A remark on the local density approximation with the gradient   corrections and the X$_\alpha$ method
  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 X$_\alpha$ 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. 
Y.-B. Xie, B.-H. Wang, W.-X. Wang