Analytic representation of multi-ion interatomic potentials in transition metals

The first-principles, density-functional version of the generalized pseudopotential theory (GPT), previously developed for empty- and filled-d-band metals, recently has been extended to pure transition metals with partially filled d bands [Phys. Rev. B 38, 3199 (1988)]. Within this formalism, a rigorous real-space expansion of the bulk total energy has been obtained in terms of widely transferable, structure-independent interatomic potentials, including both central-force pair interactions and angular-force triplet and quadruplet interactions. In the central transition metals, the three- and four-ion potentials, ${\mathit{v}}_3$ and ${\mathit{v}}_4$, are essential to a proper description of materials properties, but are necessarily multidimensional functions which cannot be easily tabulated for application purposes.