Quantum mechanical calculations zeolites

The major effect of new advanced techniques on catalyst structure is found in zeolite catalysis. NMR techniques, especially MASNMR, have helped to explain aluminum distribution in zeolites and to increase our understanding of critical parameters in zeolite synthesis and crystallization. MASNMR, combined with TEM, STEM, XPS, and diagnostic catalytic reaction probes, has advanced our knowledge of the critical relationship between the structure and reactivity patterns of zeolites in the chemical fuels industry. Throughout the symposium upon which this book is based, many correlations were evident between theoretical quantum mechanical calculations and the structures elucidated by these techniques. 

The Future and Impact of Quantum Mechanical Calculations in the Description and Characterization of Zeolites... 

Two methods for including explicit electrostatic interactions are proposed. In the first, and more difficult approach, one would need to conduct extensive quantum mechanical calculations of the potential energy variation between a model surface and one adjacent water molecule using thousands of different geometrical orientations. This approach has been used in a limited fashion to study the interaction potential between water and surface Si-OH groups on aluminosilicates, silicates and zeolites (37-39). 

The zeolite matrix allows the preparation of dispersions with distinctly different and narrow particle size distributions in a range where size dependent electronic properties can be studied (quantum size particles). Quantum-mechanical calculations suggest that the energy level of the first excited state of the exciton increases with decreasing particle size of the semiconductors in correspondence with the experimentally observed blue-shift of the optical absorption edge (refs. 8-10). 

In summary, a high diversity of potential models for molecular mechanics calculations of zeolites hitherto exists. From the theoretical point of view, an appropriate force field should be able to predict structures and vibrations with similar accuracy. On the other hand, the structure of a system under study is determined by the energy minimum, whereas normal modes are dependent on the curvature (second derivative) of the potential energy surface. Consequently, force fields obviously successful in predicting structural features might not automatically be appropriate for simulating vibrational spectra. The only way to overcome this difficulty is to include experimental spectroscopic data into the parametrization process [60]. Alternatively, besides structures and energies a matrix of force constants obtained in quantum mechanical calculations can be included into the quantum mechanical data base used to tune the parameters of the potential function [51]. 

Later on, the hypothesis of H3O+ formation was questioned, since ab-initio quantum mechanical calculations by Krossner and Sauer [655] on H2O adsorbed on zeolitic [sSi-(OH)-Al=] groups have shown that an (unsolvated) hydroxo-nium ion H3O+ would not be a stable entity (cf. also [656]). Rather, on the respective potential energy surface (PES) an H3O+ ion would be located on a saddle... 

The interpretation of the above IR results of the H20/zeolite system was supported by inelastic neutron scattering (INS) studies by Jobic et al. [658] of H2O adsorbed on hydrogen mordenite. These experiments were carried out in the range below 2000 cm. Activated and water-free H-mordenite gave INS bands at 320 and 1060 cm. On the basis of quantum mechanical calculations, these were assigned to the out-of-plane (yoh) and in-plane (6oh) deformation vibrations of the zeolitic OH groups, since these were predicted at 322 and 1047 cm". On... 

In an attempt to model the chemistry of zeolites, both structural and the interactions with non-framework atoms, a number of different computational methods have been used or developed. In this section a description will be given of some of these methods, however in the case of more complex techniques, such as quantum mechanical calculations, direction will be given to the original references. 

The acidity of silica-aluminas is easily explained by Tanabe s model. Substitution of a Si atom by tetrahedral AI atom in a silica-rich host lattice generates AlOT units with a localized negative charge that may be balanced by a cation or a proton. There exists an extensive body of literature on quantum-mechanical calculations of acidity from the proton affinity of small clusters [88] that confirmed this picture [89] it was concluded that the 0 — Hiond weakens and the proton is more easily ionized if the hydroxyl is located in bridging positions between Al and Si atoms. A general discussion on the acidity concept in zeolites can be found in Refs, 21 and 90. 

The interatomic potentials define the force field parameters that contribute to the lattice energy of a relaxed or energy minimized structure. The fundamental question is how reliable is a force field The force field used in evaluating a potential function must be consistent and widely applicable to all similar systems. It must be able to predict the crystal properties as measured experimentally. Two main approaches, namely empirical and semi-empirical, are usually employed in the derivation of potential parameters. Empirical derivations involve a least square fitting routine where parameters are chosen such that the results achieve the best correlation with the observed properties. The semi-empirical approach uses an approximate formulation of the quantum mechanical calculations. An example of such an approximation is the electron gas method [57] which treats the electron density at any point as a uniform electron gas. The following is the analytical description of the potential energy function and interatomic potentials we recommend for use in simulation of zeolites and related system. 

