  In this work, we use modern electronic structure methods to model the
catalytic mechanism of different variants of the molybdenum cofactor (Moco). We
investigate the dependence of various Moco model systems on structural
relaxation and the importance of environmental effects for five critical points
along the reaction coordinate with the DMSO and NO$_3^-$ substrates.
Furthermore, we scrutinize the performance of various coupled-cluster
approaches for modeling the relative energies along the investigated reaction
paths, focusing on several pair coupled cluster doubles (pCCD) flavors and
conventional coupled cluster approximations. Moreover, we elucidate the Mo--O
bond formation using orbital-based quantum information measures, which
highlight the flow of $\sigma_{\rm M-O}$ bond formation and $\sigma_{\rm
N/S-O}$ bond breaking. Our study shows that pCCD-based models are a viable
alternative to conventional methods and offer us unique insights into the
bonding situation along a reaction coordinate. Finally, this work highlights
the importance of environmental effects or changes in the core and,
consequently, in the model itself to elucidate the change in activity of
different Moco variants.
