Framework density, classification

The classification is shown in an abbreviated form in Table III with an example to illustrate each group. Included is information on the void fraction, expressed as cc per cc of dehydrated zeolite as derived from the water content for the fully hydrated zeolite, the framework density expressed in grams/cc, the approximate dimensions of the main channels (as derived from the structure of the hydrated zeolite), and the type of channel system, 1 for one-dimensional, etc. In many instances, of course, the dimensions of the apertures change substantially with dehydration. Consequently, the aperture dimensions are not necessarily consistent with the adsorption properties of the dehydrated zeolite. We need considerable information on the structures of dehydrated zeolites. In such a... 

Semiempirical approaches to quantum chemistry are thus characterized by the use of empirical parameters in a quantum mechanical framework. In this sense, many current methods contain semiempirical features. For example, some high-level at initio treatments of thermochemistry employ empirical corrections for high-order correlation effects, and several advanced density functionals include a substantial number of empirical parameters that are fitted against experimental data. We shall not cover such approaches here, but follow the conventional classification by considering only semiempirical methods that are based on molecular orbital (MO) theory and make use of integral approximations and parameters already at the MO level. 

The surfaces of zeolites ean thus display Brpnsted or Lewis acid sites or a combination of the two, depending on how the zeolite is prepared. Brpnsted acid sites are converted into Lewis acid sites as the temperature is increased above approximately 500°C and water is driven off The overall catalytic activity of zeolites as solid acids depends on the number and the properties of the acid site. The strength of the acid sites is directly related to the framework composition of the zeolite. Zeolites with low Si/Al ratios can have higher concentrations of catalytic sites, and zeolites with high Si/Al ratios show strong acidity. Their classifications are shown in Table 2. An H-Y or H-ZSM-5 zeolite with a low density of acid groups is like an ideal solution of dispersed noninteracting protons in a solid matrix. 

As already stated, density methods are designed to be used in the framework of probability theory and, in particular, of the Bayes theorem described in Equation (1). Therefore, classification of unknown objects is carried out on the basis of the posterior probabilities that a sample belongs to the different categories. Accordingly, by combining Equations (51) and (1) and making the normalization factor in Equation (1) explicit, the posterior probability... 

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