Coordination-dependent equations of state and pair potentials for cold metal crystals

Using a nearest-neighbor Heisenberg Hamiltonian approach, stemming from ideas of Poshusta and Klein, and based on results of Malrieu et al. for alkali and noble metals, a coordination-number- (c)-dependent equation of state at T=0 for metal crystals is proposed. From such a representation of the pressure and the cohesive energy, a method of Carlsson et al. can be used to extract a pair potential ${\mathrm{\phi }}_{\mathit{c}}$(r) which is density independent. Recent work of Robertson et al., stimulated by glue models of interatomic forces, fits into the above class of coordination-dependent properties over a limited range of near-neighbor distance.