Renormalized atoms: Cohesion in transition metals

Abstract

The renormalized-atom method is used to calculate the cohesive energy of the $3d$ and $4d$ transition-metal elements and the equilibrium lattice constant and bulk modulus of two representative elements. Ti and Cu. The results agree with experiment to within 20% for most elements. The method of calculation allows the cohesive energy to be decomposed into a number of contributions whose relative importance can be investigated both as a function of valence and as a function of density. No evidence of $d\ensuremath{-}d$ repulsion is found for the transition or noble metals. Instead the "spring" which holds the atoms apart is the result of the increasing kinetic energy of the conduction electrons as the density is increased. The $d\ensuremath{-}d$ interaction is uniformly attractive and produces the minimum in the Wigner-Seitz radius near the center of a transition-metal period. Band structures calculated from renormalized-atom and $X\ensuremath{\alpha}$ potentials are compared and the relationships among them are discussed in some detail.