Applying hybrid-functional and many-body methods to rare earths: a study of cerium

The presence of localized, partially occupied f-electron states dictates many of the peculiar physical properties of rare-earth materials. In particular, the description of the iso-structural α-γ phase transition in Ce metal poses great challenges to density-functional theory (DFT) based approaches since local/semilocal (LDA/GGA) functionals completely fail to produce the phase transition. Here we address this problem by investigating bulk-like Ce clusters of increasing size using hybrid functionals, that incorporate a portion of exact-exchange, and full exact-exchange plus correlation at the level of the random phase approximation (EX+cRPA). This allows us to systematically study the effects of non-local exchange and correlation in this important system. The exchange (and self-interaction) contributions to the phase transition are studied using different hybrid functionals and electron correlations are treated on the level of the random phase approximation (RPA). In all clusters we find two stable configurations with different lattice constants and distinct electronic and magnetic properties, resembling the bulk situation. However, all hybrid functionals predict that the high volume phase (linked to the γ-Ce phase) is lower in energy at zero temperature, in contrast to experiment. Decreasing the amount of exact-exchange in the hybrid functional eventually restores the correct phase ordering, at the expense of introducing an adjustable parameter. We show that EX+cRPA - a physically meaningful screening of exact-exchange - achieves the same effect from first principles.