  The repercussions of an inaccurate account of electronic states near the
Fermi level EF by hybrid functionals in predicting several important metallic
properties are investigated. The diffculties in- clude a vanishing or severely
suppressed density of states (DOS) at EF, significantly widened valence
bandwidth, greatly enhanced electron-phonon (el-ph) deformation potentials, and
an overestimate of magnetic moment in transition metals. The erroneously
enhanced el-ph coupling calculated by hybrid functionals may lead to a false
prediction of lattice instability. The main culprit of the problem comes from
the simplistic treatment of the exchange functional rooted in the original Fock
exchange energy. The use of a short-ranged Coulomb interaction alleviates some
of the drawbacks but the fundamental issues remain unchanged.
