The hydrogen diffusion in NiO is closely relevant to various applications of Ni-based metals, which are inevitably passivated by native oxides. The precise description of hydrogen diffusion in NiO is always complicated by the coexistence of many influential electronic-structure and lattice-dynamics mechanisms, which are unraveled by the combinatorial first-principles calculations based on density-functional theory (DFT) here. Firstly, based on two widely recognized semilocal density functionals (i.e., PBE and PBEsol), the electronic correlation potential for the $\mathrm{Ni}\text{−}3d$ orbital is efficiently described by the $\mathrm{DFT}+U$ model, with the Hubbard-$U$ value determined by using the linear-response theory. The benchmark calculations of crystal structure, bulk modulus, electronic-structure properties, vibrational spectra, and thermal expansion of NiO comprehensively confirm the high systematic accuracy of $\mathrm{PBEsol}+U$ model. Then, it is used to calculate the diffusion paths, kinetic energies, and diffusion rates of H in NiO, where the synergistic effects of multiple factors (e.g., electronic correlation, interatomic bonding, magnetic superexchange interaction, local lattice distortion, atomic vibrations, and thermal expansion) are quantitatively portrayed. The high directional anisotropy is found in the hydrogen diffusion paths and is attributed to the magnetic anisotropy in NiO, allowing the kinetic tunability by thermal and magnetic-field manipulations. A kinetic Monte Carlo method is designed to simulate the multiscale diffusion behaviors of H in NiO, and to yield the diffusion coefficients. A spatial-dimensionality transition is discovered in the simulated diffusion trajectories of H upon heating. Finally, the isotope effects on hydrogen-diffusion rates are also predicted, and will be important for many radioactive situations.

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• Defects
• Electronic structure
• First-principles calculations
• Lattice dynamics
• Magnetic coupling
• Thermal properties