We report that the solids with narrow valence bands cannot be described by the local density approximation with the gradient corrections in the density functional theory as well as the Xα method. In particular, in the case of completely filled valence bands, the work function is significantly underestimated by these methods for such types of solids. Also, we figured out that these deficiencies cannot be cured by the self-interaction-corrected-local-density-approximation method.
@article{arxiv.physics/0612008,
title = {A remark on the local density approximation with the gradient corrections and the X$_\alpha$ method},
author = {Y. -B. Xie and B. -H. Wang and W. -X. Wang},
journal= {arXiv preprint arXiv:physics/0612008},
year = {2007}
}