Pair Buckingham

The range of systems that have been studied by force field methods is extremely varied. Some force fields liave been developed to study just one atomic or molecular sp>ecies under a wider range of conditions. For example, the chlorine model of Rodger, Stone and TUdesley [Rodger et al 1988] can be used to study the solid, liquid and gaseous phases. This is an anisotropic site model, in which the interaction between a pair of sites on two molecules dep>ends not only upon the separation between the sites (as in an isotropic model such as the Lennard-Jones model) but also upon the orientation of the site-site vector with resp>ect to the bond vectors of the two molecules. The model includes an electrostatic component which contciins dipwle-dipole, dipole-quadrupole and quadrupole-quadrupole terms, and the van der Waals contribution is modelled using a Buckingham-like function. 

Buckingham theory and, 330 chain decomposition, 325 cooperative behavior of defects, 338 deuterium shifts, 361 dispersive interactions, 330 elastic strain, 333 electrostatic coupling, 352 exchange of positions, 351 heteroisotopic pairs, 348... 

The characteristic time of this diffusion was estimated by carrying out the molecular dynamic relaxation of the film surface within the limits of the above model at 500°C. In MD calculations, the pair interaction energy between atoms is approximated by the Buckingham pair potential (Zr O, O-O) (see Table 9.4). To describe covalent bonds more correctly, a three-body O-Zr-O term in the Stillinger-Weber form was introduced in addition to the Coulomb term. 

The intermolecular interactions are usually assumed to be pair-additive functions such as the Lennard-Jones 12-6 or 9-6 potentials or the Buckingham expontential-6 type of potentials and are parameterized using methods similar to those described in the previous paragraph to reproduce the crystallographic structure and the lattice energy. For the case of liquid systems the parameterization of non-bonded interactions can be done to reproduce the liquid densities and the heats of vaporization. 

The simplest interaction potential for a pair of atoms i and j separated by rij is the Buckingham potential ... 

The structure and dynamics of the lattice were simulated by using empirical potentials of pair wise interactions. The interaction between ion cores is assumed to be long-range purely Coulombic. The interaction between electron shells has two components a long-range purely Coulombic interaction and a short-range interaction described by the Buckingham potential. 

Sayle et al. (2008) also developed (Figure 9) a route exploiting the classical atomistic simulation to make combined studies of theoretical and experimental works. A typical selected system is ceria. Since the pair potential model based on electrostatic interaction and Buckingham short range presentations are often adequate to describe the fluorite structure of ceria, Sayle et al. explored the application of such models in nano-sized particles. A series of works have been reported on the assembly behaviors of nano-building blocks into complex nanostructures, including the ceria nanoparticles self assembly in ice mold (Karakoti... 

Hobza, R, Sponer, J., and Polasek, M., H-honded and stacked DNA base pairs cytosine dimer. An ab initio second-order M0ller-Plesset study, J. Am. Chem. Soc. 117, 792-798 (1995). McDowell, S. A. C. and Buckingham, A. D., Isotope effects on the stability of the carbon monoxide-acetylene van der Waals molecule and the hydrogen fluoride dimer, Chem. Phys. Lett. 182, 551-555 (1991). 

Previous Reviews. A general survey of the effects of molecular interactions on the optical properties of matter was recently given by Buckingham [435]. The work concerning ab initio and approximate computations of pair polarizabilities has recently been reviewed by Hunt [80] a careful comparison of the data available from various measurements reveals a high degree of consistency with the fundamental theory. Hunt has also reviewed the utility of the DID model and its limitations [79]. The results of measurements of the polarizability invariants of rare-gas pairs have been reviewed by one of the authors [271]. Substantial discussions of induced polarizabilities can be found in a number of review articles on CILS and dielectric properties [11,27, 143, 274, 343, 376]. 

A. D, Buckingham and K. L. Clarke-Hunt. The pair polarizability anisotropy of SF in the point-atom-polarizability approximation. Molec. Phys., 40 643-648 (1980). 

G. C. Tabisz and A. D. Buckingham. Remarks concerning CILS by tetrahedral molecular pairs. Faraday Symposia Chem. Soc., 77 170-172 (1977). 

In some cases (see van der Avoird et al., 1980, and references therein) atom-atom potentials, which are subsequently used to calculate crystal properties, have been obtained from an independent source, viz., from ab initio quantum-chemical calculations. The individual terms in an atom-atom potential of the form in Eq. (3), for example, are then fitted to the corresponding interaction energy contributions calculated for a more or less extensive set of geometries of a molecular pair. It appears that the Buckingham form (in Eq. 3) especially can yield a reasonably accurate representation of an ab initio calculated potential, provided that the individual terms are given different force centers (sites) whose positions are shifted away from the atomic nuclei and optimized in fitting the ab initio data. 

Note that one may use a pair of relations similar to Equations (3.5) and (3.9) to exclude the energy derivatives. This gives an integral relation, valid both for free and confined systems. One of the useful relations of such a kind was derived in an approximate way by Kirkwood [52] and Buckingham [53] to estimate the polarizability. For a simple proof and the history of these relations, widely used nowadays, see [54]. 

Fig. 2.6 Atom-atom potentials. For specific calculations of the intermolecular interaction of pure aromatic hydrocarbons, the overall potential is computed as the sum of individual atom-atom potentials V r). Here, r is the distance of the atoms of neighbouring molecules. Each of the three possible atom pairs (C-C, C-H and H-H) in neighbouring molecules is defined by its own set of parameters. Thus, using the Buckingham...

The functional form of the van der Waals term in the HSEA force field (Eq. [1]) was adapted from early work by Kitaygorodsky and is a parameterization of a general Buckingham potential (Eq. [2]). The unique feature of the Kitaygorodsky expression is that the Buckingham x parameter has been formulated as a function of the equilibrium distance (to) between the interacting atom pairs (i and j) ... 

---