Density-dependent pair potentials and the compressibility problem

Abstract

The consistent treatment of the static and dynamic properties of metallic systems using interatomic potentials which are based on a one-body potential plus pair interactions containing volume or mean density dependence is examined. The focus is on the discrepancy between the compressibility of metals calculated in two alternative and legitimate ways, i.e. from elastic constants deduced from the long-wavelength limit of phonon spectra and from a homogeneous deformation. A simple, physically motivated resolution of this long-standing 'compressibility problem' is proposed which for simple metals provides an interpretation of earlier treatments involving third- and fourth-order perturbation terms in the total energy. The resolution hinges on taking reasonable account of inhomogeneities in the electron density which modulate the one-body and pair potentials. Subtleties in the interplay between these two terms in the particular case of interatomic potentials based on weak pseudopotential theory are exposed and pitfalls are pointed out in the haphazard application of empirical interatomic potentials. The consequences of the work for the phonon spectra are investigated and a first-principles method for treating this and related situations is outlined.