Lattice energy, minimizing

As molecular packing calculations involve just simple lattice energy minimizations another set of tests have focused on the finite temperature effects. For this purpose, Sorescu et al. [112] have performed isothermal-isobaric Monte Carlo and molecular dynamics simulations in the temperature range 4.2-325 K, at ambient pressure. It was found that the calculated crystal structures at 300 K were in outstanding agreement with experiment within 2% for lattice dimensions and almost no rotational and translational disorder of the molecules in the unit cell. Moreover, the space group symmetry was maintained throughout the simulations. Finally, the calculated expansion coefficients were determined to be in reasonable accord with experiment. 

Numerous organic species are known to lead to the crystallization of the MFI-type structure (7). but the tetrapropylammonium cations can be considered to be the most specific. To our knowledge no thermodynamic data such as standard formation enthalpies (AfH°) and stabilization energies attributed to the organic species have been published to corroborate this experimental observation. The published thermodynamic data (AfG°, AfH°, AfS°. Cp) are for natural zeolites (8-11) or for organic-free synthetic zeolites. However. some data have been obtained by calculations using lattice energy minimization and extended Hiickel theory (1 2) or by semi-empirical methods based on addition of the thermodynamic functions of the oxide compo-... 

Since this approach does not account for long-range electrostatic potentials present in the extended material, the second approach chosen was the rigid-ion lattice energy minimization technique, widely used in solid-state chemistry. This method is based on the use of electrostatic potentials, as well as Born repulsion and bond-bending potentials parametrized such that computed atom—atom distances and angles and other material properties, such as, for instance, elastic constants, are well reproduced for related materials. In our case, parameters were chosen to fit a-quartz. 

Results of Lattice Energy Minimization Calculations. Relative lattice energies of faujasite, mordenite, silicalite and sodalite were compared. For the framework and cation positions of faujasite and sodalite the same data were used as before, from Hseu (18) and Olson (19), and Baerlocher (20) and Chao (21), respectively. For mordenite and sodalite the data of Meier (22) and Mortier (23 ) (on mordenite) and Baerlocher and Meier (24) (on sodalite) were used. 

Figure 3 Illustrations of feasible uninodal zeolite structures generated by thing theory and modelled using lattice energy minimization...

Day GM, Chisholm J, Shan N, Motherwell WDS, and Jones W. An Assessment of Lattice Energy Minimization for the Prediction of Molecular Organic Crystal Structures. Cryst Growth Des 200, 4 1327-1340. 

The first stage of any lattice simulation is to equilibrate the structure, i.e. bring it to a state of mechanical equilibrum. The simplest procedure is to equilibrate under conditions of constant volume, i.e. with invariant cell dimensions. Extensions to the procedure were introduced by Parker (1982, 1983) who introduced the use of constant pressure minimization in the computer code METAPOCS, in which lattice energy minimization was performed with respect... 

Figure 9.4 Minimum energy distributions of (a) Na+ and (b) K+ in ETS-10. In each case both the framework and cation position were optimized by lattice energy minimization.

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