We have carried out a theoretical study on the structure-function relationship for the selective oxidation of lower alkanes (C-1-C-4). The H abstraction mechanism has been examined over the model catalysts of high-valence d(0) transition metal oxides in the tetrahedral coordination. The intrinsic connections among the H abstraction barrier, the strengths of the O-H and the M-O bonds, the ability of electron transfer, as well as the energy gap of frontier orbitals of the oxides have been rationalized in terms of thermodynamics cycles and the frontier orbital analysis. In particular, we emphasize the role that the O-H bond strength plays in determining the reactivity of a metal oxide.