Clusters 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. 

As was shown in previous section, the many-body forces play a crucial role in metal cluster stability. So, a model potential must include many-body terms, at least 3- and, sometimes, 4-body ones. For clusters of larger size, the fitted parameters in these terms will include ( absorb ) many-body effects of higher orders. 

Gregory J K, Clary D C. 1996. Structure of water clusters. The contribution of many body forces, monomer relaxation, and vibrational zero-point energy. JPhys Chem 100 18014-18022. Hahnemann S. 1833. Organon of Medicine. 5th edn. Translated by R E Dudgeon (1893). Indian edn (1994). Pralap Medical Publishers Pvt Ltd, New Delhi, pp 224. 

Kaplan IG, Hernandez-Cobos J, Ortega-Blake I, Novaro O (1996) Many body forces and electron correlation in small metal clusters. Phys Rev A 53 2493-2500... 

De is the depth of the well in the potential curve and Re the equilibrium distance (Fig. 10). In the absence of many-body forces the energy of interaction in clusters is simply a superposition of expressions of type (8). For the trimer ABC, we have... 

We may conclude that many-body forces are not important for the structure of solid hydrogen chloride (for further details see Sections 4.3 and 5). The energy of interaction in the dimer and in the solid fit very well into our relations. This is more a test of our assumptions of binary potentials in equations 8 and 18 than a limit on the role of many-body forces because the only available value was derived from cluster calculations based on the assumption of pairwise additivity. From the concepts and data discussed in this section it is obvious that an accurate description of clusters and condensed phases formed from polar molecules like HF and H20 which are both characteristic hydrogen bond donors and acceptors, requires a proper consideration of many-body forces. 

Clusters—The Contribution of Many-Body Forces, Monomer Relaxation, and Vibrational Zero-Point Energy. 

Much work has recently been carried out to quantify the three-body and many-body interactions in small clusters (mostly rare gases and water), which have implications on the liquid state properties, however here we consider some studies that have directly determined their influence on the bulk fluid properties. In reference87 the significant influence of three-body interactions on properties of rare gas fluids is discussed, and a recent manuscript by Szalewicz et al,107 thoroughly reviews the importance of many-body forces in general. Here we just summarise some important recent results. 

Chapter 33 - On the importance of many-body forces in clusters and condensed phase. Pages 919-962, Krzysztof Szalewicz, Robert Bukowski and Bogumit Jeziorski... 

On the importance of many-body forces in clusters and condensed phase... 

The interaction energies of clusters of molecules can be decomposed into pair contributions and pairwise-nonadditive contributions. The emphasis of this chapter is on the latter components. Both the historical and current investigations are reviewed. The physical mechanisms responsible for the existence of the many-body forces are described using symmetry-adapted perturbation theory of intermolecular interactions. The role of nonadditive effects in several specific trimers, including some open-shell trimers, is discussed. These effects are also discussed for the condensed phases of argon and water. 

J. K. Gregory and D. C. Clary, /. Phys. Chem., 100, 18014 (1996). Structure of Water Clusters. The Contribution of Many-Body Forces, Monomer Relaxation, and Vibrational Zero-Point Energy. 

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... 

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