Zeolites cluster calculations

We used DFT to optimize the geometries of various Hammett bases on cluster models of zeolite Brpnsted sites. For p-fluoronitrobenzene and p-nitrotoluene, two indicators with strengths of ca. -12 for their conjugate acids, we saw no protonation in the energy minimized structures. Similar calculations using the much more strongly basic aniline andogs of these molecules demonstrated proton transfer from the zeolite cluster to the base. We carried out F and experimental NMR studies of these same Hammett indicators adsorbed into zeolites HY and HZSM-5. 

Quantum Chemical Calculations on the Electronic Structure of Zeolite Clusters... 

Not all quantum chemical calculations on zeolite clusters involve necessarily millions of integrations, and in the case of iso-electronic chemical systems fulfilling certain geometrical criteria, almost trivial back-of-an-envelope type calculations can yield rigorous upper and lower energy bounds. Fortunately, some zeolite structural units fulfill these geometric criteria. 

At the time of their inception, cluster calculations of adsorbate-zeolite systems were largely treated by using a semiempirical method. In the mid-... 

In addition to the cluster calculations, we report details of recent first-principles calculations based on the density functional formalism. These calculations employ periodic boundary conditions to allow investigation of the entire zeolite lattice, and therefore the use of a plane-wave basis set is applicable. This has a number of advantages, most notably that the absence of atom-centered basis functions results in no basis set superposition error (BSSE) (272), which arises as a result of the finite nature of atom-centered basis sets. Nonlocal, or gradient, corrections are applicable also, just as they are in the cluster calculations. 

The question of methanol protonation was revisited by Shah et al. (237, 238), who used first-principles calculations to study the adsorption of methanol in chabazite and sodalite. The computational demands of this technique are such that only the most symmetrical zeolite lattices are accessible at present, but this limitation is sure to change in the future. Pseudopotentials were used to model the core electrons, verified by reproduction of the lattice parameter of a-quartz and the gas-phase geometry of methanol. In chabazite, methanol was found to be adsorbed in the 8-ring channel of the structure. The optimized structure corresponds to the ion-paired complex, previously designated as a saddle point on the basis of cluster calculations. No stable minimum was found corresponding to the neutral complex. Shah et al. (237) concluded that any barrier to protonation is more than compensated for by the electrostatic potential within the 8-ring. 

Dehydrogenation of methane on a zeolite cluster has also been proposed to proceed via interaction of a CH fragment with the deprotonated zeolite lattice. DFT calculations performed with a 3T-atom cluster (248) and HF calculations with a lT-atom cluster (254) gave very similar results. The calculated transition state determined from the DFT calculations (248) that leads to dehydrogenation is shown in Fig. 17. 

The use of zeolite clusters in quantum chemical calculations has now progressed to quite a sophisticated level. Elementary steps of reaction mechanisms can now be characterized and the results used to distinguish which steps are the most plausible. Computational power is such that clusters and methods can avoid obvious pitfalls (too small a cluster, basis set, etc.). Several key concepts that have arisen from theoretical studies are illustrated in the preceding discussion. These include the following carbo-cations exist as parts of transition state structures, rather than as stable intermediates, and their stabilization is controlled by the zeolite lattice. The transition states are very different from the ground states to either side of them, and each different reaction has been shown to proceed via a different transition state. 

Figure 5.8. Calculated transition state geometry for H—D exchange between a zeolite cluster and methane.

Pople s CNDO/2 method and a hexagonal cluster model used in calculations to simulate charge densities Wiberg bond orders of Al - O and Si - O in the six - ring sites and the total energies of the zeolite clusters. 

The cluster calculations for Li+, Na+, and K+ ions in six-membered windows (S,. and Sn sites) were performed by Beran (104). It was concluded that in this series the properties of a zeolite framework (charge distribution, bond orders, Lewis acidity or basicity as characterized by LUMO and HOMO energies) only slightly depend on the type of cation. The decrease of water adsorption heats in this sequence was explained by the assumption that the strength of the water-cation interaction correlates with the strength of the interaction between a cation and lattice oxygen atoms. 

Another important zeolite-catalyzed chemical reaction is the decomposition of NO. Cu-exchanged zeolites, especially Cu-ZSM-5, have been shown to catalyze the decomposition of NO in the presence of hydrocarbons and excess oxygen. The increasing awareness of the detrimental effects of automobile exhaust has prompted several theoretical studies on the active site and reaction mechanism. ° Cu-ZSM-5 was described using an empirical force field and energy minimization to locate the copper ions in ZSM-5. Isolated copper atoms and copper clusters were found in the micropores, mostly associated with framework aluminium species. A cluster of two copper ions bridged via an OH species not part of the zeolite framework ( extra-framework ) was proposed as the active site. Quantum mechanical cluster calculations were carried out to study the elementary steps in the NO decomposition. A single T-site model was used to represent the zeolite framework. 

The discussion of reactivity focused on the activation of hydrocarbons by zeolitic protons. The deprotonation energy of a proton is weakly dependent on the zeolite crystallographic position but may be strongly zeolite composition dependent, especially at high concentrations of three valent cations (Al, Ga) in the zeolite framework. Nonetheless, the deprotonation energy is a local property of the OH bond, which can be estimated using quantum-chemical calculations by extrapolation from properly terminated cluster calculations. 

The elementary rate constant for proton activation is weakly dependent on the micropore size as long as steric constraints do not affect the transition state. Because of the zwitterionic nature of the transition state, dielectric screening by the oxygen atoms of the micropore tends to decrease the cluster-calculated transition state energies to 10 to 30% of the activation energies. Steric constraints on the transition state may substantially increase the cluster-computed activation energies by similar amounts. These steric constraints can be computed from periodical DFT calculations or from transition-state model structures using Monte Carlo adsorbate-zeolite pore interaction calculations. 

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