Zeolites parameterization

Hope et al. (116) presented a combined volumetric sorption and theoretical study of the sorption of Kr in silicalite. The theoretical calculation was based on a potential model related to that of Sanders et al. (117), which includes electrostatic terms and a simple bond-bending formalism for the portion of the framework (120 atoms) that is allowed to relax during the simulations. In contrast to the potential developed by Sanders et al., these calculations employed hard, unpolarizable oxygen ions. Polarizability was, however, included in the description of the Kr atoms. Intermolecular potential terms accounting for the interaction of Kr atoms with the zeolite oxygen atoms were derived from fitting experimental results characterizing the interatomic potentials of rare gas mixtures. In contrast to the situation for hydrocarbons, there are few direct empirical data to aid parameterization, but the use of Ne-Kr potentials is reasonable, because Ne is isoelectronic with O2-. 

We first consider the parameterization of the enthalpy changes of adsorption. It has been established that the heats of adsorption of various paraffins in zeolites vary linearly with carbon number (124-126). Therefore, we define the enthalpy of formation for a surface species as... 

Many of the earlier computations of thermodynamic parameters associated with hydrocarbon adsorption into zeolites entailed development of interatomic potentials so as to fit reasonably with one particular set of experimental data. As a result, although the correspondence between simulation and experiment was often reasonable [102], the transferability of the potential set from one zeolite composition to ano er or from one type of simulation to another was poor. In principle, if the parameterization truly describes the fundamental physics in an approximate way, it should be viable to develop a more generally applicable set of potentials. 

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. 

Kramer and co-workers used ab initio calculations of H4TO4 (T = Si, Al, P) clusters to derive parameters for the rigid ion potential model. The potential energy surface of the clusters was scanned along two modes of distortion, and the resulting potential curves were fitted using Eq. [15]. The set of parameters was refined by the use of experimental data on a-quartz. This procedure resulted in a parameterization that well reproduced both structure and elastic moduli of silicates, aluminosilicates, and aluminophosphates. Subsequently, this approach was extended to protonated forms of zeolites. ... 

In an additional refinement, Schroder and Sauer carried out a parameterization of the shell model on the basis of ab initio data. This model turned out to be more flexible than the MM force field in the description of the structure of the H-forms of zeolites. In addition, the authors note that the vibrational spectra are substantially better simulated with the ab initio shell model potential than with the ab initio MM force fields. 

The next problem to investigate was whether the cationic positions could also be determined in zeolite A and faujasites by semiempirical methods. From this aspect the MNDO method is the best choice, since most of alkali and alkaline earth elements are parameterized within this approximation. 

An example of molecular model parameterization Benzene In NaX zeolite... 

Snyder, M.A. Vlachos, D.G. Rational, hierarchical parameterization of complex zeolite-guest molecular models. Mol.Sim. 2004, 30, 561-577. 

What is the simplest adsorption model that can adequately define sorption in the system of interest for purposes of our study The simpler the model, the less information is needed to parameterize it. The distribution coefficient model requires only entry of the mass of sorbent in contact with a volume of water and a value for K,. Pesticide adsorption can often be modeled adequately using a simple K ) approach (cf. Lyman et al. 1982). For smectite and ver-miculite clays and zeolites that have dominantly pH-independent surface charge, ion-exchange or power-exchange models may accurately reproduce adsorption of the alkaline earths and alkali metals. If the system of interest experiences a wide range of pH and solution concentrations, and adsorption is of multivalent species by metal oxyhydroxides, then an electrostatic model may be most appropriate. 

Quantum chemical calculations on metal clusters in zeolite A [12] and semi-empirical ligand field interpretations of spectroscopic data of transition metal ions [6] have proven to be successful in structural characterizations of molecular sieves and their guest species. The present tendency in catalysis towards a more fundamental approach justifies the expectation that ESR, combined with other spectroscopic techniques, will become important. However, this requires an accurate and unambiguous parameterization of the ESR spectra. The parameter set thus obtained forms a firm basis for a theoretical investigation of the coordination environment of the paramagnetic entity. 

The range and the order of stability computed with a local AE basis set are in good agreement with the experimental measurements available, particularly as concerns the B3LYP results (third row in Table 10). Also the G(B3LYP) parameterization of the semiclassical method provides results that are in reasonably good agreement with the experimental evidence. However, the ab initio approach is still to be preferred in the case of more complicated systems, such as Ti-substituted zeolites, for example, where the parameterization procedure may become critical. 

Figure 4 provides a flowchart for the derivation of a molecular mechanics force field for zeolites. This example flowchart illustrates the way force field parameters can be obtained and how a suitably parameterized force field can be used to predict properties that are not directly accessible to ah initio calcula-tions. To illustrate this procedure with a specific example, we consider the derivation of the CFF force field for zeolites described in Refs. 84 and 85. 

Figure 4 Derivation of a molecular mechanics force field for zeolites. Whereas ab initio calculations cannot directly compute the desired properties of zeolites themselves, these calculations can be done on smaller, representative models of the zeolite for force field parameterization which, in turn, can be used to compute those properties.

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