MC„ clusters

COMPLEXES OE C H RING SYSTEMS WITH A METAL ATOM A/nC-SHAPEI) MC CLUSTERS... 

Except for the trimethylenemethane complex, complexes of the types shown in Figure 4.8 can be treated as arachno mixed metal-carbon MC clusters, formally containing (n -1- 4) skeletal bond pairs to hold their (n + 1) skeletal atoms together. ... 

Using successively an inverse Cluster Variation Method and an IMC algorithm, we determined a set of nine interactions for each alloy (for the IMC procedure, we used a lattice size of 4 24 ). For each alloy, the output from the inverse procedure has been used as an input interaction set in a direct MC simulation, in order to calculate a... 

Finally, Nagaoka et al have made a very interesting study applying MC-FEP techniques to the vinyl alcohol - acetaldehyde tautomerism.32 Using a cluster of the solute with three water molecules as a solute , the free energy for the tautomerism was calculated along different reaction pathways, which had been previously found by ab initio calculations including an SCRF solvation term. They were able to deduce that a two-step mechanism is favoured over a concerted one for the transfer of the proton. 

Moffitt MC, Neilan BA (2004) Characterization of the nodularin synthetase gene cluster and proposed theory of the evolution of cyanobacterial hepatotoxins. Appl Environ Microbiol... 

COLOR FIGURE 5.21 Snapshot of a methanol bridge cluster for a MC simulated monomeric Cjg chromatographic surfaces. Solutes involved in the cluster are highhghted in darker, opaque coloring. (Reproduced from Zhang, L., et al., J. Chromatogr. A, 1126, 219, 2006. With permission.)... 

Abbreiriaticm BWG = Btagg-Williams-Gorsky, CVM = Cluster Variation method, T = Tetrahednm approximation, T/0 = Tetrahedron/Octahedron approximation, MC = Monte Carlo, SC = Simple cubic approximation, SP = simple prism approximation, Pt point approximation, Tr triangle approximation... 

De Mori et al. have taken a different approach to take advantage of MC simulations. They used a coarse-grained Hamiltonian to presample phase space in an approximate manner. This is followed by MD simulations starting from representative structures from the most dominantly populated clusters within the MC ensemble. Such a hierarchical strategy was employed to study the folding of a small protein [144] and the oligomer formation of short, amyloidogenic peptides [145]. 

For the sake of completeness, we recall that the idea of the single-root formalism exploiting the Hilbert space approach was also proposed by Banerjee and Simons [31] and Laidig and Bartlett [34,35]. In both approaches they start from the complete active space MC SCF wave function, however, in order to eliminate redundant cluster amplitudes they approximate the wave operator by... 

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