Binding energy many-body forces

Abstract. The physical nature of nonadditivity in many-particle systems and the methods of calculations of many-body forces are discussed. The special attention is devoted to the electron correlation contributions to many-body forces and their role in the Be r and Li r cluster formation. The procedure is described for founding a model potential for metal clusters with parameters fitted to ab initio energetic surfaces. The proposed potential comprises two-body, three-body, and four body interation energies each one consisting of exchange and dispersion terms. Such kind of ab initio model potentials can be used in the molecular dynamics simulation studies and in the cinalysis of binding in small metal clusters. 

Medium-range interactions can be defined as those which dominate the dynamics when atoms interact with energies within a few eV of their molecular binding energies. These forces determine a majority of the physical and chemical properties of surface reactions which are of interest, and so their incorporation in computer simulations can be very important. Unfortunately, they are usually many-body in nature, and can require complicated functional forms to be adequately represented. This means that severe approximations are often required when one is interested in performing molecular dynamics simulations. Recently, several potentials have been semi-empirically developed which have proven to be sufficiently simple to be useful in computer simulations while still capturing the essentials of chemical bonding. 

The dimers of Be, Mg and Ca are very weakly bound by the electron correlation effects, at the self-consistent field (SCF) level they are not stable. The binding energy of alkaline earth dimers is only 2-4 times larger than that in Kr2 and Xe2 dimers. Thus, alkaline dimers can be attributed to the van der Waals molecules. The situation is changed in many-atom clusters, even in trimers (Table II). This is evidently a manifestation of the many-body effects. The crucial role of the 3-body forces in the stabilization of the Be clusters was revealed at the SCF level previously [3-5], and more recently was established at the Mpller-Plesset perturbation theory level up to the fourth order (MP4) [6,7]. The study of binding in the Ben clusters [8-10] reveals that the 3-body exchange forces are attractive and give an important contribution to... 

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