Cluster substitution/expansion

Uetal cluster chemistry (ttgend exchange, duster substitution, expansion)... 

The series of hydrido phosphine-substituted clusters, [HWRu3(p4-BH)(CO)n x(PPh3)xCp] (x = 1, 2) have been prepared. The chemistry of the tungsten diyne [W(C = CC = CH)(CO)3Cp] with a number of ruthenium cluster complexes has been elaborated, and is summarised in Scheme 6. Reaction with [Ru3(CO)io(NCMe)2] afforded 151 which readily converted to the hydrido-alkynyl cluster 152 on refluxing in benzene. Reaction with the phosphine-substituted [Ru3( u-dppm)(CO)io] afforded three isomers of 153, a product analogous to 152. Cluster core expansion of 152 by reaction with [Co2(CO)s] or [Ru3(CO)i2]/[Fc2(CO)9] gave the linked clusters 154 and 155, respectively. 

Preparation of hydridopolyborates followed by subsequent protonation or substitution reactions (cluster expansion). 

The material reviewed in this Chapter hitherto has focused on metallacarboranes in which the metal atom is a vertex in an icosahedral cage framework. Until recently, monocarbollide metal compounds with core structures other than 12 vertexes were very rare since suitable carborane precursors were not readily available." However, Brellochs recent development of the reaction of decaborane with aldehydes to give 10-vertex monocarboranes permits a considerable expansion in this area of boron cluster chemistry. As a consequence, several intermediate-sized monocarboranes are now easily accessible and we have recently begun to exploit the opportunities that these present. In particular, we have focused thus far on complexes derived from the C-phenyl-substituted species [6-Ph- zJo-6-CBgHii] It is clear from these initial studies that a wealth of new chemistry remains to be discovered in this area, not only from among the metal derivatives of PhCBg car-boranes such as those discussed in this section, but also in the metal complexes of other newly available carboranes. 

Anionic clusters are good nucleophiles (see Section III,A) and are often easy to make. On the other hand, the electrophilic nature of most monometallic complexes is obvious from ligand substitutions. The combination of these properties makes a strategy for cluster expansion. This strategy was used for the first time by Hieber (130) in making Fe4(CO)fc from Fe3(CO),7 and Fe(CO)s. It is probably active in many syntheses of large metal carbonyl clusters because the Re, Os, Rh, Ir, Ni, and Pt clusters involved are almost always anionic. However, simple stoichiometries can rarely be written for such reactions (122). This route makes mixed metal clusters accessible, e.g.,... 

Since each additional interaction vertex in the cluster expansion contributes two segment summations and one momentum integral, with these substitutions a total factor of n2 d = neaccompanies the additional excluded... 

The time-of-flight mass spectrum recorded for an expansion of fluorobenzene (FB) with deuterated methanol presents mass peaks corresponding to deuterated anisole+—evidence of an intracluster nucleophilic substitution reaction. In the clusters, the two decay channels of FB(CD3OD) are ... 

The embedded (MogOisliCbAsCYjHs), 4 cluster exhibits the Z>3 symmetry characteristic of previously reported isolated clusters of the type (MogOis) (ChAsRM4 (101. The cluster expansion observed upon substituting As for P in these materials reflects in part the larger covalent radius of As compared with P. 

Tables III-XVII give calculated permanent moments. Selected comparisons with experimental values or calculations of others are also listed. All values are in atomic units, and traceless rather than Cartesian forms are distinguished with Greek letters, 6 (quadrupole) and G (octupole). Coordinates for the atomic centers are listed. These specify the geometry used, which were equilibrium geometries, and implicitly the multipole expansion center (x = 0, y = 0, z = 0). The moments are given at both the SCF level and at the well-correlated level of coupled-cluster theory [95-102]. ACCD [103-106] was the particular coupled-cluster approach, and the moments were evaluated by expectation [102] with the cluster expansion truncated at single and double substitutions.

Ivanciuc T, Klein DJ, Ivanciuc O (2005) Posetic Cluster Expansion for Substitution-Reaction Diagrams and its Application to Cyclobutane, J Math Chem, submitted... 

Introduce the Mayer function Q, replace exp(—Vij/ksT) by 1 + Qij. When i and j molecules are not overlapped the term Qij vanishes otherwise Qij = — 1. Substituting into Equation 2.14, the multi-products in the equation are reduced to the power expansion of Qij. Here the cluster expansion is used. 

Like CC, BWCC is fully extensive. Furthermore, the truncated forms of the Brillouin-Wigner coupled cluster expansion involving single and double substitutions usually designated BWCCD corresponding to the approximation (67) and BWCCSD corresponding to the approximation... 

When eq 8.3 is substituted into the cluster expansion for the distribution functions in the fluid, and simplified through cancellations in graphs by taking into account eq 8.2, the result is a formal graphical expansion for the pair distribution function in terms of renormalized hydrogen-bond /-functions. This concept of saturation at the dimer level is a key element in Wertheim s theory, discussed below. 

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