Cluster-based computing

Mainframes are large computers comprised of a cluster of tightly coupled machines or having multiple processors. These units will often be set up for specific applications as database servers, or for handling calculations such as those generated by quantum mechanics-based computational chemistry methods. 

Figure 11.6 Molecular orbital energy level diagrams computed for iron octahedrally coordinated to oxygen. Left divalent iron in the [Fe06]-1° cluster (based on Sherman, 1991) right trivalent iron in the [Fe06]-9 cluster (from Sherman, 1985a). Orbital energies have been scaled relative to zero for the non-bonding 6rlu level.

Figure 11.9 Molecular orbital energy level diagrams computed for tetravalent manganese. (a) Tetrahedral [MnOJ-4 cluster, (b) octahedral [MnOJ-8 cluster (based on Sherman, 1984).

Cluster-based and dissimilarity-based methods for compound selection were first discussed in the Eighties but it is only in the last few years that the area has attracted substantial attention as a result of the need to provide a rational basis for the design of combinatorial libraries. The four previous sections have provided an overview of the main types of selection method that are already available, with further approaches continuing to appear in the literature. Given this array of possible techniques, it is appropriate to consider ways in which the various methods can be evaluated, both in absolute terms and when compared with each other. A method can be evaluated in terms of its efficiency, /.< ., the computational costs associated with its use, and its effectiveness, /.< ., the extent to which it achieves its aims. As we shall see, it is not immediately obvious how effectiveness should be quantified and we shall thus consider the question of efficiency first, focusing upon the normal algorithmic criteria of CPU time and storage requirements. 

Azuaje F. Clustering-based approaches to discovering and visualising microarray data patterns. Brief Bioinform. 2003 4 31-42. Quackenbush J. Computational analysis of microarray data. Nat. Rev. Genet. 2001 2 418-427. 

DFT is the modern alternative to the wave-function based ab initio methods and allows to obtain accurate results at low computational cost, that also helps to understand the chemical origin of the effect. DFT, like Hartree-Fock (HF) methods, exploit molecular symmetry which is crucial in the case of computational studies of the JT effect. It also includes correlation effects into the Hamiltonian via the exchange-correlation functional. HF and many-body perturbation methods are found to perform poorly in the analysis of JT systems for obvious reasons, at contrast to the methods based on DFT, or multiconfigurational SCF and coupled cluster based methods [73]. The later are very accurate but have some drawbacks, mainly the very high computational cost that limits the applications to the smaller systems only. Another drawback is the choice of the active space which involves arbitrariness. 

In this section, we show that the accuracy of the GPW and GAPW methods can be achieved with high computational efficiency. We illustrate both the serial performance and the scalability on parallel computers using a high-end supercomputer as well as a modern cluster based on a PC-like architecture. 

Steindl, T. M., Crump, C. E., Hayden, E. G., Langer, T. Pharmacophore modeling, docking, and principal component analysis based clustering combined computer-assisted approaches to identify new inhibitors of the human rhinovirus coat protein. 7. Med. Chem. 2005, 4S(20), 6250-6260. 

In this work, classification through HCA was based on the Euclidean distance and the average group method. This method established links between samples/cluster. The distance between two clusters was computed as the distance between the average values (the mean vector or centroids) of the two clusters. The descriptors employed in HCA were the same selected in... 

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