Quantum mechanics zeolite

PALS is based on the injection of positrons into investigated sample and measurement of their lifetimes before annihilation with the electrons in the sample. After entering the sample, positron thermalizes in very short time, approx. 10"12 s, and in process of diffusion it can either directly annihilate with an electron in the sample or form positronium (para-positronium, p-Ps or orto-positronium, o-Ps, with vacuum lifetimes of 125 ps and 142 ns, respectively) if available space permits. In the porous materials, such as zeolites or their gel precursors, ort/zo-positronium can be localized in the pore and have interactions with the electrons on the pore surface leading to annihilation in two gamma rays in pick-off process, with the lifetime which depends on the pore size. In the simple quantum mechanical model of spherical holes, developed by Tao and Eldrup [18,19], these pick-off lifetimes, up to approx. 10 ns, can be connected with the hole size by the relation ... 

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 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 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 notable exception are chemisorbed complexes in zeolites, which have been characterized both structurally and spectroscopically, and for which the interpretation of electronic spectra has met with a considerable success. The reason for the former is the well-defined, although complex, structure of the zeolite framework in which the cations are distributed among a few types of available sites the fortunate circumstance of the latter is that the interaction between the cations, which act as selective chemisorption centers, and the zeolite framework is primarily only electrostatic. The theory that applies for this case is the ligand field theory of the ion-molecule complexes usually placed in trigonal fields of the zeolite cation sites (29). Quantum mechanical exchange interactions with the zeolite framework are justifiably neglected except for very small effects in resonance energy transfer (J30). ... 

Molecular-dynamic simulations are characterized by a solution of Newton s laws of motion for the molecules travelling through the zeolite pore system under control of the force field given by the properties of the host lattice, by interactions between the host and the molecules, and by interactions between the molecules. To date this has been possible only for the diffusion of simple molecules (e.g. methane or benzene) inside a zeolite lattice of limited dimensions [29, 37, 54], To take into account the effects of a chemical reaction as well would require quantum-mechanical considerations however, such simulations are in their infancy. 

A way to describe the zeolite framework at a low computational cost is to use quantum mechanic - molecular mechanic methods (QM/MM) (see Figure 6). With QM/MM, only the site of interest (viz. reactants and catalytic active site) are treated at a quantum mechanic level, whereas the zeolite framework is described using force field equations of molecular mechanic." ... 

Abstract The chemical activation of light alkanes by acidic zeolites was studied by a combined Classical Mechanics/Quantum Mechanics approach. The diffusion and adsorption steps were investigated by Molecular Mechanics, Molecular Dynamics and Monte Carlo simulations. The chemical reactions step was studied at the DPT (B3LYP) level with 6-31IG basis sets and 3T and 5T clusters to represent the acid site ofthe zeolite. 

In principle, the diffusion steps (a) and (e) could be studied through molecular dynamics simulations as long as rehable forces fields are available to describe the zeolite structure and its interaction with the substrates. Also, if the adsorption takes place without charge transfer between the reagents/products and the zeolite, steps (b) and (d) could also be investigated either by molecular dynamics or Monte Carlo simulations. Step (c) however can only be followed by quantum mechanical techniques because the available force fields cannot yet describe the breaking and formation of chemical bonds. 

Among the chemical reactions of interest catalyzed by zeolites, those involving alkanes are specially important from the technological point of view. Thus, some alkane molecules were selected and a systematic study was conducted, on the various steps of the process (diffusion, adsorption and chemical reaction), in order to develop adequate methodologies to investigate such catalytic reactions. Linear alkanes, from methane to n-butane, as well as isobutane and neopentane, chosen as prototypes for branched alkanes, were considered in the diffusion and adsorption studies. Since the chemical step requires the use of the more time demanding quantum-mechanical techniques, only methane, ethane, propane and isobutane were considered. 

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. 

The diffusion, adsorption and chemical steps for the dehydrogenation and cracking reactions of light alkanes catalyzed by zeolites were studied using a combined classical mechanics (MM, MD and MC) / quantum mechanics approach. 

