  In this work, we report the pressure dependence of the effective Coulomb
interaction parameters (Hubbard U) in paramagnetic NiO within the constrained
random phase approximation (cRPA). We consider five different low energy models
starting from the most expensive one that treats both Ni-d and O-p states as
correlated orbitals (dp-dp model) to the smallest possible two-orbital model
comprising the eg states only (eg-eg model). We find that in all the considered
models, the bare interactions are not very sensitive to the compression.
However the partially screened interaction parameters show an almost linear
increment as a function of compression, resulting from the substantial
weakening of screening effects upon compression. This counterintuitive trend is
explained from the specific characteristic changes of the basic electronic
structure of this system. We further calculate the nearest neighbor inter-site
d-d interaction terms which also show substantial enhancement due to
compression. Our results for both the experimental and highly compressed
structures reveal that the frequency dependence of the partially screened
interactions can not be ignored in a realistic modeling of NiO. We also find
that the computed interaction parameters for the antiferromagnetic NiO are
almost identical to their paramagnetic counter parts.
