  The incorporation and diffusion of helium (He) with and without intrinsic
vacancy defects in cubic ZrO$_{2}$ are investigated through first-principles
total-energy calculations, in which the projector-augmented-wave (PAW) method
with the generalized gradient approximation (GGA) is used. The calculated
formation energies of intrinsic point defects indicate that cubic ZrO$_{2}$ has
a tolerant resistance to radiation damage. The incorporation energy of He
impurity shows that it is preferable to occupy the Zr vacancy at first, whereas
the solution energy suggests that He would be accommodated in the interstitial
site at thermodynamic equilibrium concentration. By calculating the He
migration energies corresponding to both interstitial and vacancy assisted
mechanisms, we suggest that it is most likely for He to diffuse by hopping
through a single vacancy. Remarkably, our calculated vacancy-assisted diffusion
energy of He is consistent well with the experimental measurement.
