Non-additive forces in atomic clusters

The closed recurrence formula which expresses the energy of m-body interactions through the energies of 2-, 3- and (m - 1)-body ones is obtained. The m-body contributions to the interaction energy of silver clusters are calculated by the all-electron non-local spin density method. The importance of not only 3- but also 4- and 5-body forces for cluster stability has been revealed. The stable geometry of planar and spatial silver clusters is determined by the competition of attractive additive forces and repulsive non-additive forces. The larger magnitude of non-additive forces for three-dimensional conformations in comparison with two-dimensional ones is the reason that for Ag n with n = 4-6 the most stable geometries are planar.