Cohesive properties of the lanthanides: Effect of generalized gradient corrections and crystal structure

Two different approximations to the density functional, the local (spin) density approximation (LDA) in the Hedin-Lundqvist parametrization and the Perdew-Wang generalized gradient approximation (GGA), are compared using the lanthanide series plus barium as testing ground. Our total-energy calculations are parameter-free and all-electron, with a full-potential linear muffin-tin orbital basis set. The equilibrium volumes, bulk moduli, and generalized cohesive energies are calculated, assuming both the fcc and hcp crystal structures, and compared to experimental data. We find that GGA corrects most of the overbonding tendency of LDA for these elements. Our results also suggest that the standard model of the lanthanides, according to which the $4f$ shell can be viewed as chemically inert, is not fully appropriate for the early lanthanides (not including La), and that the trend in the bulk modulus is much less smooth than previously thought.