  The electronic spectral function of BaNi$_2$As$_2$ is investigated using both
the angle-resolved photoemission spectroscopy (ARPES) and a combined
computational scheme of local density approximation together with dynamical
mean-field theory (LDA+DMFT). In contrast to well studied isostructural iron
arsenide high temperature superconductors, the BaNi$_2$As$_2$ demonstrate weak
correlation effects although Ni-3d elections have even lager on-site
interaction than Fe-3d ones. LDA+DMFT effective mass enhancement for bands
crossing the Fermi level is found to be only about $1.2$ which agrees well with
ARPES data. This reduction of the correlation manifestation with respect to
iron pnictides comes from the increase of 3d-orbital filling, when going from
Fe to Ni. The electron correlations cause remarkable reconstruction of the bare
BaNi$_2$As$_2$ LDA band structure below $-0.8$ eV due to self-energy effect. A
simplified toy model to understand weakness of correlation effects in
BaNi$_2$As$_2$ and to describe the LDA+DMFT self-energy shape is discussed. For
more realistic comparison of LDA+DMFT spectral function maps with ARPES data we
take into account several experimental features: the photoemission
cross-section, the experimental energy and angular resolutions and the
photo-hole lifetime effects. Thus presented here LDA+DMFT calculations with
experimental features included provide nearly qualitative agreement with ARPES
data and assure the observation of a dramatic apparent decrease of the
correlation strength compared to the Fe compounds.
