Periodic electronic structures

The periodic electronic structure calculations methods constitute the other available approach." These methods require a relative high computational effort, beside progress in computer power allows calculations on systems of size of interest." The advantage of periodic approach method is that the entire... 

We will give further details about the periodic electronic structure calculations method as we will use results obtained with this method to support the discussion. First, we will describe how cluster approach can be used to investigate reactions catalyzed by acidic zeolites. Next, periodic electronic stmcture calculations will be used to enlighten the effects of the approximations of the cluster approach. These approximations relate mainly with the missing description of the zeolite framework contributions on the molecules involved in the reactions. Finally, by increasing the size of the aromatics involved in the isomerization reactions, we will show how steric constraints affect the course of a reaction. 

One way of introducing the interactions with more distant solvent molecules is to use a supercell approach (see, e.g., ref. 1). Then, a finite system including the solute and a smaller number of solvent molecules is repeated periodically in all three directions. Due to the periodicity, electronic-structure calculations can be carried through, but the drawback is that also the solute is repeated periodically. This means that if the repeated unit is too small, interactions between the solute molecules become non-negligible and may affect the results. 

The DFT energies of the reaction on a 4T zeolite cluster are compared with the periodical electronic structure results for chabazite. 

Embedded or periodical calculations are essential to compute these effects properly. A recent study of alkylation of toluene using a DFT periodical electronic structure code demonstrated the feasibility of this approach [131]. We illustrate here how Eq. (13) can be used to compute corrections to the activation energy from the cluster approach by adding the repulsive interaction that results from the formation of bulky intermediates. We use as an example the bimolecular hydride transfer reaction. The activation energy of the corresponding elementary rate constant can then be written... 

Willock and co-workers (434) recently published a detailed review of periodic electronic structure calculations applied to the oxide systems of catalytic... 

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