Ab initio theory of many-body interaction and cauchy relations in compressed rare-gas crystals

Abstract

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-particle, three-particle, and many-body interactions to the crystal energy under compression has been analyzed. The short-range three-particle potential has been calculated from first principles and proposed in the simple form. The three-particle 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 argon are in good agreement over a wide pressure range.