“Polytopal Rearrangement Model of Stereoisomerization” and Its Potential as the Basis for a Systematic Model of All Stereoisomerism

The term “polytopal rearrangement” describes any shape changing process operating on a coordination “polyhedron”─the solid figure defined by the positions of the ligand atoms directly attached to the central atom of a coordination entity. Developed in the latter third of the last century, the polytopal rearrangement model of stereoisomerization is a general mathematical approach for analyzing and accommodating the complexity of such processes for any coordination number. The motivation for the model was principally to deal with the complexity, such as Berry pseudorotation in pentavalent phosphorus species, arising from rearrangements in inorganic coordination complexes of higher coordination numbers. The model is also applicable to lower coordination centers, for example, thermal “inversion” at nitrogen in NH₃ and amines. We present the history of the model focusing on its essential features, and review some of the more subtle aspects addressed in recent literature. We then introduce a more detailed and rigorous modern approach for describing such processes using an assembly of existing concepts, with the addition of formally described terminology and representations. In our outlook, we contend that the rigorous and exhaustive application of the principles of the polytopal rearrangement model, when combined with torsional isomerism, will provide a basis for a mathematically complete, general, and systematic classification for all stereoisomerism and stereoisomerization. This is essential for comprehensively mapping chemical structure and reaction spaces.