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.
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