Ion-pairing potential

Friedman (1971). This approach is described as the hypernetted chain procedure and in it ion-ion pair potentials are expressed as the sum of four terms. These are ... 

Since ion-ion-pair potentials have been thoroughly investigated for rock-salt-type crystals by Tosi and Fumi (15) and those for other type salts have not been as well studied, the MD simulations have been carried out for alkali fluoride and chloride crystals of the rock-salt type NaF, KF, CsF, LiCl, NaCl, and KC1. Due to the limitation of computer times, the simulations have been carried out for only 12 to 20 ps depending on the systems. The experimental conditions for the simulations are summarized in Table II. 

Figure 17. Contributions to the ion-ion pair potential as a function of distance apart, r, of two ions i and j, radii n and rj the contributions correspond to the terms in equation (21) for sodium chloride in water with Ay — 400J mol-1.

Two crucial parameters determine the dynamics of the reaction. The first is the D- AB distance at which the electron transfer occurs, i.e., the distance for which the ion-pair potential D+ AB crosses the covalent curve D AB. Assuming a flat covalent curve and R large enough for the Coulomb interaction to be dominant, the crossing occurs at... 

K.-P. Schroder and J. Sauer,/. Phys. Chem., 100,11043 (1996). Potential Functions for Silica and Zeolite Catalysts Based on Ab Initio Calculations. 3. A Shell Model Ion Pair Potential for Silica and Aluminosilicates. 

Force constant and potential energy (C7) calculations indicate that the experimentally measured U does not vary with dielectric constant in a manner predicted by ion-pair potentials both electrostatic and repulsion forces in the solution are important. Solvation measurements provide information about the former vibration studies about the latter. 

In contrast to the ion pair potentials discussed in the preceding section, a different approach has been used successfully in organic chemistry. Organic molecules are mainly covalently bonded. In contrast to an ionic bond, a covalent bond is directional, so it is insufficient to use the simple ion pair model that works so well for inorganic sobds. Rather, the directed character of the bond has to be accounted for in tbe force field. A convenient approach for accomplishing this has its origin in vibrational spectroscopy. 

To distinguish a force field like the one in Eq. [23] from ion pair potentials, we shall call the former a molecular mechanics force field, a notation adopted in Allinger s pioneering work on predicting structures of hydrocar-bons and used for his series of force fields. > > 77 In contrast to ion pair potentials, molecular mechanics force fields include higher order terms from Eq. [14], usually up to fourth order for torsions. 

Table 3 compares advantages and disadvantages of the ion pair potential and molecular mechanics force field types. Ion pair potentials are much simpler and are therefore easier to parameterize. The parameterization is often based on experimental data of solids alone. Because bond lengths and bond angles in... 

Table 3 Advantages and Disadvantages of Ion Pair Potentials and Molecular Mechanics Force Fields ... 

Finally, since they do not consider bonds, ion pair potentials are able to describe changes in coordination. In some areas, notably geophysical and glass simulations, this capability can be important because it allows the study of phase transitions, as we shall mention later in connection with applications. 

If we look at the functional forms of ion pair potentials and molecular mechanics force fields, we see that both force fields share Coulomb and van der Waals terms. It should therefore be possible to make use of the particular strengths of each force field by combining the two types in studies involving inorganic as well as oi anic components. 

For ceramic materials, defects within the lattice are inextricably linked with transport properties. The diffusion of a cation in a ceramic, for example, involves the formation of vacancy or interstitial states within the crystal, and the migration of these species leads to a net transport of material through the lattice. These processes may be modeled by means of ion pair potentials in conjunction with the Mott-Littleton defect approach, direct molecular dynamics techniques, 24 or Monte Carlo methods to describe overall transport on the basis of calculated individual process statistics. 

For ionic oxides like these, empirical ion pair potentials can be used to perform atomistic simulations. Defect structures due to oxygen vacancies created by substitution of La + by divalent cations such as Ca, Sr, or Ba + can be simulated with these potentials. Evain et al. used empirical atom-atom... 

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.

The ability of a force field to reproduce vibrational spectra is often used as another criterion of quality. Table 14 compares observed and calculated vibrational spectra of a-quartz derived from various potential functions. This table shows that the molecular mechanics force field of de Vos Burchart is clearly superior to both Tsuneyuki s and Vessal s ion pair potentials. 

Vibrations of water in natrolite have been studied by Demontis et al.279 They were unable to accurately reproduce the vibrational spectrum and attributed their poor results to the influence of the zeolite s electric field on the water molecules. The authors later developed an electric field dependent force field for water2 to improve the simulation capabilities for hydrated zeolites. Water in ferrierite has also been studied in great detail by Leherte and coworkers234,257-262 using an ion pair potential. Finally, water complexes in cation-exchanged zeolites were investigated by Dil mukhambetov et al.28i... 

Models have also been developed which predict periodic structures by using lattice energy minimization and vibrational spectra using lattice dynamics. In this case the proper determination of potential functions used to describe the interactions between atoms is critical for canying out adequate predictions. Very recently a very powerful shell model ion-pair potential for aluminosilicates has been derived by fitting its parameters to data obtained from quantum-chemical calculations on molecular models that represent typical subunits of zeolites [8j. The correct use of such potential describes accurately the long-range... 

Schroder KP, Sauer J PotanUal functions for silica and zeolite catalysts based on eb MOo calculations 3. A shell-model ion-pair potential for silica and aluminosllleetes. J Phys Cham 1996, 100 11043-11049. 

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