Difficulty in predicting shallow defects with hybrid functionals: Implication of the long-range exchange interaction

We identify an important issue in defect studies using hybrid functionals. When modeling a defect, which is supposedly an isolated system, with a finite-size supercell, the inclusion of a fraction of the Hartree-Fock interaction results in a strong cell-size dependence and an extremely slow convergence of the calculated defect properties, especially for shallow defect. These behaviors may give rise to a number of errors in calculated defect properties, including the deepening of transition level and overstabilization of shallow defects. Numerical results from hybrid functional calculations for a diverse array of systems can be understood within the Hartree-Fock theory of an electron-gas model, indicating that the long-range exchange is the main cause for the errors in the calculated defect properties within hybrid functionals.