An evaluation of three-body interatomic forces and formulation of a general model

Several deficiencies are demonstrated in previous formulations of three-body interatomic forces, and revised and extended formulations are presented for the case of the NaCl lattice. A commonly used formulation of non-central forces and a formulation of the effect of ellipsoidal atom deformation are incorrect. Atom deformation should in general introduce two degrees of freedom in the NaCl lattice, but the only previous correct formulation of deformation effects, the commonly used “breathing shell model,” includes only one degree of freedom. The “shell model” of polarizable atoms has been correctly formulated, but applications seem to have been arbitrarily restricted to the case where short-range forces act only on shells, and not on cores. Because of these errors and incompletenesses, it is concluded that no three-body forces have been convincingly established or characterized, although the necessity of their inclusion in models is clear.