Connected duster

The bidentate oxazoline ligands 85 and 86 (and derivatives thereof) are excellent reporter ligands, and several studies have used NOEs to determine the nature of their chiral pockets [61, 113, 114, 126]. NOESY studies on the cations [Ir(l,5-COD)(86)]+ and several cationic tri-nudear Ir(iii)(hydrido) compounds [110], e. g. [Ir3(p3-H)(H)5(86)3] +, 87, in connection with their hydrogenation activity, allowed their 3-D solution structures to be determined. In addition to the ortho P-phenyl protons, the protons of the oxazoline alkyl group are helpful in assigning the 3-D structure of both the catalyst precursors and the inactive tri-nudear dusters. Specifically, for one of these tri-nudear Ir(iii) complexes, 87 [110], with terminal hydride ligands at d -17.84 and d -21.32 (and a triply bridging hydride at 5 -7.07), the P-phenyl and oxazoline reporters define their relative positions, as shown in Scheme 1.5. 

Referringiiacfc to the main clusters, it can be seen that tlie samples within cluster 2 are connected by vertical lines with small distance values relative to the other clisers. This is an indication that samples within this duster are more each other (i.e.. the Interpoint distances are smaller) than are... 

It would be elegant, but disingenuous, to present this study in a logical order the true sequence of events was much less logical and it is more honest to present that here. The original motivation was to examine the trimer and tetramer of beryllium (and magnesium) with the CCSD method, and to compare the results with those from MRCI. The work was started in 1988, well before we had the capability of including any effects of connected triple excitations in the coupled-duster treatment. 

Initially, we observe that all the dusters in this subarray are strictly and consistently connected with one another by certain c >erator relations, forming a corresponding operatm series, with all the dusters similarly oriented relative to one another and controlled by the same operators. 

A Linux duster cxjnsisting of nodes with two single-core 3.06 GHz Intel Xeon processors (each with 512 KiB of L2 cache) connected via a 4x Single Data Rate InfiniBand network with a full fat tree topology. 

Towards the multireference Brillouin-Wigner coupled-dusters method with iterative connected trifles MR BWCCSDT-alpha approximation Journal of Chemical Physics 122, 181101 (2005)... 

Figure 5.1, we see a cluster that connects opposite edges of the system. The latter is called the spanning cluster. In percolation theory, we are concerned mainly with infinite systems and thus we call the spanning duster the percolation or the infinite cluster. The illustration given in Figure 5.1 reflects here a finite (small) portion of the infinite system but it has to be remembered that quantitative characterizations of the various properties are considered meaningful only at the infinite system limit... 

Throughout the book brackets are used to denote the composition of a discrete molecular cluster. In the present chapter this notation is kept for discrete dusters only. For interconnected clusters, the structure predse notation of Schafer and Schnering is used, and in the case of condensed cluster systems the connectivity is indicated by the indices only. 

Figure 5>3. Increasing connectivity of [M (X, X) dusters in halides, halide dialcogenides, and dialcogenides of the metals Nb, Mo, and Re. X links in a) RetSesClg (chain), b) MocOq (layer), and c) Nb In (network) X " links in d) Re5SegCl2 (layer) and e) MOjS6Br2 (network) X (+X ) links in f) Mo BrgSj (diain) and g) MoeBr S3 (layer). M, and X atoms are drawn with increasing size taken from ref. [6] (cf. Ikble 6-1 and text).

Figore 5-43. Projections of the crystal structures of a) Hf3 2 and b) RhsGes along the short axes. Metal atoms are connected by lines to indicate duster fragments. 

Cd-Cd- and Hg-Hg-bonded complexes can also be synthesized by reacting diaryl cadmium or diaryl mercury with the intermetallic Zintl phases K Pb, or Kj As, respectively (method xiii. Scheme 12.5) [30]. In both cases, a Zind duster anion ([Pb CdCdPh,] " or [As HgHgAs ] ") is formed in which the metal atoms are connected by a single bond (16-17, Scheme 12.9). Complex 16 crystallized as two crystallographically independent molecules in which the Cd-Cd bond length is 2.697(1) and 2.715 (2) A, respectively, while the Hg-Hg bond distance in 17 is 2.6792(9) A. 

Typical dusters willi both Orthogonal and Di onal connections... 

The correlation length % (i.e., the measure duster connectivity on a percolating lattice) is defined as... 

Percolation in the two-dimensional lattice gas is very instructive in connection with the universality concept If percolation occurs at finite lattice-gas correlation length, the critical exponents are the same as for random percolation. This can be easily understood if one takes into account that near the percolation threshold the lattice-gas correlation length I is much smaller than the typical duster radius thus, the large clusters average over the effects of correlation. This argument breaks down only at the critical point of the two-dimensional lattice-gas where both and vary simultaneously in fact, we have seen that at this point some exponents do change. 

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