Energy function, potential three-body

Two functional forms are checked for the He2-Br2 potential energy function. One is based on the pairwise atom-atom interaction, which has been widely used in all previous calculations on triatomic and tetratomic, Rgn-X2 with n=l,2, complexes. The parameters for the two-body He-He interactions are taken from Ref. ° The second one is given by summing up three-body HeBr2 interactions and the He-He one,... 

Configuration energies are determined by optimizing different structures with respect to atomic positions using the above mentioned functional expressions. In Fig.5 we compare the two different potential functional forms with the MP4 ah initio results. Solid lines are for the sum of the three-body... 

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-... 

The potential energy surface (i.e. the potential energy expressed as a function of the atomic positions) on which the classical trajectory moves is almost always semi-empirical and rather imprecisely known, because accurate quantum mechanical claculations of it are impossibly expensive except in the simplest systems. For use in a MD or MC program, the potential energy must be rendered into a form (e.g. a sum of two-body and sometimes three-body forces) that can be evaluated repeatedly at a cost of not more than a few seconds computer time per evaluation. 

The integral equation theory consists in obtaining the pair correlation function g(r) by solving the set of equations formed by (1) the Omstein-Zernike equation (OZ) (21) and (2) a closure relation [76, 80] that involves the effective pair potential weff(r). Once the pair correlation function is obtained, some thermodynamic properties then may be calculated. When the three-body forces are explicitly taken into account, the excess internal energy and the virial pressure, previously defined by Eqs. (4) and (5) have to be, extended respectively [112, 119] so that... 

Figure 9. The Jacobi coordinates for HCN. The potential energy is constructed as a sum of three two-body interactions plus a three-body term. These terms are functions of the distances between the bodies, Rcn,Rch,Rnh- Rcn is taken to be r, and Rqh and Rfm are expressed as functions of R and y.

The most common force fields include two-, three- and four-body potential energy functions. It is possible to use more complicated force... 

In addition, a simple three-body potential energy function has been considered that has the formula... 

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