Cohesive energy of 3d transition metals: Density functional theory atomic and bulk calculations

We report generalized gradient approximation (GGA) cohesive energies for 3d metals. The problem of obtaining atomic reference energies in density-functional theory is considered. The effect of going to nonspherical atomic charge distributions is much larger at the GGA than at the local-density approximation (LDA) level, but allowing fractional occupations of 3d and 4s shells has negligible effect. When nonsphericity effects are taken into account in the atomic reference energies, the average absolute error of 0.3 eV in the GGA cohesive energies is much smaller than the LDA error of 1.3 eV. The working of the GGA is analyzed in terms of the cohesive energy density and the charge inhomogeneity division of the exchange energy. The low-gradient limit in the GGA functionals is not important as regions with charge inhomogeneity s<0.2 have negligible contributions.