Three-body interaction potential

M. Quack, J. Stohner, and M. A. Suhm, Analytical three body interaction potentials and hydrogen bond dynamics of hydrogen fluoride aggregates (HF)n, n>3.J. Mol. Struct. 599, 381 425 (2001). 

The Stillinger-Weber potential, so far the most widely used interaction potential for silicon, comprises a two- and a three-body interaction potential. The crystalline phase of silicon at low pressures is in the diamond cubic structure, and it melts into a high-density liquid phase. Stillinger and Weber, after a search through a class of interaction potentials with two- and three-body interactions, defined their empirical potential as follows ... 

Lastly, any underlying atomistic model can be used, whether quantum mechanically or classically based. In practice, semi empirical interatomic potentials such as EAM ° and Stillinger-Weber (three-body interaction) potentials have usually been used to model the atomistic regime. 

E. M. Mas, R. Bukowski, and K. Szalewicz, Ab initio three body interactions for water. I. Potential and structure of water trimer. J. Chem. Phys. 118, 4386 4403 (2003). 

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. 

CCSD(T) HeBr2 interaction potential, dashed lines correspond to the pairwise atom-atom form, while filled circles indicate the MP4 ab initio values. Open circles are for the potential values obtained using the sum of the three-body MP4 potential for HeBr2, at the specific geometries with the same basis set as in the He2Br2 calculations. Fig.Sa represents the potential energy curves as a function of the distance R between the center of masses of Br2 and He2 in the tetrahedron structure. As can be seen both forms represent well the ab initio data at this configuration. In Fig. 5b an one-... 

Ternary moments are generally associated with greater quantum corrections than binary moments, Tables 5.2 and 6.3. Quantum corrections are most significant near the repulsive core of the interaction potential. Apparently, for three-body interactions, core penetration is more significant spectroscopically than for two-body interactions. 

The form of the potential for the system under study was discussed in many publications [28,202,207,208]. Effective pair potentials are widely used in theoretical estimates and numerical calculations. When a many-particle interatomic potential is taken into account, the quantitative description of experimental data improves. For example, the consideration of three-body interactions along with two-particle interactions made it possible to quantitatively describe the stratification curve for interstitial hydrogen in palladium [209]. Let us describe the pair interaction of all the components (hydrogen and metal atoms in the a. and (j phases) by the Lennard Jones potential cpy(ry) = 4 zi [(ff )12- / )6], where Sy and ai are the parameters of the corresponding potentials. All the distances ry, are considered within c.s. of radius r (1 < r < R), where R is the largest radius of the radii of interaction Ry between atoms / and /). 

Figure 19. Static structure factor S(q) in the small- region, at T = 297.6 K, for p = 0.95, 1.37, 1.69, and 1.93 nm-3 (from the bottom to the top), calculated with the ODS integral equation. The dotted lines correspond to the calculations with the twobody potential alone and the solid lines correspond to those that combine the two- and three-body interactions. The squares are for the experimental data of Formisano et al. [13] and the filled circles, at zero-q value, for the PVT data of Michels et al. [115]. Taken from Ref. [129].

Various choices have been made for the binding potential Vi (and the corresponding wave functions) and the interaction Vi2, which will be discussed below. If the former is described by a regularized zero-range potential so that V] (r) three-body contact potential V(ri,r2) <5(ri — r2)S(r2), then the amplitude (4.1) can be reduced... 

In this section we present some results obtained with the SAPT code for three-body interactions, SAPT3 371. Routine applications of SAPT to three-body interactions are relatively scarce. Here we concentrate on the water clusters with a special emphasis on the simulations of the liquid water properties starting from ab initio SAPT potentials for pair and three-body interactions and on clusters of water with hydrogen chloride in the context of protolytic dissociation of HC1 in small water clusters. Other applications of SAPT to, e.g. Ar2-HF trimer can be found in Ref. (313). 

The structure of this complex is shown in Fig. 9. Ab initio calculations of the three-body potential determined the relative importance of each term. They showed [78,79] that the total three-body interaction is very anisotropic with respect to the in-plane and out-of-plane rotations of HC1 within the cluster (see Fig. 10). It is instructive to have a closer look at the composition of this three-body term. 

Strength). At dilute concentrations, the probability of a three-body interaction is small. Therefore, the equilibrium radial distribution fiinc-tiong(r) is independent of concentration to a first approximation. Under these circumstances, the hard sphere potential is given by... 

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