  Motivated by the recent X-ray absorption spectroscopy (XAS) and resonant
inelastic X-ray scattering (RIXS) experiments, we use a detailed impurity model
to explore the nature of the parent compound and hole doped states of (La, Nd,
Pr)NiO$_2$ by including the crystal field splitting, the Ni-$3d$ multiplet
structure, and the hybridization between Ni-$3d$, O-$2p$, and Nd-$5d$ orbitals.
For simplicity and stimulated by the recent electronic structure calculations,
the latter are formally replaced with symmetric orbitals centered at the
missing O sites in the Nd layer, forming a two-dimensional (2D) band strongly
hybridizing with the Ni-$3d^9_{z^2}$ state. This hybridization pushes the main
part of the $3d^9_{z^2}$ spectral function up in energy by several eV and
stabilizes the singlet with considerable $d^9_{z^2}$ and other configurational
components. For the parent compound, we find that states of Ni-$3d^9_{z^2}$
character spread over a large energy range in the spectra, and cannot and
should not be represented by a single orbital energy, as suggested in other
approximations. This is qualitatively consistent with the RIXS measurements
showing a broad distribution of the Ni-$3d^9_{z^2}$ hole state, although the
shape of the Ni-$3d^9_{z^2}$ related structure is much more complicated
requiring reinterpretations of the RIXS data. For the hole-doped systems, we
show that adding these additional ingredients can still result in the
lowest-energy hole doped state having a singlet character.
