The ligand polyhedral model

Favorable packing of the CO ligands about the cluster core was qualitatively and later (semi)quantitatively investigated by Johnson et al. who, while searching for the best fit between the metal cluster and the optimum ligand polyhedron, eventually derived what is known as the Ligand Polyhedral Model (LPM). According to the LPM  

For example, in the M3(CO)i2 (M = Fe, Ru, Os) family, LPM states that whereas a triangle of Fe atoms (with Fe-Fe bond lengths close to 2.6 A) fits into the hole of an icosahedron (made by twelve spheres of 3.0 A radius) those of Ru or Os atoms (with M-M bond lengths close to 2.85 A) cannot these larger triangles will, however, fit into an anticubeoctahedron which, given its larger radius ratio (1.00 

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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Fluxional Molecules. - The ligand polyhedral model has been applied to carbonyl clusters containing thirteen carbonyl groups. ... 

The dianionic species, [Fe3(CO)n] 4 and [Fe4(CO)i3] 5 (see Scheme 10), are used for preparation of hetcro-nuclear cluster compounds. " Polymer-bound 4 and 5 are obtained by treatment of 1 with aminated polystyrenes in Me0H-H20. The ligand polyhedral model (LPM) has been successfully applied to [M4(CO)i3] species including It is claimed that a new neutral binary iron carbonyl formulated as Fe4(CO)i4 (characterized by IR) is formed by co-deposition of mass-selected Fc4 and... 

Attempts to distinguish between possible mechanisms for CO ligand mobility in Group 9 carbonyl clusters, i.e. merry-go-round versus Johnson and Benfield s ligand polyhedral model, have proven inconclusive. A series of Co-NMR studies on [Co4(CO)i2] and analysis of the thermal motion of the CO ligands using new structural data for [Rh4(CO)i2] failed to provide conclusive evidence for the type of fluxional processes observed. 

It is often difficult to represent inorganic compounds with the usual structure models because these structures are based on complex crystals space groups), aggregates, or metal lattices. Therefore, these compounds are represented by individual polyhedral coordination of the ligands such as the octahedron or tetrahedron Figure 2-124d). 

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