Molybdenum dithiocarbamate (MoDTC) is a well-known lubricant additive, which, in tribological conditions, is capable of forming layers of MoS2 with excellent friction reduction properties. Despite being widely employed in commercial engine oils, a comprehensive theoretical description of the properties of MoDTC is still lacking. In this work, we employ density functional theory to study the structural, electronic, and vibrational properties of MoDTC. We investigate the relative stability of different isomers, different hydrocarbon terminations, and oxidized complexes. Oxidation was found to be energetically favorable for a wide range of conditions, and the most favorable position for oxygen atoms in MoDTC turned out to be the ligand position. These results, along with the calculated reaction energies for different dissociation paths, can be useful to better identify the elementary steps of the decomposition process of MoDTC.