Potential energy calculations, zeolite

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). 

Auerbach et al. (101) used a variant of the TST model of diffusion to characterize the motion of benzene in NaY zeolite. The computational efficiency of this method, as already discussed for the diffusion of Xe in NaY zeolite (72), means that long-time-scale motions such as intercage jumps can be investigated. Auerbach et al. used a zeolite-hydrocarbon potential energy surface that they recently developed themselves. A Si/Al ratio of 3.0 was assumed and the potential parameters were fitted to reproduce crystallographic and thermodynamic data for the benzene-NaY zeolite system. The functional form of the potential was similar to all others, including a Lennard-Jones function to describe the short-range interactions and a Coulombic repulsion term calculated by Ewald summation. 

Hartree-Fock-level ab-initio calculations can provide reliable potential energy diagrams for small clusters. Such calculations can be applied to the zeolite lattice if the clusters are chosen carefully and use is made of the property that bonding is highly localized in these materials. Calculations were done using the GAMESS ab-initio package. 

The molecular field distribution within the channels must be investigated, taking into consideration the structure of the zeolite, and the calculation of the potential energy of interaction between the zeolite and particular molecules must be made. These investigations would be assisted greatly by spectroscopic studies which would make it possible to establish the nature of the zeolite surface, the presence and the nature of structural defects, and the state of the adsorbed molecules. 

Here, is the potential energy of ith molecule located at u inside the zeolite cavity interacting with the zeolite lattice — r l) is the potential energy of interaction of the ith and /th molecules located, respectively, at the points and In the calculations of Vi) = 1 (jr — r j),... 

Owing to the high symmetry of the lattice for the LiA and NaA zeolites, an analysis was made only of the section comprising 1/48 of the total cavity volume (Figure 9). The volume of the corresponding section for CaA zeolite was 1/24 of the total volume of the cavity. The potential energy was calculated for the inner cavity of the selected section for 16 different directions in the case of LiA and NaA zeolites and for 31 directions in the case of the CaA zeolite. For each of these directions, the (fi) was calculated for 40 different positions of the molecule. The lattice sums... 

The calculation of the potential energy of interaction of a long chain of n-alkanes with the zeolite CaA has been described (24). These results agree with the experimental values for the heat of adsorption. 

Figure 3. Force centers assumed in Model I for the calculation of the potential energy of interaction of the neopentane molecule with NaX zeolite site S// with the charged oxygen atoms (open circles) and cations (filled circles) are indicated...

Figure 4. Two orientations of a neopentane molecule with respect to site Sjj of type X zeolite which are assumed in the calculation of potential energy of adsorption...

Table III shoves the comparison of the calculated potential energy of neopentane on NaX zeolite with the experimental value of the heat of adsorption (O. M. Dzhigit, A. V. Kiselev, L. G. Ryabukhina, Zh. Fix. Khim. 1970, 44, 1790). Two models, 1 and II (Figure 3), of the distribution of the force centers in zeolite NaX and two orientations, (1) and (2), of the neopentane molecule at site Sn (Figure 4) were used. The calculations show that for approximate evaluation of potential energy, it is only necessary to take into consideration about 50 nearest charged oxygen atoms and 4 cations. In model II, the influence of other cations (which are situated in sites Sn of the supercage) were taken into consideration. The other cations, which are distributed more randomly, do not influence seriously the electrostatic fleld in the space occupied by the neopentane molecule near one of the Sn sites (calculations by L. G. Ryabukhina and A. A. Lopatkin).

In the present work, the values of Zi, Z, and for the systems Ar-NaA and CH4-CaA were calculated at a number of temperatures, and thus the corresponding coefBcients in Expansions 6 and 9 were obtained. The configuration integral, Z, was calculated by means of Equation 4. The potential energy, Ui r), was determined for the great number of positions of a molecule within the zeolite cavity. The details... 

The main advantages of MM force field models are that the terms in the potential energy representation correlate with the usual chemical intuition and that such models can easily be combined with force fields for modeling organic molecules. The latter permits the use of a consistent approach for calculation of sorbate-zeolite systems. A drawback is that a large number of parameters must be determined on the basis of either experimental information or quantum chemical calculations (or by a combination of both). 

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. ... 

Ab initio calcxilations of FTIR spectra confirmed [3] that both low-frequency OH bands can originate from the vibrations of OH of protonated acetone. On the other hand, the c alculation revealed that these bands can be caused also by the bending vibrations of zeolite bridging OHs H-bonded to acetone. However, the calculated energetics of the movement of the hydrogen between oxygens of the skeleton and the acetone carbonyl exhibited only one minimum on the potential energy surface, which implied the preferential formation of the "neutral" form [3]. 

The location of extra framework cations is a major problem in characterising zeolites. Simulation is becoming an increasingly powerful tool for the exploration and rationalisation of cation positions, since it not only allows atomic level models to be compared to bulk experimental behaviour, but can also make predictions about the behaviour of systems not readily accessible to experimental probing. In the first part of this work we use the Mott-Littleton method in conjunction with empirical potential energy functions to predict and explore the locations of calcium cations in chabazite. Subsequently, we have used periodic non-local density functional calculations to validate these results for some cases. 

Kebarle. " Recently, Mota et al. calculated the potential energy surface of the C3H9+ cation [MP4(SDTQ)/6-311++G /MP2(full)/6-31G level]).The C-proponium cation (43) was again found to be of lowest energy but the complex xec-C ilh + H2 lies only 0.3 kcal mol above structure 43. The C-H bond lengths in the 3c-2e interactions are 1.272 and 1.188 A, whereas the C-C bond distance is 2.099 A.They also found that the interconversion between the -H-protonated cation (45) and the C-proponium cation (43) has no energy barrier. This may indicate that on zeolites where steric effects are important the primary, that is more accessible hydrogens are protonated initially to yield the... 

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