Clustering description

The interest in semiconductor QD s as NLO materials has resulted from the recent theoretical predictions of strong optical nonlinearities for materials having three dimensional quantum confinement (QC) of electrons (e) and holes (h) (2,29,20). QC whether in one, two or three dimensions increases the stability of the exciton compared to the bulk semiconductor and as a result, the exciton resonances remain well resolved at room temperature. The physics framework in which the optical nonlinearities of QD s are couched involves the third order term of the electrical susceptibility (called X )) for semiconductor nanocrystallites (these particles will be referred to as nanocrystallites because of the perfect uniformity in size and shape that distinguishes them from other clusters where these characteriestics may vary, but these crystallites are definitely of molecular size and character and a cluster description is the most appropriate) exhibiting QC in all three dimensions. (Second order nonlinearites are not considered here since they are generally small in the systems under consideration.)... 

If ligands smaller or larger than the cyclopentadienyl ring are incorporated, the total number of bonding electrons used for the cluster description will vary, whereas the number for the aromaticity formalism is not changed. 

As already outlined for other complexes, the bonding in 63 can be described by both the nslde and the cluster systematics. The ligand offers its 7r6-system to the Cr(CO)3 fragment and accepts electron density from the filled d-orbitals. In the cluster description, compounds 63 have seven-vertex nido geometries with In + 4 = 18 framework electrons, supplied by C(2 x 3), B(2 x 2), and N(2 x 4). 

Sanchez J. M., DucasteUe E. and Gratias D., Generalized Cluster Description of Multicomponent Systems, Physica 128A, 334 (1984). 

A second cluster description soon followed this original report, namely, the synthesis of Ce5Te3(TeS(SiMe3)3 via cleavage of a Te-Si bond and subsequent ligand redistribution in hexane. This compound was isolated... 

WangJ, Ge W, LiJ Eulerian simulation of heterogeneous gas-sobd flows in CFB risers EMMS-based sub-grid scale model with a revised cluster description, Chem Eng Sci 63 1553-1571, 2008a. 

J. M. Sanchez, F. Ducastelle, and D. Gratias. Generalized cluster description of multicomponent systems. PhysicaA, 128 334-350,1984. 

B3LYP/6-31G(d) optimized structures of C59, Csg, and C57 clusters. Description indicates highlighted rings. "A-B" denotes A- and B-membered ring. Circle denotes an unsaturated atom (Reprinted with permission from Lee and Flan (2004). Copyright 2004, American Institute of Physics)... 

In contrast to the numerical taxonomy quality function, the conceptual clustering quality function takes into account the utility of the concepts representing the clusters, as seen below, where the parameter CONCEPTS is the set domain of concepts which may be used to describe the clusters. In the context of conceptual clustering, a concept is a valid cluster description as specified within the cluster description language. Consequently, the set of possible concepts need not be explicitly enumerated. An important bias in this method is the use of the simplicity of a cluster description as a metric for the quality of clustering. 

CEs of Configurational Functions In 1984, Sanchez et al. [81] published the seminal paper Generalized cluster description of multicomponent systems, which became the cornerstone of the CE method. The CE provides a means to find a term-by-term expansion of a configurational function like E(simple Ising model and thus includes different sorts of interactions - in particular, many-body interactions between more than two sites of a lattice - and allows for more than two possible occupations on a site. While the latter is needed for the research of multicomponent systems, which are so significant for today s materials science, the inclusion of many-body interactions that go beyond the site-to-site interaction of the Ising model is of uttermost importance to model any many-body system in physics. 

Sanchez, J.M., Ducastelle, L., and Gratias, D. (1984) Generalized cluster description of multicomponent systems. Physica, 128A, 334. 

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