The reaction pathway and energetics for methane-to-methanol conversion by first-row transition-metal oxide ions (MO(+)s) are discussed from density functional theory (DFT) B3LYP calculations, where M is Sc. Ti, V, Cr, Mn, Fe, Co, Ni, and Cu. The methane-to-methanol conversion by these MO+ complexes is proposed to proceed in a two-step manner via two transition states: MO+ + CH4 --> OM+(CH4) --> [TS] --> OH-M+-CH3 --> [TS] --> M+(CH3OH) --> M+ + CH3OH. Both high-spin;and low-spin potential energy surfaces are characterized in detail. A crossing between the high-spin and the low-spin potential energy surfaces occurs once near the exit channel for ScO+, TiO+, VO+ CrO+, and MnO+, but it occurs twice in the entrance and exit channels for FeO+, CoO+, and NiO+. Our calculations strongly suggest that spin Inversion can occur near a crossing region of potential energy surfaces and that it can play a significant role in decreasing the barrier heights of these transition states. The reaction pathway from methane to methanol is uphill in energy on the early MO+ complexes (ScO+, TiO+, and VO+); thus, these complexes are not good mediators for the formation of methanol. On the other hand, the late MO+ complexes (FeO+, NiO+, and CuO+) are expected from the general energy profiles of the reaction pathways to efficiently convert methane to methanol, Measured reaction efficiencies and methanol branching ratios for MnO+, FeO+, CoO+, and NiO+ are rationalized from the energetics of the high-spin and the low-spin potential energy surfaces. The energy diagram for the methane-to-methanol conversion by CuO+ is downhill toward the product direction, and thus CuO+ is likely to be an excellent mediator for methane hydroxylation.