Buckingham potential model

Sun et al. (2005) have used MD with a pair potential energy function known as the Buckingham potential model to predict the phase transition, lattice constant, thermal expansivity, isothermal bulk modulus and heat capacity for GaN in the isothermal isobaric N, P, T) ensemble for a temperature range of 300 K to 3000 K and for pressures from 0 to 65 GPa. In the isothermal-isobaric ensemble, the number of atoms, N, pressure, P, and temperature, T, are held constant while allowing the volume, V, and internal energy, E, to vary. 

The interaction between atoms separated by more than two bonds is described in terms of potentials that represent non-bonded or Van der Waals interaction. A variety of potentials are being used, but all of them correspond to attractive and repulsive components balanced to produce a minimum at an interatomic distance corresponding to the sum of the Van der Waals radii, V b = R — A. The attractive component may be viewed as a dispersive interaction between induced dipoles, A = c/r -. The repulsive component is often modelled in terms of either a Lennard-Jones potential, R = a/rlj2, or Buckingham potential R = aexp(—6r ). 

A second and repulsive energy term must be introduced to take account of the electron-electron repulsion that arises at very short interatomic distances. Several models are used to describe this repulsive term. Often used is the Buckingham potential, which, however, includes both attractive and repulsive components ... 

A number of techniques have been employed to model the framework structure of silica and zeolites (Catlow Cormack, 1987). Early attempts at calculating the lattice energy of a silicate assumed only electrostatic interactions. These calculations were of limited use since the short-range interactions had been ignored. The short-range terms are generally modelled in terms of the Buckingham potential,... 

Benzene-benzene interactions were modeled with a Buckingham potential that was shown to yield reasonable predictions of the properties of liquid and solid benzene. Benzene-zeolite interactions were modeled by a short-range Lennard-Jones term and a long-range electrostatic term. In total, 16 benzene molecules were simulated in a unit cell of zeolite Y, corresponding to a concentration of 2 molecules per supercage. Calculations ran for 24 ps (after an initial 24-ps equilibration time) for diffusion at 300 K. 

The repulsion increases exponentially, and it is steeper than the bond length deformation potential. The attractive force is usually modeled by a 1/r6 term, while various possibilities exist for the repulsion. The functions used in modem programs include, apart from the Morse potential (Eq. 2.13), the Lennard-Jones potential (Eq. 2.25)[401 (e.g., AMBER1411), the Buckingham potential (Eq. 2.26)[421 (e.g., MOMEC[81), or a modification thereof, the Hill potential (Eq. 2.27) (e.g., MM2, MM3[1,2,231). 

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... 

Lennard-Jones potentials have been used widely in modeling rare gas and molecular crystals. Morse potentials become more appropriate when covalent systems are being studied D may then be interpreted as the covalent bond-dissociation energy and re the equihbrium bond length. Buckingham potentials have been very widely used in the study of ionic and semi-ionic sohds. ... 

The next set of terms usually added allow for van der Waals-type interactions between the ions. The most popular form of the potential in solid state modelling is the Buckingham potential A exp —rlp)—Clr but there are other forms in use such as the Lennard-Jones — the general form and potentials derived... 

From a historical point of view, rare gases have been fundamental for the development of models. Although the first proposed model turned out not very realistic at a later analysis even for these simple systems, still they provided a framework for many models of everyday usage, such as the LJ or Buckingham potentials. In polyatomic systems, only at very large separations can the interaction be described by multipolar terms located at the center of the distributions. At short to medium distances, a most important range for condensed phases, multipolar multicenter expansion are used, whereby the centers may be located at the position of the nuclei or not. 

A steric interaction field is obtained by calculating the van der Waals interaction energy Evdw between probe and target in each grid point [Kim, 1992b]. Different potential energy functions were proposed to model van der Waals interactions between atoms. The most common are Lennard-Jones potential, Buckingham potential, and Hill potential [Leach, 1996]. 

The most frequently used model potentials are Rigid sphere, point center of repulsion, Sutherland s model, Lennard-Jones potential, modified Buckingham potential, Kihara potential, Morse potential. Their advantages and disadvantages are thoroughly discussed elsewhere [39] [28]. 

There are many potential models that have been proposed in the Hterature. Among the popular ones that are currently enjoying widespread applications are the Lennard-Jones (LJ 12-6) equation and the Buckingham Exp-6 equation. The parameters of these equations are usually obtained by matching the theory (i.e., DFT) or simulation results (e.g., MC simulations) against various experimental properties, e.g., second virial coefficient, viscosity, vapor pressure, saturated liquid density, or surface tension, at the temperature at which the adsorption is carried out. 

Vessal et al. (1989, 1993) have used a four-range Buckingham potential to model the short range interactions between different ions. The different components of the potential are as follows ... 

The present authors have used short range interactions between Si-0 and 0-0 modeled by four-range Buckingham potentials, with an O-Si-0 three-body potential of the type used by Vassal et a/.[10, 11], These are expressed as... 

The short-range interactions between alkali/alkaline earth ions and oxygen ions were modeled by using a simple Buckingham potential ... 

When a liquid or gaseous alkane system is simulated, the potential energy will include all those intra-molecular terms as well as non-bonded interactions between the atoms of different butane molecules, which might be modelled by Lennard-Jones or, more commonly in recent treatments of alkanes, Buckingham potentials. The potential energy function for an alkane then consists of sums over all the potential energy terms. There are many choices for the detailed specification of parameters. See [340] for a well described model for n-alkane chains. 

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