Electronic-structure calculations of praseodymium metal by means of modified density-functional theory

Electronic-structure calculations of elemental praseodymium are presented. Several approximations are used to describe the Pr $f$ electrons. It is found that the low-pressure, trivalent phase is well described using either the self-interaction corrected (SIC) local-spin-density (LSD) approximation or the generalized-gradient approximation (GGA) with spin and orbital polarization (OP). In the SIC-LSD approach the Pr $f$ electrons are treated explicitly as localized with a localization energy given by the self-interaction of the $f$ orbital. In the GGA+OP scheme the $f$-electron localization is described by the onset of spin and orbital polarization, the energetics of which is described by spin-moment formation energy and a term proportional to the total orbital moment, $L_z^2$. The high-pressure phase is well described with the $f$ electrons treated as band electrons, in either the LSD or the GGA approximations, of which the latter describes more accurately the experimental equation of state. The calculated pressure of the transition from localized to delocalized behavior is 280 kbar in the SIC-LSD approximation and 156 kbar in the GGA+OP approach, both comparing favorably with the experimentally observed transition pressure of 210 kbar.