  Late transition-metal oxides with small charge-transfer energy $\Delta$ raise
issues for state-of-the-art correlated electronic structure schemes such as the
combination of density functional theory (DFT) with dynamical mean-field theory
(DMFT). The accentuated role of the oxygen valence orbitals in these compounds
asks for an enhanced description of ligand-based correlations. Utilizing the
rocksalt-like NiO as an example, we present an advancement of charge
self-consistent DFT+DMFT by including self-interaction correction (SIC) applied
to oxygen. This introduces explicit onsite O correlations as well as an
improved treatment of intersite $p-d$ correlations. Due to the efficient SIC
incorporation in a pseudopotential form, the DFT+sicDMFT framework is an
advanced but still versatile method to address the interplay of charge-transfer
and Mott-Hubbard physics. We revisit the spectral features of stoichiometric
NiO and reveal the qualitative sufficiency of local DMFT self-energies in
describing spectral peak structures usually associated with explicit nonlocal
processes. For Li$_x$Ni$_{1-x}$O, prominent in-gap states are verified by the
present theoretical study.
