  In this work, we investigate collective electronic fluctuations and, in
particular, the possibility of the charge density wave ordering in an
infinite-layer NdNiO$_2$. We perform advanced many-body calculations for the
ab-initio three-orbital model by taking into account local correlation effects,
non-local charge and magnetic fluctuations, and the electron-phonon coupling.
We find that in the considered material, electronic correlations are strongly
orbital- and momentum-dependent. Notably, the charge density wave and magnetic
instabilities originate from distinct orbitals. In particular, we show that the
correlation effects lead to the momentum-dependent hybridization between
different orbitals, resulting in the splitting and shifting of the flat part of
the Ni-$d_{z^2}$ band. This strong renormalization of the electronic spectral
function drives the charge density wave instability that is related to the
intraband Ni-$d_{z^2}$ correlations. Instead, the magnetic instability stems
from the Ni-$d_{x^2-y^2}$ orbital, which remains half-filled through the
redistribution of the electronic density between different bands even upon hole
doping. Consequently, the strength of the magnetic fluctuations remains nearly
unchanged for the considered doping levels. We argue that this renormalization
is not inherent to the stoichiometric case but can be induced by hole doping.
