Cohesion and promotion energies in the transition metals: Implications of the local-density approximation

Abstract

The accuracy of the local-density (LDA) or local-spin-density (LSDA) approximations when applied to transition metals is of great concern. Estimates of the cohesive energy compare the total energy of the solid with that of the free atom. This involves chosing the reference state of the free atom which, as a rule, will not be the free atom’s ground state in LDA or LSDA. Comparing one reference state versus another, e.g., the dn−1s vs dn−2s2 for a transition metal, corresponds to calculating an s-d promotion energy Δ, which may be compared with experiment. Gunnarsson and Jones (GJ) [Phys. Rev. B 31, 7588 (1985)] found for the 3d row that the calculated Δ displayed systematic errors which they attributed to a difference in error within the LSDA in the treatment of the coupling of the outer-core electrons with the d versus non-d valence electrons. This study has been extended to relativistic calculations for the 3d, 4d, and 5d rows and for other promotions. The situation is more complicated than suggested by GJ, and its implications for cohesive energy estimates will be discussed.