Shell model potentials

Flarrison NM, Leslie M (1992) The derivation of shell model potentials for MgCL from ab initio theory. Mol Simul 9 171-174... 

Dynamics Simulation of MgO Surfaces in Liquid Water Using a Shell-Model Potential for Water. 

Dynamics Simulations of Water with Novel Shell-Model Potentials. 

Simulation of Superionic UO2 Using Shell-Model Potentials. 

For metals and ceramics considered separately, reliable interaction potentials have been developed in the past. For many metals, embedded-atom-type potentials ° have proven successful. Alternatives and refinements have been developed.For ceramics, rigid-ion and shell model potentials and their refinements " have proven equally capable. 

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. 

K. de Boer, A. R J. Jansen, and R. A. van Santen, in Zeolites and Related Microporous Materials State of the Art 1994, J. Weitkamp, H. G. Karge, H. Pfeifer, and W. Holderich, Eds., Elsevier Science Publishers, Amsterdam, 1994, pp. 2083-2087. Interatomic Potentials for Zeolites. Derivation of an Ab Initio Shell Model Potential. 

The highly ionic nature of MgO means that quite accurate empirical potentials can be constmcted. The polarizable shell model potential is the most widely used for MgO and also for a wide range of other ionic materials. It is instmctive to discuss the main elements of this potential in order to understand the nature of interactions between the ions. The dominating contribution to the interaction is electrostatic and in the simplest approximation can be represented by associating a point charge (usually the formal charge) with each ion. In addition there is a short-range repulsive term due to the overlap of electron density between the ions (Born-Mayer) and a weakly attractive... 

Figure 11. Density of vibrational frequencies of calcite, computed by the RIM (rigid-ion-model) potential (above), by the SM (shell model) potential and by Kieffer s model (below, thick and thin lines, respectively).

Characteristics Ion Pair and Shell Model Potentials Molecular Mechanics Potentials... 

Tables 4-12 contain the results of lattice energy minimizations for several dense silica modifications and some microporous solids. These tables are divided into two parts the upper part contains results for ion pair potentials (including shell model potentials), and the lower part gives results for molecular mechanics potentials.Note that the results in these tables reflect the fact...

Tables 8-11 list results for some commonly studied zeolites. Faujasite and silicalite are industrially important catalysts when they contain aluminum. The structural features of sodalite are predicted best by both Jackson and Catlow s potentiaPS and Schroder s empirical force field. a pgr faujasite, all force fields are similar in their ability to predict the observed unit cell dimensions, whereas the best for mordenite and silicalite is Sierka and Sauer s potential, which consistently reproduces unit cells both for dense and microporous silica. In general, shell model potentials provide slightly better structural agreement with experiment for zeolites than do ion pair potentials and molecular mechanics force fields.

It is instructive to compare the performance of empirically derived force fields with those potentials derived from quantum mechanical calculations. Sierka and Sauer <> compared results from Jackson and Catlow s empirical shell model potential with Schroder and Sauer s Hartree-Fock based and their own density functional based shell model potentials. The mean deviation between computed and observed unit cell parameters was found to be 0.7%, 1.9%, and 1.4%, respectively, for the three potentials. This means that the empirical shell model potential is twice as accurate as the best quantum chemically derived force field for unit cell predictions. However, the calculated vibrational spectra of silicalite are in good agreement with experiment for both of the quantum chemically derived potentials,whereas agreement is not as satisfactory for the empirical force field. ... 

Similar results were found for these hydroxyl groups when shell model potentials derived from ab initio and density functional calculations were used. Table 15 includes results obtained when using Schroder and Sauer s Hartree-3Fock based potential as well as for Sierka and Sauer s density functional based potential. ... 

Table 15 Relative Energies A and OH Harmonic Stretching Frequencies Vq of the Bridging Hydroxyl Group in Faujasite from Shell Model Potentials...

Generally, force fields available for the study of dense silica polymorphs and zeolites can also be used to obtain reliable structures and vibrational spectra for the frameworks of these materials. In the past it seemed necessary to use molecular mechanics force fields to be able to predict vibrational spectra correctly, but it was shown several years ago that shell model potentials also have this capability. 0 175 Shell model potentials, therefore, seem to be the best-suited force fields for silica polymorphs. These potentials model the more ionic character of the SiO bond, include polarization, allow coordination changes, and contain only a few adjustable parameters. Molecular mechanics potentials have value in molecular dynamics calculations and allow for easier extension with respect to studying the adsorption behavior of organic sorbates in zeolites, whereas the use of shell model potentials is cumbersome. 

In this chapter we have shown how force fields can be utilized in materials science applications. There are similarities between force fields used in life science and in materials science. Owing to the variety of molecules studied in materials science, however, there are several complementary approaches to modeling such systems. Molecular mechanics force fields as used in life science (i.e., in biomolecules) can also be applied to organic materials such as polymers or liquid crystals. Ionic materials such as oxides are better described by means of ion pair or shell model potentials. For some systems with ionic as well as covalent character in their bonds (e.g, zeolites), both approaches are feasible. 

Ion pair and shell model potentials are in general computationally simpler than molecular mechanics force fields because the former have simple functional forms and use relatively few parameters. The accuracy of these potentials may, however, be limited, especially for the detailed simulation of vibrational spectra. The use of ab initio data for the construction and parameterization of a... 

M C. Wojcik and K. Hermansson, Chem. Phys. Lett., 289,211 (1998). The Problem of the Detaching Shell in the Shell Model Potential for Oxides. 

M. Sierka and J. Sauer, Faraday Discuss, 106, 41 (1997). Structure and Reactivity of Silica and Zeolite Catalysts by a Combined Quantum Mechanics-Shell-Model Potential Approach Based on DFT. 

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