Rigid ion potential

Equation [15] is often referred as a rigid ion potential model. 

Both the rigid ion and shell potential models have been used in energy minimization studies of dense and microporous silica and molecular sieves. Kramer and coworkers reported parameters of the rigid ion potential model for silicates, aluminosilicates, and aluminophosphates. The model also includes parameters for extra-framework cations such as Na and Cl . Both the rigid ion and shell models were used by Catlow and coworkers in modeling silicate and zeolite structures. ... 

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. ... 

Structural Monte Carlo simulations can explore significantly larger system sizes due to the fact that they only treat interatomic interactions with no focus on the electronic structure . The interatomic potentials that are necessary for structural simulations can be derived either from experiment or from rigorous QM methods. Potentials of choice for ionic systems are typically additive potentials such as the rigid ion potentials, that depend on charges, bond distances, and bond angle or shell model potentials that also contain terms that describe polarization. Potential parameters can be deduced by comparison with theory ] or experiment. 

A. Trlocca, Short- and medium-range stmcture of multicomponent bioactive glasses and melts an assessment of the performances of shell-model and rigid-ion potentials. J. Chem. Phys. 129, 084504 (2008)... 

Order-disorder-type ferroeiectrics where a discrete symmetry group is broken due to the ordering of the ions in a rigid lattice potential (e.g., KH2PO4). 

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. 

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. 

De Boer and coworkers ° °" parameterized the shell model for silica polymorphs on the results of ab initio calculations of the potential energy surfaces, polarizabilities, and dipole moments of Si(OH)4 and (0H)3Si-0(H)-Si(OH)3 clusters. The structural characteristics and elastic moduli calculated with this set of parameters for three structures compared well with results computed with the use of both the rigid ion and the empirical shell models. ... 

Computations of minimum-energy configurations for some off-centre systems were first carried out on the basis of polarizable rigid-ion models, mainly devoted to KChLi" " [95,167-169]. Van Winsum et al. [170] computed potential wells using a polarizable point-ion model and a simple shell model. Catlow et al. used a shell model with newly derived interionic potentials [171-174]. Hess used a deformation-dipole model with single-ion parameters [175]. At the best of our knowledge, only very limited ab initio calculations (mainly Hartree-Fock or pair potential) have been performed on these systems [176,177]. 

The first extension of this approach to ionic energetic crystals was done by Sorescu and Thompson [104] for ADN. Using the rigid-ion approximation, the intermolecular potential used was composed by pairwise Lennard-Jones (LJ), hydrogen bonding (HB), and Coulombic (C) terms of the form... 

Rafizadeh et al [68] have examined the lattice dynamics of jS-NaNa in terms of the rigid-ion (or atomic) and rigid-molecule models (see Appendix). Both approaches included coulomb forces explicitly and, where possible, used analytical potential functions of the Lennard-Jones type, (r) = 4e[(a/r) - (a/r) ], where e is the well depth and o is the distance of closest approach. The parameters for Na-Na and N-N (intermolecular) interactions were fixed from lattice-dynamic results for pure sodium and a-N2. The N3-N3 interactions in the rigid-... 

Several attempts have been undertaken to derive such MM force constants for modeling zeolite frameworks [39]. Typical examples are the rigid ion and the shell model which assume that the character of the bonds in the lattice is largely ionic. Within the rigid ion model developed by Jackson and Catlow [40], the potential energy is given by... 

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