Cluster models construction

In cluster models constructed to mimic adsorption at on top positions an all electron description must always used for the on top metal centre. The accuracy of this type of embedding model is very high compared with full all electron calculations [19-21]. Modelling the adsorption at bridge positions should ideally be done using two all electron centra. Such calculations do, however, become rather costly, and a simplified approach is to correct the ECP results close to the bridge site by comparing ECP and all electron results obtained for two metal atoms and the adsorbate. 

In the N3 bridged compounds, there is a stronger electron-electron interaction through the N/ bridging molecule between two adjacent Ni spins, than between the NO2 bridged compounds. A cluster model constructed on the basis of the accurate structure determined by X-ray diffraction is used in the DV-Xa calculation for NINAZ, NDMAZ, and NDMAP. These are typical Haldane gap materials, which include the N3-bridging ligand. 

The DV-Xx molecular orbital calculations are performed with the cluster models constructed using the geometrically optimized crystal structures. The calculated... 

While quantum-chemical calculations related to gas-phase reactions or bulk properties have become now a matter of routine, calculations of local properties and, in particular, surface reactions are still a matter of art. There is no simple and consistent way of adequately constructing a model of a surface impurity or reaction site. We will briefly consider here three main approaches (1) molecular models, (2) cluster models, and (3) periodic slab models. 

Explain the difference between constructing a cluster model for covalent and ionic crystals. 

For calculations of Eu2+ ions occupying BR, aBR, and mO sites, the EuOg-, EuOj-, and EuOjp clusters were constructed from the crystal structures of BAM as shown in fig. 35. The lattice relaxations were not considered. In the model cluster for the BR site, Eu2+ ions are coordinated by 9 oxygen ions and the Eu-0 bond lengths are 3.249 A (6 bonds) and 2.802 A... 

Detailed structural data from the X-ray structure analysis diffraction data was used in the construction of the cluster model for the DV-Xa calculation. 

Cluster models shown in Figure 23.2 were constructed from respective crystal structure [11,12]. The crystal structure of LiX is NaCl-type. The bond lengths of Li-Cl and Li-Br are 2.570 and 2.751 A, respectively. The calculation is performed for four clusters, LLiX6J5 for model I, [Lii3X6]7 for model II, [Lii3Xi4] for mode III, and [Li19X14]5+ for model IV. The model clusters were embedded in the... 

The catalytic activity of aluminophosphates has been discussed by Tada et al. (133-135). It seems also of interest to perform a theoretical investigation of possible active centers (both BAS and LAS) in these systems and to compare them with the respective centers in aluminosilicates. Such a comparison implies certain requirements both to the scheme of computations and to the choice of the cluster models. Most important is that the procedure of saturating the dangling bonds of a cluster should affect the results to a minimal extent. A simple way of attaining this aim is to construct closed clusters with terminal bonds mutually saturating each other (41). 

Molecular mechanics (MM), molecular dynamics (MD), and Monte-Carlo (MC) methods were employed to simulate the adsorption of methane, ethane, propane and isobutane on silicalite and HZSM-5. The silicalite was simulated using the same cluster-model adopted in the diffusion calculations. The H-ZMS-5 structure was constructed according to the procedure suggested by Vetrivel et al. [32], which consists in replacing one atom at the channel intersection by and protonating the oxygen atom bridging the Ta and Tg sites in order to preserve the lattice neutrality. 

The development of the best method for constructing cluster models for solids has concerned many researchers. Gilbert (1972) and Adams (1962) independently developed a Hartree-Fock theory of localized or-... 

Cluster models have been quite popular for some time now as a basis for the discussion of chemisorption systems (9-11), especially among quantum chemists who were able to contribute with their methods and tools to surface science via these constructs. (The references of this paragraph are intended to provide examples only since an exhaustive list would be too lengthy to be appropriate here.] Transition metal clusters have been the most intensively studied systems ftom the beginning due to the interesting chemisorptive and catalytic properties of such surfaces. At first one-electron aspects dominated cluster model applications (12,13), photoelectron spectra providing the bridge between theory and experiment (14). The simpler quantum chemical methods... 

A cluster model used for the calculation of TiFe system is shown in Fig. 17. For simplicity, this is constructed on the basis of the CsCl-type crystal structure of TiFe [49], although the hydrogenation induces a small distortion in the crystal structure. In this model a hydrogen atom is located on the central site of the octahedron consisting of two Fe( 1) atoms and four Ti atoms. In order to examine alloying effects on the hydriding properties, one of the two Fe( 1) atoms is substituted... 

These models are usually constructed by scooping out a small representative region (see Fig, 3A) containing 5-30 atoms from the real M/C interface. Cluster models emphasize chemistry as local by only considering a small active region. Unfortunately, some early cluster studies used unrealistically small clusters, which were poor representations of the real interface they attempted to model. In such cases, important long-range effects are missed. 

Sometimes the ceramic side of the cluster is embedded in an array of the nominal anion and cation point charges in the proper structure, to emulate the real Madelung potential in the ceramic — this definitely improves the realism of the cluster model.A Green s function constructed from the perfect host crystal has also been used to embed a ceramic cluster. 

The question of cluster structure arises from the preceding observations. In order to study this problem, an apparatus was built in Orsay. Thanks to it and to the construction of cluster models, the structure of Ar clusters containing from a few atoms to several thousand atoms is now completely elucidated. A description of the experiment is given in Section II. The construction of noncrystalline models is presented in Section III, and their relaxation, together with structural transitions, is studied in Section IV. Section V discusses other intermediate models and gives a brief comparison with metallic clusters. Finally, Section VI deals with the structure of clusters made of several polyatomic molecules. 

Depending on the crystal structure, appropriate cluster models are employed in the calculation. Here, cluster means a hypothetical molecule to represent a metal crystal. For example, a cluster model used for the ZrMn system is shown in Fig.l. This is constructed based on the crystal structure of ZrMn,Hj (11). Hydrogen atoms are located at the central site of one tetrahedron, the comers of which are occupied by two Zr atoms and two Mn atoms. 

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