The optimized effective potential (OEP) method combined with many-body perturbation schemes is one of promising approaches to go beyond the local density approximation of the density functional theory. Although the method is very powerful, it has not been widely used so far. One of the reasons is that some ambiguity inherent to the OEP prevents us to apply it to spin-polarized cases [1]. Another more practical reason is that its computational cost is rather high.
In order to overcome these points, first, we reformulated the OEP method to render it applicable to general correlation functionals including the RPA correlation functional [2]. The following points are emphasized: i) Level-crossing at the Fermi surface is taken into account; ii) eigenvalue variations in a Kohn-Sham functional are correctly treated; and iii) the resultant OEP equation is different from those reported to date.
Seoond, we have introduced a method that accelerates the OEP scheme in a static RPA-level correlation functional in the framework of KKR. Further to improve the computational speed, the Krieger-Li-Iafrate (KLI) approximation is exploited for solving the OEP equation. It is likely that KLI approximation does not deteriorate the description of the magnetic transition metals (Fe, Co, and Ni) examined here, despite the fact that their magnetic properties are rather sensitive to the treatment of correlation energy.