronic structure of molecules and investigation of actual motion of nuclei, only resorting to the graph theory and employing the group-theoretical conceptions. Here we should define two terms permutation isomers and permutation isomerism reaction. 

Thus, valuable information concerning the possible nature of permutation isomerism reactions was obtained only by the methods of the graph theory and group theory, without analysis of electronic and nuclear densities. 

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