Force Axilrod-Teller

Figure 4. Percent deviation in instantaneous total system energy calculated by MTS method from that determined by CMD method for 108 particles interacting with Lennard-Jones plus Axilrod-Teller forces. System parameters same as those in Figure 3. Percent deviation calculated as (Ecun — E)trs)100/EcuD-...

Preliminary Results Showing Effect of Three Body Axilrod-Teller Force on Internal Energy and Pressure... 

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. 

Bc3 cluster the 3-body forces cannot be approximated solely by the Axilrod-Teller term. The reasons for the satisfactory approximation of many-body energy by the Axilrod-Teller term in the bulk phases of the rare gases were discussed by Meath and Aziz . As follows from precise calculations of the 3-body interaction energy in the Hcg , Neg and Ara trimers, both the Axilrod-Teller and the exchange energies are important. Nevertheless, in some studies of many-body interactions, the exchange effects are still neglected and the many-body contribution is approximated by only dispersion terms, for example see... 

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]. 

Unfortunately, even with the neighbor list applied to the three body forces, the CMD program for 108 Lennard-Jones plus Axilrod-Teller particles executes about 15 times slower than the same program for 108 Lennard-Jones particles. In the work reported here, source programs were written in FORTRAN IV using single precision arithmetic, compiled on an IBM FORTRAN IV-G compiler, and executed on the IBM 370/165 at Clemson University. 

Since, in the LMTS method described above, the three body forces are explicitly evaluated only two of every ten time steps, we might expect the LMTS method to be about 5 times as fast as the CMD method. The results in Table I confirm this i.e., using the LMTS method, a simulation of 108 Lennard-Jones plus Axilrod-Teller particles requires about 20 CPU minutes for 2000 time steps on an IBM 370/165. This execution speed remains about 2.5 times slower than a CMD method, pairwise additive Lennard-Jones simulation. 

Figure 3. Comparison of z-component of two-(2B) and three-body (3B) forces on particle 27 in conventional molecular dynamics simulation of Lennard-fones plus Axilrod-Teller fluid. At — time step = 2.15 (10 ) sec, pa = 0.65, kT " = 1.033. Note that the scale for three-body force is an order of magnitude smaller than that for the two-body force.

B. M. Axilrod and E. Teller, "Interaction of the van der Waals type between three atoms," J. Chem. Phys., 11, 299-300 (1943) see also the pedagogical article by C. Farina, F. C. Santos, and A. C. Tort, "A simple way of understanding the non-additivity of van der Waals dispersion forces," Am. J. Phys., 67, 344-9 (1999) for the step from two-body to three-body interactions. 

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