From quantum mechanical calculations. By solving the Schrodinger equation using various approximations, we can obtain forces between different atoms and molecules. These forces can be fitted into a force field. This usually works very well for intra-molecular bonded interactions like bond-stretching, bond-bending, and torsion interactions, but less well for van der Waals interactions. Note that hydrocarbon-zeolite interactions are dominated by van der Waals interactions (see, for example, ref. [24] and chapter 4). Recently, there have been several quantum-mechanical studies of water and methanol in Sodalite [25,26] using the Car-Parrinello technique [27],... 

Since the discovery of alkylation, the elucidation of its mechanism has attracted great interest. The early findings are associated with Schmerling (17-19), who successfully applied a carbenium ion mechanism with a set of consecutive and simultaneous reaction steps to describe the observed reaction kinetics. Later, most of the mechanistic information about sulfuric acid-catalyzed processes was provided by Albright. Much less information is available about hydrofluoric acid as catalyst. In the following, a consolidated view of the alkylation mechanism is presented. Similarities and dissimilarities between zeolites as representatives of solid acid alkylation catalysts and HF and H2S04 as liquid catalysts are highlighted. Experimental results are compared with quantum-chemical calculations of the individual reaction steps in various media. 

The currently available quantum chemical computational methods and computer programs have not been utilized to their potential in elucidating the electronic origin of zeolite properties. As more and more physico-chemical methods are used successfully for the description and characterization of zeolites, (e.g. (42-45)), more questions will also arise where computational quantum chemistry may have a useful contribution towards the answer, e.g. in connection with combined approaches where zeolites and metal-metal bonded systems (e.g. (46,47)) are used in combination. The spectacular recent and projected future improvements in computer technology are bound to enlarge the scope of quantum chemical studies on zeolites. Detailed studies on optimum intercavity locations for a variety of molecules, and calculations on conformation analysis and reaction mechanism in zeolite cavities are among the promises what an extrapolation of current developments in computational quantum chemistry and computer technology holds out for zeolite chemistry. 

The previous two sections of this review deal with classical simulation methods. A description of the activation of adsorbates by acidic sites, together with any bond breaking or bond formation that may take place, is the realm of quantum mechanical (QM) simulations. These types of calculations are particularly well-suited to zeolite-adsorbate systems when the cluster approximation is used. The active acidic site in the zeolite is modeled by a molecular cluster, formed by cutting out a small portion of... 

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. 

The virial isotherm equation, which can represent experimental isotherm contours well, gives Henry s law at low pressures and provides a basis for obtaining the fundamental constants of sorption equilibria. A further step is to employ statistical and quantum mechanical procedures to calculate equilibrium constants and standard energies and entropies for comparison with those measured. In this direction moderate success has already been achieved in other systems, such as the gas hydrates 25, 26) and several gas-zeolite systems 14, 17, 18, 27). In the present work AS6 for krypton has been interpreted in terms of statistical thermodynamic models. 

A very high stereoselectivity was observed in the reduction of 4-tert-butylcyclohexanone to the m-alcohol (> 95%), which is the industrially relevant product. The observed high selectivity to the thermodynamically unfavorable cis-alcohol was explained by a restricted transition-state for the formation of the trans-alcohol within the pores of the zeolites (Scheme 5). This reaction was found not only to be catalysed by Al-Beta, van der Waal et al. reported the catalytic activity of aluminum-free zeolite titanium beta (Ti-Beta) in the same reaction.74 Again, a very high selectivity to the cis-alcohol was observed indicating similar steric restrictions on the mechanism. Kinetically restricted product distributions were also reported for the 2-,3- and 4-methylcyclohexanone the cis, trans- and ds-isomers being the major products, respectively. In this case the tetrahedrally coordinated Ti-atom was assumed to behave as the Lewis acid metal center. Recent quantum-chemical calculations on zeolite TS-1 and Ti-Beta confirm the higher Lewis acidic nature of the latter one.75... 

Contrary to the previous steps of the catalytic process, we cannot use force-field-based techniques because the available force fields are unable to describe the breaking and formation of chemical bonds. Thus, the chemical reaction step must be investigated by quantum mechanical techniques. Right away this imposes some limitations on the size of the cluster to be used in the calculations. In principle, since the catalytic sites are well localized within the zeolite framework, one should expect the chemical reactions to occur at very locahzed points of the zeoUtic structure. Thus, one could think of representing the acid sites by much smaller clusters than the ones used in the diffusion and adsorption studies. 

Theoretical modeling of the structure and reactivity of zeolitic materials, with special emphasis on the mechanism of catalytic reactions, has been the subject of several exhaustive review articles in the past decade. Theoretical approaches that have been used to describe such systems range from empirical molecular mechanics calculations to various ab initio methods as well as different variants of the mixed quantum/classical (QM/MM) algorithms. In the present contribution we focus our attention mainly on those studies which were accomplished by ab initio pseudopotential plane wave density functional methods that are able to treat three-dimensional periodic models of the zeolite catalysts. Where appropriate, we attempt a critical comparison of with other theoretical approaches. 

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