Born-Mayer repulsions

An important aspect of empirical potential parameterization is the question of transferability. Are, for example, models derived in the study of binary oxides, transferable to ternary oxides Considerable attention has been paid to this problem by Cormack etal who have examined the use of potentials in spinel oxides, for example, MgAl204, NiCr204, and so on in addition Parker and Price have made a very careful study of silicates especially Mg2Si04. These studies conclude that transferability works well in many cases. However, systematic modifications are needed when potentials are transferred to compounds with different coordination numbers. For example, the correct modeling of MgAl204 requires that the potential developed for MgO, in which the magnesium has octahedral coordination, be modified in view of the tetrahedral coordination of Mg in the ternary oxide. The correction factor is based on the difference Ar between the effective ionic radii for the different coordination numbers. If an exponential, Born-Mayer, repulsive term is used, the preexponential factor is modified as follows ... 

The Born-Mayer repulsive exponential function is given as... 

Born-Mayer repulsion. The parameter y was fixed to agree with the findings of Tosi on the alkali halides. The three remaining parameters were adjusted so that theory and experiment would agree for the crystal energy and its first two volume derivatives, at zero temperature and pressure. This model gives a good account of the phonon dispersion curves of bcc sodium, and of the thermodynamic properties of sodium up to room temperature. ... 

Similarly as in the Tang-Toennies model210 211 212 the repulsive term is taken in the Born-Mayer form297,... 

These results indicate that the Born-Mayer expression with four repulsive parameters... 

Born-Mayer equation — This equation predicts the lattice energy of crystalline solids [i]. It is based on a simple model, in which the attraction and repulsion for a given arrangement of ions is calculated. The Born-Mayer energy (EB-m) is given by [i] ... 

As mentioned earlier, the shell model is closely related to those based on polarizable point dipoles in the limit of vanishingly small shell displacements, they are electrostatically equivalent. Important differences appear, however, when these electrostatic models are coupled to the nonelectrostatic components of a potential function. In particular, these interactions are the nonelectrostatic repulsion and van der Waals interactions—short-range interactions that are modeled collectively with a variety of functional forms. Point dipole-and EE-based models of molecular systems often use the Lennard-Jones potential. On the other hand, shell-based models frequently use the Buckingham or Born-Mayer potentials, especially when ionic systems are being modeled. 

We present how to treat the polarization effect on the static and dynamic properties in molten lithium iodide (Lil). Iodide anion has the biggest polarizability among all the halogen anions and lithium cation has the smallest polarizability among all the alkaline metal cations. The mass ratio of I to Li is 18.3 and the ion size ratio is 3.6, so we expect the most drastic characteristic motion of ions is observed. The softness of the iodide ion was examined by modifying the repulsive term in the Born-Mayer-Huggins type potential function in the previous workL In the present work we consider the polarizability of iodide ion with the dipole rod method in which the dipole rod is put at the center of mass and we solve the Euler-Lagrange equation. This method is one type of Car-Parrinello method. 

For application to nonmolecular solids, the bond description is similar but certain modifications are needed. First, the covalent energy must be multiplied by the equivalent number n of two electron covalent bonds per formula unit that must be broken for atomization. The evaluation of n will be discussed in detail presently. Second, the ionic energy must be evaluated as the potential energy over the entire crystal, corrected for the repulsions among adjacent electronic spheres. This is done by using the Born-Mayer equation for lattice energy, multiplying this expression by an empirical constant, a, which is 1 for the halides and less than 1 for the chal-cides, as follows ... 

The first term is the classical interaction between point charges and the second term is a repulsive Born-Mayer potential. 

Here qi is the effective charge of an atom is a dispersion interaction constant and Ay and bij are parameters of the Born - Mayer atom-atom repulsion potential. To calculate the long range Coulomb term in Eq. (1) one generally has to employ the Ewald summation technique. To obviate this inconvenience, the Coulomb term has been multiplied by the screening factor (and the dispersion term has been neglected) ... 

The Born-Mayer equation is an alternative (and possibly more accurate) form based on the assumption of an exponential form for the repulsive energy. Both equations predict lattice energies for compounds such as alkali halides that are in reasonably close agreement with the experimental values from the Born-Haber cycle. Some examples are shown in Table 1. A strict comparison requires some corrections. Born-Haber values are generally enthalpies, not total energies, and are estimated from data normally measured at 298 K not absolute zero further corrections can be made, for example, including van der Waals forces between ions. 

The short range repulsive part is represented by a Born-Mayer exponential ( ) type, the region of the well by a Morse potential (M) and the long range attractive part by a dispersion potential with a dipole-dipole and a dipole-quadrupole term. These parts are connected by cubic spline functions (S)... 

If it is assumed that the ions are nonpolarizable (or rigid), the coulomb term is that between point charges, i.e., V r) =Zf Z lr, and can be treated using the Ewald method [103]. The repulsive term is most often assumed to be of Born-Mayer type [Equation (3)]. 

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... 

At the equilibrium interatomic distance d UIdd = 0, i.e. the attractive and the repulsive forces are equal. From here we obtain the well known Born-Land6 and Born-Mayer equations. 

Third-order elastic constants of LaSe at 0 K were calculated using the Born-Mayer potential model. The repulsive interaction was considered up to the second nearest neighbors. The interatomic distance To = 3.030A leads to the values in lO N/m ( lO dyn/cm ) Cin = -21.439, c°i2 = Cii6=-1.860, C123 = cJse = C144 = 0.743. The temperature dependence for is given by = + where are (in lO N-m K ) am =6.837, an2 = 3.601,... 

As the C-H acid molecules approach some base, their equilibrium distance is determined by the sum of the corresponding van der Waals radii. In this case, the distance between two equilibrium positions of the proton is equal to about 1.6 A. For such a tunneling distance, the exponential term in (4.14) turns out to be extremely small, i.e. 10 . Clearly, the proton transfer reaction can take place only at much shorter distances for which the tunneling probability sharply increases in accordance with (4.14). However, the molecules are hindered from coming close to each other by the repulsive forces which sharply increase with decreasing distance. These forces may be described by the Born-Mayer potential[446] ... 

Fumi F. G. and Tosi M. P. (1964). Ionic sizes and Born repulsive parameters in the NaCl-type alkali halides, I The Huggins-Mayer and Pauling forms. J. Phys. Chem. Solids, 25 31 3. 

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