Local Cluster Models

I Extended Hiickel (9), Xa Scattered Wave (15), semiempirical SCF methods 16)) gave way to more sophisticated treatments, based both on ab initio Hartree-Fock SCF (17), Cl (18-20)) and on local density methods (DVM-Xa, 22), LCGTO-Xa (23), LCGTO-LSD-MP (24))- These more elaborate studies furnish structural and energetic information on chemisorption bonds -within the restriction of a local cluster model (9), of course. 

In the present chapter, which deals with theoretical concepts applied to vanadium and molybdenum oxide surfaces, we will restrict the discussion to binary oxide systems. So far, mixed metal oxide systems have not been studied by quantitative theory. Theoretical methods that have been used to study oxide surfaces can be classified according to the approximations made in the system geometry where two different concepts are applied at present, local cluster and repeated slab models. Local cluster models are based on the assumption that the physical/chemical behavior at selected surface sites can be described by finite sections cut out from the oxide surface. These sections (surface clusters) are treated as fictitious molecules with or without additional boundary conditions to take the effect of environmental coupling into account. Therefore, their electro-... 

Theoretical studies on various physical and chemical parameters of vanadium oxide surfaces have been performed using both repeated slab as well as local cluster models. However, the vast majority of studies has focused on the (010) surface of the pentoxide, V2O5. This is a result of rather little experimental information on details of V Oy surface systems other than V205(010) that has attracted great interest due to its possible importance in catalytic applications. Further, most of the theoretical work has been based on cluster type studies where local surface behavior, in particular near surface oxygen sites, is discussed in detail. This will be reflected in the following discussion. 

This example shows that dipolar interactions can produce unexpected effects in systems containing polynuclear clusters, so that their complete quantitative description requires a model in which the dipolar interactions between all the paramagnetic sites of the system are explicitly taken into account. Local spin models of this kind can provide a description of the relative arrangement of the interacting centers at atomic resolution and have been worked out for systems containing [2Fe-2S] and [4Fe-4S] clusters (112, 192). In the latter case, an additional complication arises due to the delocalized character of the [Fe(III), Fe(II)] mixed-valence pair, so that the magnetic moments carried by the two sites A and B of Fig. 8B must be written... 

Ludwig s (2001) review discusses water clusters and water cluster models. One of the water clusters discussed by Ludwig is the icosahedral cluster developed by Chaplin (1999). A fluctuating network of water molecules, with local icosahedral symmetry, was proposed by Chaplin (1999) it contains, when complete, 280 fully hydrogen-bonded water molecules. This structure allows explanation of a number of the anomalous properties of water, including its temperature-density and pressure-viscosity behaviors, the radial distribution pattern, the change in water properties on supercooling, and the solvation properties of ions, hydrophobic molecules, carbohydrates, and macromolecules (Chaplin, 1999, 2001, 2004). 

Quantum-chemical cluster models, 34 131-202 computer programs, 34 134 methods, 34 135-138 for chemisorption, 34 135 the local approach, 34 132 molecular orbital methods, 34 135 for surface structures, 34 135 valence bond method, 34 135 Quantum chemistry, heat of chemisorption determination, 37 151-154 Quantum conversion, in chloroplasts, 14 1 Quantum mechanical simulations bond activation, 42 2, 84—107 Quasi-elastic neutron scattering benzene... 

Molecular simulation methods have been applied to investigate the nucleation mechanism of gas hydrates in the bulk water phase (Baez and Clancy, 1994), and more recently at the water-hydrocarbon interface (Radhakrishnan and Trout, 2002 Moon et al., 2003). The recent simulations performed at the water-hydrocarbon interface provide support for a local structuring nucleation hypothesis, rather than the previously described labile cluster model. 

Despite the formation of clathrate-like clusters and complete 512 cages during these simulations, the increased ordering observed from the radial distribution functions and local phase assignments resulted in the authors concluding that their simulation results are consistent with a local order model of nucleation, and therefore do not support the labile cluster model. 

In order to verify which of the above nucleation mechanisms accurately represents hydrate nucleation, it is clear that experimental validation is required. This can then lead to such qualitative models being quantified. However, to date, there is very limited experimental verification of the above hypotheses (labile cluster or local structuring model, or some combination of both models), due to both their stochastic and microscopic nature, and the timescale resolution of most experimental techniques. Without experimental validation, these hypotheses should be considered as only conceptual aids. While the resolution of a nucleation theory is uncertain, the next step of hydrate growth has proved more tenable for experimental evidence, as discussed in Section 3.2. 

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