Cluster model computational results

A new and efficient computational strategy has been presented, that simplifies the calculation of the vibrational frequencies of a molecular system adsorbed on moderate to large cluster models. This procedure is based on a certain hypothesis and assumption. Nevertheless, present results show that these do not affect the numerical accuracy of the calculated frequencies. An important consequence of this strategy is that largely simplifies the study of the effect of a uniform electric field on the frequencies of an adsorbed species. This is because it is not necessary to recalculate the normal coordinates at each value of the electric field. The method has been presented in connection to a cluster model representation of the surface, but it can be directly applied to periodical approaches without further modification. 

It therefore seems quite natural to choose silica, silica aluminas, and aluminium oxide as the objects of the first systematical quantum-chemical calculations. These compounds do not contain transition elements. They are built of the individual structural fragments primary, secondary, etc. This enables one to find the most suitable cluster models for quantum-chemical computations. The covalent nature of these structures again makes quite efficient a comparatively simple method of taking into account the boundary conditions in the cluster calculations. Finally, these systems demonstrate clearly defined Bronsted and Lewis acidity. This range of questions comprises the subject of the present review. This does not by any means imply that there are no quantum-chemical computations on the cluster models of the surface active sites of transition element oxides. It would be more proper to say that the few works of this type represent rather preliminary attempts, being far from systematic studies. Also, many of them unfortunately include some disputable points both in the statement of the problem and in the procedure of calculations. In our opinion, the situation is such that it is still unreasonable to try to summarize the results obtained, and therefore this matter is not reviewed in the present article. 

The first direct quantum-chemical calculations used too simplified cluster models, sometimes as simple as a single metal ion. Such an approximation is obviously too poor for chemisorption computations. Thus, comparative calculations by Sauer et al. (54) have shown, for instance, that the neglect of the environment of a cation may result in overestimating the interaction energy by several times. 

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). 

The overwhelming majority of the theoretical studies were performed on cluster models of the catalytic site, hi spite of the fact that the role of space confinement and the secondary interactions with the framework atoms is well-known, there are only a few electronic structure calculations on lattice models involving hydrocarbons, using either periodic DFT calculations, or embedding methods. In this brief account of the subject we attempt to overview some of the recent computational results of the literature and present some new data obtained from ab initio DFT pseudopotential plane wave calculations on Cl - C4 alkanes in the chabazite framework. 

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