“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.