Molecular with three-body interactions

A. Nakano, P. Vashishta, and R. K. Kalia, Comput. Phys. Commun., 77, 303 (1993). Parallel Multiple-Time-Step in Molecular Dynamics with Three-Body Interaction. 

Molecular Dynamics Simulations of Simple Fluids with Three-Body Interactions Included... 

Molecular Dynamics with Three-Body Interactions... 

Multiple Time Step (MTS) Method Applied to Three Body Forces. In order to improve the execution speed of simulation programs with three body interactions Included, the multiple time step method of Streett, t al. ( ) has been applied to the evaluation of the three body forces. The multiple time step method attempts to take advantage of the fact that molecular motions in a fluid may be reduced to components which operate on very different time scales. More precisely, one can often identify components of the force on a molecule which have relatively large differences in their rates of change with time. It is the quickly varying component of the force which limits the size of the time step At which must be used to obtain stable solutions... 

Figure 18. Pair correlation function g(r), 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 by the ODS integral equation with both the two-body interactions (dotted lines), and the two- plus three-body interactions (solid lines). The curves for p= 1.37, 1.69, and 1.93 nm-3 are shifted upward by 0.5, 1, and 1.5, respectively. The comparison is made with molecular dynamics simulation (open circles). Taken from Ref. [129].

The leading nonadditive term in the many-body expansion of a potential is the three-body interaction. Similarly like dimers, trimers (and larger clusters) can be selectively studied by molecular beam spectroscopy. A number of such trimers have been the subjects of investigations. Among them are the Rg2-diatom trimers mentioned above, with the most extensive data available for Ar2-HF [64]. Both empirical [29,30] and ab initio [33] nonadditive potentials have been obtained for this system. A large number of spectral data are available also for the water trimer [65,66]. An accurate three-body potential for water has recently been developed [34]. 

Prom a practical point of view these last facts are very bad news indeed we have seen earlier in some detail the problems associated with the calculation of the large numbers of electron-repulsion integrals when a molecular wavefunction is expanded in terms of a basis set. If this calculation is to be complicated by a space-dependent law of interaction and three-body interactions then it will become prohibitively expensive in computing resources. 

Transfer matrix calculations of the adsorbate chemical potential have been done for up to four sites (ontop, bridge, hollow, etc.) or four states per unit cell, and for 2-, 3-, and 4-body interactions up to fifth neighbor on primitive lattices. Here the various states can correspond to quite different physical systems. Thus a 3-state, 1-site system may be a two-component adsorbate, e.g., atoms and their diatomic molecules on the surface, for which the occupations on a site are no particles, an atom, or a molecule. On the other hand, the three states could correspond to a molecular species with two bond orientations, perpendicular and tilted, with respect to the surface. An -state system could also be an ( - 1) layer system with ontop stacking. The construction of the transfer matrices and associated numerical procedures are essentially the same for these systems, and such calculations are done routinely [33]. If there are two or more non-reacting (but interacting) species on the surface then the partial coverages depend on the chemical potentials specified for each species. 

Water Potentials. The ST2 (23), MCY (24), and CF (2J5) potentials are computationally tractable and accurate models for two-body water-water interaction potentials. The ST2, MCY and CF models have five, four, and three interaction sites and have four, three and three charge centers, respectively. Neither the ST2 nor the MCY potentials allow OH or HH distances to vary, whereas bond lengths are flexible with the CF model. While both the ST2 and CF potentials are empirical models, the MCY potential is derived from ab initio configuration interaction molecular orbital methods (24) using many geometrical arrangements of water dimers. The MCY+CC+DC water-water potential (28) is a recent modification of the MCY potential which allows four body interactions to be evaluated. In comparison to the two-body potentials described above, the MCY+CC+DC potential requires a supercomputer or array processor in order to be computationally feasible. Therefore, the ST2, MCY and CF potentials are generally more economical to use than the MCY+CC+DC potential. 

We will mainly be concerned with two- and three-body atomic and molecular systems whose components preserve their identity during the radiative encounters. In other words, we will consider non-reactive atomic or molecular systems, such as interacting helium and argon atoms, He-Ar, or hydrogen pairs, H2-H2, in their electronic ground states. 

Induced dipole autocorrelation functions of three-body systems have not yet been computed from first principles. Such work involves the solution of Schrodinger s equation of three interacting atoms. However, classical and semi-classical methods, especially molecular dynamics calculations, exist which offer some insight into three-body dynamics and interactions. Very useful expressions exist for the three-body spectral moments, with the lowest-order Wigner-Kirkwood quantum corrections which were discussed above. 

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]. 

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