Cluster and Periodic Calculations of the Ethene Protonation Reaction Catalyzed by theta-1 Zeolite: Influence of Method, Model Size, and Structural Constraints
The protonation of ethene by three different acid sites of theta-1 zeolite was theoretically studied to analyze the extent and relevance of the following aspects of heterogeneous catalysis: the local geometry of the Bronsted acid site in a particular zeolite, the size of the cluster used to model the catalyst, the degree of geometry relaxation around the active site, and the effects related to medium- and long-range interactions between the reaction site and its environment. It has been found that while the reaction energy is very sensitive to the local geometry of the site, the activation energy is mainly affected by the methodology used and by electrostatic effects on account of the carbo…
A simple proof for the formula to get symmetrized powers of group representations
A general formula to decompose the p-power of irreducible representations of an arbitrary space group into sum of sets of irreducible representations of such a group, having identical permutational symmetry, is presented. Its proof is based upon a straightforward application of the properties of the generalized projection (shift) operators. © 1993 John Wiley & Sons, Inc.
Atoms and molecules in cavities: A method for study of spatial confinement effects
A general method for solving the problems of spatially confined quantum mechanical systems is proposed. The method works within the framework of the model space approximation. In the case of atoms and molecules trapped into any-shape microscopic cavity (like molecular sieves or fullerenes), the method reduces to a simple modification of the commonly used basis-set quantum chemical calculations. The modification consists of a particular rotation and projection in the model space, leading to solutions better adapted to the boundary conditions of the spatial confinement than the functions that describe the free systems. To illustrate how this method works, it has been applied to the hydrogen a…
Orbital-controlled reactions catalysed by zeolites: Electrophilic alkylation of aromatics
The role of orbital control in product selectivity during electrophilic aromatic alkylation catalysed by zeolites was studied both theoretically and experimentally. In order to discuss this, the alkylation of toluene and m-xylene by methanol was carried out on a series of large-pore zeolites (HY). The changes in the para to ortho ratio observed on changing the framework Si/Al ratio of the zeolites were related to ab initio molecular orbital calculations of the LUMO energy of structurally alike model clusters but containing different tetrahedral cations around the active site. The observed correlation is discussed in terms of the HSAB principle by taking into account the influence of the cat…