Cluster shape

In a very recent review of Met-Cars and other metal carbon clusters (246), the authors concluded If experimentalists and theoreticians presently agree to consider that the form with Td symmetry represents the most abundant isomer of Ti8C12 and other Met-Cars, it is mainly because the topological, physical, and chemical properties specific to that cluster shape explain or agree with the experimental information presently available. 

It can be seen that application of the 18-electron rule to clusters necessitates this arbitrary assignment of the number of orbitals of a particular predominant character. The number of orbitals per metal used for cluster skeletal bonding is a consequence of N and E. It varies from two for the M(CO)4 unit in Os3(CO)12 to three for an M(CO)3 unit in Ir4(CO)12. Since these two metal moieties differ, this variation seems reasonable. However, the distribution for an M(CO)3 unit varies with cluster shape as in Ir4(CO)12 and [Os6(CO)18]". ... 

Besides the remarkable directionality of the motion, the images also demonstrate a periodic variation of the cluster from an elongated to a circular shape (Fig. 39). The diagrams in Fig. 39 depict the time dependence of the displacement and the cluster size. Until the cluster was finally trapped, the speed remained fairly constant as can be seen from the constant slope in Fig. 39 a. The oscillatory variation of the cluster shape is shown in Fig. 39b. Although a coarse model for the motion has been presented in Fig. 39, the actual cause of the motion remains unknown. The ratchet model proposed by J. Frost requires a non-equiUb-rium variation in the energetic potential to bias the Brownian motion of a molecule or particle under anisotropic boundary conditions [177]. Such local perturbations of the molecular structure are believed to be caused by the mechanical contact with the scaiming tip. A detailed and systematic study of this question is still in progress. 

Rearrangements of clusters, i.e. changes of cluster shape and increase and decrease of the number of cluster metal atoms, have already been mentioned with pyrolysis reactions and heterometallic cluster synthesis in chapter 2.4. Furthermore, cluster rearrangements can occur under conditions which are similar to those used to form simple clusters, e.g. simple redox reactions interconvert four to fifteen atom rhodium clusters (12,14, 280). Hard-base-induced disproportionation reactions lead to many atom clusters of rhenium (17), ruthenium and osmium (233), iron (108), rhodium (22, 88, 277), and iridium (28). And the interaction of metal carbonyl anions and clusters produces bigger clusters of iron (102, 367), ruthenium, and osmium (249). 

As indicated, we incorporate a single overall excluded-volume parameter bxv (of order unity) to compensate for the many errors of approximating Vexcl as a simple sum of cluster volumes, neglecting, for example, cluster shape effects on interstitial packing vacancies. A nonzero bXY value brings in the complex nonlinear dependence on all cluster populations,... 

Whereas in ligand bridged dinuclear complexes, removal or addition of two electrons makes or breaks one metal-metal bond (15) this does not seem to be the case for clusters, presumably because of their delocalized bonding. At least for one case, however, two-electron reduction can induce a significant change in cluster shape (18,42) the 84-electron cluster Os6(CO),g with framework 1 is easily reduced to the 86-electron anion Os6(CO) g with framework 2, in accordance with skeletal electron counting rules. 

B. Addition and Elimination Reactions without Change of the Cluster Shape... 

In the common three-connect cluster shapes illustrated in Figure 2.3 the number of electrons that can be associated with the closed clusters is 5n, where n is the... 

Answer. A count of 42 eve or 11 sep yields n= 10 so a bicapped square antipris-matic c/oso-cluster shape is predicted and was found in a solid-state structure determination. 

Exercise 3.3. The compound Os5(CO)i6 has the structure shown in Figure 3.4. Justify the cluster shape using both the eve count and the sep count. 

Group 10 metal clusters with carbonyl and phosphine ligands sometimes fail to follow the counting paradigm, but the reason for this failure differs from those discussed up to now. The situation is illustrated by the two Pt carbonyl clusters shown in Figure 3.21 where the eve counts are four less than those obtained for group 8/9 metal clusters for the same cluster shapes. What is the origin of these lower electron counts ... 

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