The quantum mechanical and molecular mechanics methods used are those we have discussed earlier molecular mechanics in the case of ionic solids and zeolites generally meaning the use of interatomic potential methods. The art of QM/MM is how to deal with the boundary of the two regions. One method used for ionic materials is to have a boundary region which features in both the quantum mechanical and molecular mechanics calculations. The addition boundary scheme... 

The main result of extensive simulations of A1 placement in the FAU-framework topology is that random insertion of A1 into the structure, subject to Loewenstein s rule and to a weaker second neighbor Al-Al repulsion term, does not reproduce the measured Si-nAl distribution patterns [4]. The details of the aluminum distributions are therefore determined by additional or different factors. This is consistent with Melchior s model of FAU-framework construction from pre-formed 6-iing units [47,48], The simulation results also highlight the likely limitations of quantum mechanical studies of aluminum T-site preferences. If the factors controlling the aluminum distributions in zeolites X and Y are also at work in other systems, purely energetic arguments will likely have limited direct relevance for application to real materials. 

First principles approaches are important as they avoid many of the pitfalls associated with using parameterized descriptions of the interatomic interactions. Additionally, simulation of chemical reactivity, reactions and reaction kinetics really requires electronic structure calculations [108]. However, such calculations were traditionally limited in applicability to rather simplistic models. Developments in density functional theory are now broadening the scope of what is viable. Car-Parrinello first principles molecular dynamics are now being applied to real zeolite models [109,110], and the combined use of classical and quantum mechanical methods allows quantum chemical methods to be applied to cluster models embedded in a simpler description of the zeoUte cluster environment [105,111]. 

Although there are many ways to describe a zeolite system, models are based either on classical mechanics, quantum mechanics, or a mixture of classical and quantum mechanics. Classical models employ parameterized interatomic potentials, so-called force fields, to describe the energies and forces acting in a system. Classical models have been shownto be able to describe accurately the structure and dynamics of zeolites, and they have also been employed to study aspects of adsorption in zeolites, including the interaction between adsorbates and the zeolite framework, adsorption sites, and diffusion of adsorbates. The forming and breaking of bonds, however, cannot be studied with classical models. In studies on zeolite-catalyzed chemical reactions, therefore, a quantum mechanical description is typically employed where the electronic structure of the atoms in the system is taken into account explicitly. 

Conventional methods based on quantum mechanical models use matrix diagonalization to find a self-consistent solution of the time-independent Schrodinger equation. Unfortunately, the cost of matrix diagonalization grows extremely rapidly with the number of atoms in the system. Consequently, methods based on quantum mechanical models tend to be computationally expensive. As a result, the zeolite framework is often treated as a cluster instead of as a periodical system. To overcome this obstacle, hybrid models have been put forward in which the problem is circumvented the reaction center is described in a quantum mechanical way, whereas the surroundings are described in a classical way. ... 

Quantum mechanical approaches using a cluster approximation have been used extensively to determine proton affinities.The influence of the local composition on the structure and proton affinity of a zeolite was studied... 

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 choice of a theoretical model usually depends on the goals of the study, but sometimes other considerations, such as computer resources available, can also play a role in this selection process. A study of zeolite framework acidity or catalytic activity requires an explicit consideration of the electronic structure of the system, and quantum mechanical (QM) models are best suited for such investigations. Since the high CPU demands greatly limit the size of the systems that can be simulated with quantum mechanical models, the zeolite framework is often represented in these simulations by a cluster that presumably resembles the active site. The cluster approximation has the obvious drawback that influences of the crystal lattice are neglected. 

R. Millini, G. Perego, and K. Seiti, Stud. Surf. Sci. Catal., 84,2123 (1994). Ti Substitution in MFI Type Zeolites A Quantum Mechanical Study. 

U. Eichler, M. Brandle, and J. Sauer, J. Phys. Chem., 101,10035 (1997). Predicting Absolute and Site-Specific Acidities for Zeolite Catalysts by a Combined Quantum Mechanics/ Interatomic Potential Function Approach. 

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