Teller potential, Axilrod

A simpler potential of the form of Eq. (10) has been used by Pearson et al. to model Si and SiC surfaces . The two-body term is of the familiar Lennard-Jones form while the three-body interaction is modeled by an Axilrod-Teller potential . The physical significance of this potential form is restricted to weakly bound systems, although it apparently can be extended to model covalent interactions. 

Little study has been made of nonaddltlve effects in fluids composed of nonspherlcal molecules. Singh and coworkers have developed a thermodynamic perturbation theory for this purpose (24. 25). Stogryn has given the analog of the Axilrod-Teller potential for nonspherlcal molecules (26). 

Figures 1 and 2 show the Axilrod-Teller potential for several representative triangular shapes formed by three atoms.

These figures indicate that the Axilrod-Teller potential is... 

In the simulations reported here the Lennard-Jones potential was truncated at = 2.5a. Figures 1 and 2 indicate that the Axilrod-Teller potential is of shorter range than the Lennard-Jones model for most triangular shapes hence, the Axilrod-Teller potential was truncated when any one of the lengths or... 

Test of the Linear Multiple Time Step Method Applied to the Axilrod-Teller Potential in Molecular Dynamics Simulations of Lennard-Jones plus Axilrod-Teller Interactions. 

Figure 5. Effect of Axilrod-Teller potential on radial distribution function at = 0.817. For Lennard-Jones fluid, kT< = 0.746 for Lennard-Jones plus Axilrod-Teller fluid, kTr = 0.740.

Three-body and higher terms are sometimes incorporated into solid-state potentials. The Axilrod-Teller term is the most obvious way to achieve this. For systems such as the alkali halides this makes a small contribution to the total energy. Other approaches involve the use of terms equivalent to the harmonic angle-bending terms in valence force fields these have the advantage of simplicity but, as we have already discussed, are only really appropriate for small deviations from the equilibrium bond angle. Nevertheless, it can make a significant difference to the quality of the results in some cases. 

Non-pairwise additivity. A significant component of the energy V (1,2,3) of three interacting atoms is given by the sum of the pair potentials, V(l,2) + F(l,3) + F(2,3). However, it is now generally accepted that the so-called Axilrod-Teller term, a long-range, irreducible (classical)... 

Most of the potential energy surfaces reviewed so far have been based on effective pair potentials. It is assumed that the parameterization is such as to account for nonadditive interactions, but in a nonexplicit way. A simple example is the use of a charge distribution with a dipole moment of 2.ID in the ST2 model. However, it is well known that there are significant non-pairwise additive interactions in liquid water and several attempts have been made to include them explicitly in simulations. Nonadditivity can arise in several ways. We have already discussed induced dipole interactions, which are a consequence of the permanent diple moment and polarizability of the molecules. A second type of nonadditive interaction arises from the deformation of the molecules in a condensed phase. Some contributions from such terms are implicitly included in calculations based on flexible molecule potentials. Other contributions arises from electron correlation, exchange, and similar effects. A good example is the Axilrod-Teller three-body dispersion interaction ... 

Computer simulation of molecular dynamics is concerned with solving numerically the simultaneous equations of motion for a few hundred atoms or molecules that interact via specified potentials. One thus obtains the coordinates and velocities of the ensemble as a function of time that describe the structure and correlations of the sample. If a model of the induced polarizabilities is adopted, the spectral lineshapes can be obtained, often with certain quantum corrections [425,426]. One primary concern is, of course, to account as accurately as possible for the pairwise interactions so that by carefully comparing the calculated with the measured band shapes, new information concerning the effects of irreducible contributions of inter-molecular potential and cluster polarizabilities can be identified eventually. Pioneering work has pointed out significant effects of irreducible long-range forces of the Axilrod-Teller triple-dipole type [10]. Very recently, on the basis of combined computer simulation and experimental CILS studies, claims have been made that irreducible three-body contributions are observable, for example, in dense krypton [221]. 

The dispersion energy is the universal attractive glue that leads to the formation of condensed phases. It is additive at second order in perturbation theory, and the form of the three-body term that arises at third order (the tripledipole dispersion term) is also well known from perturbation theory. This Axilrod-Teller term " was the only addition to the pair potential for argon that was required to quantitatively account for its solid and liquid state properties. This may be grounds for optimism that other nonadditive dispersion terms are negligible. Whether this can be extended to less symmetrical organic molecules and their typical crystalline and liquid environments has not yet been established however. 

A notable example of a potential that does include many-body terms is the Barker-Fisher-Watts potential for argon, which combines a pairwise potential with an Axilrod-Teller triple... 

Little is known concerning three body contributions to dynamic fluid properties. Fisher and Watts have calculated the self diffusion coefficient using the BFW pair potential without including the Axilrod-Teller interaction and obtained results similar to those for a Lennard-Jones fluid at the same densities (23). Schommers two dimensional Lennard-Jones plus Axllrod Teller simulations show significant three body effects on the velocity autocorrelation function however, the two dimensional self diffusion coefficient is little affected (16). Schommers is careful to point out, however, that results found in two-dimensional fluids do not necessarily extrapolate to three dimensions. 

The potential model used to test the molecular dynamics method described below was a Lennard-Jones 6, 12 pair potential plus Axilrod-Teller triplet potential. The Lennard-Jones model is given by ... 

Figure 1. Axilrod-Teller triple dipole potential for representative triangles formed by three atoms. The angle 6, is that between t,i and r,.

This section reports the results obtained from two self-consistent schemes that have been extended to deal with the triple-dipole interaction, which reduces to a state-dependent effective pair potential. The pair potential of Aziz and Slaman [106] (AS) is combined with the Axilrod and Teller [108] (AT) triple-dipole potential to describe the interactions in Xe and Kr fluids. Note that other investigations have been performed with ab initio potentials [113, 114]. 

B.M. Axilrod and E. Teller, J.Chem.Phys., 11299 (1943). The general anisotropic many-body intermolecular potentials for a system of N molecules have been derived by P. Piecuch, Mol. Phys., 59 (1986)10671085. 

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