Constructive clustering

Fig. 9. Zero-field splitting of the S = 2 ground state of [Fe3S4] clusters. Constructed for D = -2.5 and E/D = 0.23, where D and E are the axial and rhombic zero-field splitting parameters, respectively.

Actually, when a mixed solution of two ionic precursors M and M is irradiated or chemically reduced, both situations of alloyed or bilayered cluster formation may be encountered without clear prediction [102,173]. Moreover, an unambiguous characterization of the intimate structure of nanometric mixed clusters is quite difficult and requires appropriate methods, applied at different steps (or different doses) of the mixed cluster construction. 

An important consequence of the nonutilization of tangential orbitals is that platinum clusters often do not obey the normal electron counting rules and appear to be electron deficient (19,21,29,58,75,76). Electron counts are usually intermediate between those found in normal transition metal clusters (58-68) and those observed in gold clusters (58,78), but no satisfactory general electron counting theory has been developed for Pt-containing clusters. In small Pt clusters constructed from PtL2 units, theoretical studies have shown that the total electron count depends on the relative orientation of the... 

The fractal consideration of statistical polymer allows us to define the radius of gyration for clusters constructed as statistical polymers. 

Clusters based on homonuclear trimetal units are dominated by those containing transition metals from the iron triad. Clusters constructed on a Co3 framework are the only additional examples in this section. The first cluster to be reported was Co3(CO)9BNEt3 (22). This arises from the reaction of [Co(CO)4] with BBr3 in the presence of NEt3 and is clearly related to the triosmium systems of Shore et al. discussed above (Fig. 7)... 

Again, this is a rejection-free algorithm, in the sense that the cluster is always flipped. Just as in the SW algorithm, the cluster-construction process is probabilistic, but the probabilities pij involve energies of individual spin pairs in contrast with an acceptance criterion that involves the total energy change induced by a cluster flip. The implementation can be simplified by a small trick In step (2), each spin j that is added to the cluster can immediately be inverted. This guarantees that a spin is never added twice. Step (5) can then be eliminated. ... 

According to this equation, Xu and coworkers developed a method to generate hypothetical open-framework aluminophosphate structures with specified Al/P stoichiometry using the automated assembly of SBUs.[76] For each specified Al/P stoichiometry, all the possible combinations of A1 and P atoms with different coordination states could be calculated according to Equation (3.2). The A1 and P atoms of different coordination states, together with the clusters constructed by them, could be selected as the building... 

The structure of [ Cu(bpy) 2(V02)3(P04)(HP04)2], shown in Figure 80, may be best described as Cu2(bpy)2(V0)2(P04)2(HP04)2 chains linked through square pyramidal VO5 units into a 2D network. Embedded within the chain are Cu2(bpy)2(V0)2(P04)2 clusters, constructed of a central ring of edge- and comer-sharing VOs octahedra and PO4 tetrahedra capped by two... 

Fig. 2.20. The number S N) of distinct sites visited during an AT-step random walk on a plane square lattice small diamonds) and on a percolating cluster constructed over the same lattice, at threshold small triangles). In the first case, the increase is (statistically) linear at each step, the probability of finding a new site is constant. In the second case, the discovery of new sites is much slower, going as There is a tendency to retrace the same path although, in contrast, the...

Ogino et al. described cluster construction by the reaction of [Gp 2Ru2S4] with [W(GO)3(NGMe)3] to give a pair of isomeric tetranuclear Ru-W clusters 196 and 197. Two interesting aspects of this reaction should be noted. In the course of the reaction, the redistribution of the S and GO ligands took place between the Ru and W atoms without loss of any S and GO ligands. Furthermore, thermal and photochemical interconversion between them was observed.The mechanistic pathway for their formation and their redox properties were also examined. 

Secondly, since the stability of the clusters is strongly dependent on the presence/absence of low-coordinated atoms on the surface, it should be possible to stabilize the clusters through properly chosen surfactants or by modifying the surface in other ways (Frenzel et al. 2005). For our stoichiometric AB clusters, the outermost atoms are formed to equal parts by A and by B atoms. Considering nonstoichiometric clusters constructed, e.g., as a spherical cut-out of... 

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