Icosahedral interconversion

Figure 6.19 The interconversion of 1,2- and 1,7-disubstituted icosahedral species via a proposed cubooctahedral intermediate formed during four diamond-square-diamond rearrangements.

In this paper, we have introduced the polyhedral representation of reaction surfaces for chemical interconversion processes, and applied it to the interconversion of JT distortions of icosahedral molecules. In this case, the minimal hypersurface is 5D. Two types of distortions are investigated pentagonal and trigonal. Interconversions between pentagonal distortions can simply be represented by a triangulation of the projective plane. This is the prototype of a JT surface in a... 

Despite the apparent success, the above considerations are flawed because one of the possible stereochemieal choices has been overlooked - polyhedral expansion has not been considered could not Ru3(CO)i2 have an icosahedral ligand envelope with looser carbonyl contacts and a larger internal cavity The a priori dismissal of this possibility (which follows from radius ratio considerations) implies the hidden assumption that COs behave like sticky rigid spheres, which can neither interpenetrate nor become detached, i.e. that polyhedral interconversions (between polyhedra with equal edges) are always energetically favored relative to polyhedral expansions of any size. Such a rigid assumption is definitely unjustified when one further considers that ... 

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