Methanol is a liquid hydrogen carrier and potential platform molecule, and significant efforts are currently devoted to hydrogenate CO2 to methanol. In this work, hydrogenations of CO2 and captured CO2 (as dimethyl-carbamic acid, DMCA, and methylcarbamic acid, MCA) to methanol over Ru-MACHO (pre)catalysts were studied with a Ru-II-catalyst model by Density Functional Theory (DFT) calculations. For the hydrogenation of CO2, the concerted reaction was the rate-determining step involving a synchronous hydride transfer and proton transfer from the Ru-II-catalyst to coordinatively saturated intermediate methanediol. In the hydrogenation cycles of DMCA and MCA, the first hydride transfer reactions were more difficult than the concerted hydride and proton transfer from the Ru-II-catalyst to the aldehyde group of intermediate formaldehyde. These first hydride transfer reactions were identified as the rate-determining steps. The hydrogenations of DMCA and MCA were found much more favourable in methanol production than the direct CO2 hydrogenation, however, formamides could be main intermediate products due to the easier C-O breakage than C-N breakage in gem diols, and during the further hydrogenation of formamides, formaldehyde could be the main intermediate due to the easier C-N breakage than C-O breakage in alkanolamines. In all three hydrogenation cases, the amino (NH) ligand of the Ru-II-catalyst initially remained chemically innocent, and intermediates were stabilized by N-H center dot O hydrogenbonding interactions (HBIs) facilitating the continuation of catalytic hydrogenation cycles, but the NH ligand took part in multi-bond concerted reactions to produce eventually methanol.