The short-range many-body forces induced by the overlap of electron shells of atoms have been investigated. The nonorthogonality of atomic orbitals of the nearest-neighbor atoms of a crystal leads to the appearance of terms in the potential energy, which depend on the coordinates of three, four, and more nearest-neighbor atoms. An expression has been obtained for the energy of the electron subsystem of the crystal in the Hartree-Fock approximation in the basis set of atomic orbitals exactly orthogonalized at different crystal sites. The behavior of the contributions from two-body and three-body interactions to the crystal energy under compression has been analyzed. The short-range three-body potential has been calculated from first principles and proposed in the simple form. The three-body forces, obtained change the behavior of the dispersion curves for all wave vectors, in particular, thus violating the Cauchy relation. The theoretical and experimental deviations from the Cauchy relation for Ne and Ar are in good agreement under pressure.ß 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction Rare-gas crystals (RGC) are the simplest molecular crystals; therefore, they are often used as model objects to investigate the van der Waals forces. Particular interest expressed in RGC is associated with their unique properties exhibited at high pressures, which make it possible to use these materials as pressure-transmitting media in diamond anvil cells (DAC) [1].The adiabatic potential U, which is required to construct the dynamics of crystal lattices, can be calculated from first principles or approximated by the well-known function of the distance, i.e., by using the method of interatomic model (empirical) potentials. As new information concerning the phonon spectra and elastic properties of the crystals becomes available, the theory can be refined in the following ways: (i) by including the interaction of more distant neighbors [2,3], (ii) by introducing the long-range three-body interaction [4] and short-range three-body interaction [5][6][7][8][9][10], and also (iii) by taking into account the dipole deformation [11][12][13][14] and quadrupole deformation [15,16] of the atoms.Many physical properties of RGC at low pressures are adequately described using the ab initio or empirical