Application of a screened self-interaction correction to transition metals: Copper and zinc

A simplified form of the self-interaction correction (SIC) to the local-density approximation has recently been derived by Perdew and Norman and applied successfully to calculations on atoms and insulators. This success has led us to consider other solid systems. As is well known, at the end of the transition-metal series the $d$ bands are too high and too disperse relative to experiment in the local-density approximation. This is therefore a prime testing ground for the effects of the self-interaction correction which should lower and narrow such bands. In this paper the above method is applied self-consistently to copper and zinc. Reasonable $d$-band dispersions are obtained but the $d$ bands themselves are too low relative to experiment, which would indicate a relaxation shift of some sort. Indeed, the relaxation shift is due to metallic screening. Crudely incorporating this effect into a band model, we obtain reasonable $d$-band positions in both copper and zinc and correct a large part of the local-density error. Justifications for applying the SIC to transition metals with filled $d$ bands are also given. Finally, core-level shifts due to SIC and metallic screening are discussed.