Using first-principles calculations based on density functional theory, we systematically study the adsorption and diffusion behaviors of single oxygen (O) atom on the (0 0 1) surfaces of TiN, ZrN and HfN nitride coatings. The top of N site (top(N)) is the most energetic favorable site for O atom and followed by the hollow site for all the three nitrides. O atom tends to diffuse on the (0 0 1) surfaces of the nitrides from the top of transition metal top(TM) sites to a neighboring top(TM) sites by avoiding N sites. The adsorption of O on ZrN and HfN is more stable than that on TiN. Our findings could explain the experimental phenomenon that the oxide thickness of TiN is smaller than that of ZrN under the same oxidation conditions. (C) 2018 Elsevier B.V. All rights reserved.