Exact exchange potential band-structure calculations for simple metals: Li, Na, K, Rb, and Ca

We present electronic band-structure calculations of simple metals (Li, Na, K, Rb, and Ca), where we use the exact Kohn-Sham density-functional exchange (EXX) potential combined with the LDA (local-density approximation) correlation potential. The method is the same as one exploited in the previous papers [Phys. Rev. B 50, 14816 (1994); Phys. Rev. Lett. 74, 2989 (1995)]. Surprisingly, in contrast to the case of semiconductors and insulators, the resulting eigenvalues of valence bands are mostly in agreement with the corresponding LDA eigenvalues. In the case of Ca, where the empty d band exists above the Fermi energy, however, the EXX calculation modifies the position of the d bands relative to the s bands considerably, implying the importance of treating the correlation energy on the same footing as the exchange energy.