  We investigate the low-temperature charge-density-wave (CDW) state of bulk
TaS$_2$ with a fully self-consistent DFT+U approach, over which the controversy
has remained unresolved regarding the out-of-plane metallic band. By examining
the innate structure of the Hubbard U potential, we reveal that the
conventional use of atomic-orbital basis could seriously misevaluate the
electron correlation in the CDW state. By adopting a generalized basis,
covering the whole David star, we successfully reproduce the Mott insulating
nature with the layer-by-layer antiferromagnetic order. Similar consideration
should be applied for description of the electron correlation in molecular
solid.
