Cluster model approach

DFT method combined with a cluster model approach was compared regarding its suitability for describing both structures and energy profiles. This study shows that the relative stability and geometry depend on the cluster sizes in agreement with previous studies [15] but shows that the energy barrier heights of the reaction processes are not affected. 

The Cluster Model Approach to Quantum Chemical Studies... 

The combination of the cluster model approach and modem powerful quantum chemistry techniques can provide useful information about the electronic structure of local phenomena in metal oxides. The theoretical description of the electronic states involved in local optical transitions and magnetic phenomena, for example, in these oxides needs very accurate computational schemes, because of the generally very large differential electron correlation effects. Recently, two very promising methods have become available, that allow to study optical and magnetic phenomena with a high degree of precision. The first one, the Differ-... 

The theoretical studies applying cluster model approach [148, 149] and periodic approximation [150] devoted to the description of interaction of dickite and kaolinite with the FA, MFA and DMSO molecules have been performed. These works have studied the position and the orientation of the adsorbed and intercalated organic molecules with respect to the surface of mineral, interaction between the organic molecule and the mineral, interaction energy, the influence of the intercalation and adsorption on changes of geometry parameters, electron structures of organic molecules, and the surfaces of the minerals. 

The precise features of real catalysts at a microscopic scale are rather unknown but in all cases the main interactions occur through a surface. Two different theoretical models are often used to describe the electronic and other microscopic features of a surface. On the one hand, there is the solid state physics approach in which a surface is considered as a slab of a given thickness, finite in the direction perpendicular to the surface and infinite in the two other dimensions with perfect two-dimensional periodical symmetry. On the other hand, one has the cluster model approach which represents the surface with a finite number of atoms and the surface-adsorbate interaction as a supermolecule this is essentially a quantum chemical approach. It is important to realize that both approaches are crude representations of physical reality because real surfaces are far from being perfect, usually... 

The cluster model approach assumes that a limited number of atoms can be used to represent the catalyst active site. Ideally, one would like to include a few thousands atoms in the model so that the cluster boundary is sufficiently far from the cluster active site thus ensuring that edge effects are of minor importance and can be neglected. Unfortunately, the computational effort of an ab initio calculation grows quite rapidly with the number of atoms treated quantum mechanically and cluster models used in practice contain 20 to 50 atoms only. It is well possible that with the advent of the N-scaling methods " this number can dramatically increase. Likewise, the use of hybrid methods able to decompose a very large system in two subsets that are then treated at different level of accuracy, or define a quantum mechanical and a classical part, are also very promising. However, its practical implementation for metallic systems remains still indeterminate. 

Exploring adsorbate-substrate potential energy surfaces by means of the cluster model approach... 

The fact that in the cluster model approach the adsorbate plus the substrate are treated as a supermolecule permits to use the computational... 

This section reports a series of examples of application of the cluster model approach to problems in chemisorption and catalysis. The first examples concern rather simple surface science systems such as the interaction of CO on metallic and bimetallic surfaces. The mechanism of H2 dissociation on bimetallic PdCu catalysts is discussed to illustrate the cluster model approach to a simple catalytic system. Next, we show how the cluster model can be used to gain insight into the understanding of promotion in catalysis using the activation of CO2 promoted by alkali metals as a key example. The oxidation of methanol to formaldehyde and the catalytic coupling of prop)me to benzene on copper surfaces constitute examples of more complex catalytic reactions. 

The cluster model approach and the methods of analysis of the surface chemical bond have been presented and complemented with a series of examples that cover a wide variety of problems both in surface science and heterogeneous catalysis. In has been show that the cluster model approach permits to obtain qualitative trends and quantitative structural parameters and energetics of problems related to surface chemistry and more important, provide useful, unbiased information that is necessary to interpret experiments. In this way, the methods and models discussed in the present chapter are thought to be an ideal complement to experiment leading to a complete and detailed description of the mechanism of heterogeneous catalysis. 

The density functional theory and the cluster model approach enable the quantitative computational analysis of the adsorption of small chemical species on metal surfaces. Two studies are presented, one concerning the adsorption of acetylene on copper (100) surfaces, the other concerning the adsorption of ethylene on the (1(X)) surfaces of nickel, palladium and platinum. These studies support the usefulness of the cluster model approach in studies of heterogeneous catalysis involving transition metal catalysts. 

The interaction of the acetylene molecule with the (100) surface of copper was studied using the cluster model approach. All the calculations have been performed using the Density Functional Theory. The BLYP method included in the Gaussian 98 [30] package was used. This method combines the gradient corrected exchange functional of Becke [31] with the gradient corrected correlation functional of Lee et al [32]. 

In the present work, the interaction of the ethylene molecule with the (100) surfaces of platinum, palladium and nickel is studied using the cluster model approach. All these metals have a face centered cubic crystal structure. The three metal surfaces are modelled by a two-layer M9(5,4) cluster of C4V symmetry, as shown in Fig. 6, where the numbers inside brackets indicate the number of metal atoms in the first and second layer respectively. In the three metal clusters, all the metal atoms are described by the large LANL2DZ basis set. This basis set treats the outer 18 electrons of platinum, palladium and nickel atoms with a double zeta basis set and treats all the remainder electrons with the effective core potential of Hay and Wadt... 

Our calculations also support the picture, already suggested by several experimental studies, of a significantly distorted adsorbate on the three metal surfaces there is a lengthening of the CC bond and a rehybridization of the carbon atoms from sp toward sp On these three surfaces, the a-donation is stronger than the d-rt backdonation, leading to positively charged species on the surface. The results obtained, also show that on platinum, palladium and nickel (100) surfaces the ethylene molecule adsorbs preferentially on the di-o mode. This conclusion is based not only on the adsorption energies (whose calculation is known to be the major problem of the cluster model approach) but also on a comparision between the calculated vibrational frequencies and the available experimental results. 

The results presented support the usefulness of the cluster model approach in the study of chemical processes on solid surfaces. 

The cluster model approach can be viewed as the chemist s approach since it reduces a very large system to a supermolecule, yet it is currently the only way to study excited states and therefore to contribute to the interpretation of electronic spectra. On the other extreme, one finds the physicist point of view, which makes uses of translational symmetry and treats the system as a perfect periodic solid. Therefore, as in the cluster model approach, the periodic approach constitutes a severe approximation since the same structure is reproduced in two or three space directions. 

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