  We studied the relationship between the charge doping and the correlation,
and its effects on the spectral function of the BaFe$_2$As$_2$ compound in the
framework of the density functional theory combined with the dynamical mean
field theory (DFT+DMFT). The calculated mass enhancements showed that the
electronic correlation varies systematically from weak to strong when moving
from the heavily electron-doped regime to the heavily hole-doped one. Since the
compound has a multi-orbital nature, the correlation is orbital-dependent and
it increases as hole-doping increases. The Fe-3d$_{xy}$ (xy) orbital is much
more correlated than the other orbitals, because it reaches its half-filled
situation and has a narrower energy scale around the Fermi energy. Our findings
can be consistently understood as the tendency of the heavily hole-doped
BaFe$_2$As$_2$ compound to an orbital-selective Mott phase (OSMP). Moreover,
the fact that the superconducting state of the heavily hole-doped
BaFe$_2$As$_2$ is an extreme case of such a selective Mottness constrains the
non-trivial role of the electronic correlation in iron-pnictide
superconductors. In addition, the calculated spectral function shows a behavior
that is compatible with experimental results reported for every charge-doped
BaFe$_2$As$_2$ compound and clarifies the importance of the characterization of
its physical effects on the material.
