Range-Separated Approach to the RPA Correlation Applied to the van der Waals Bond and to Diffusion of Defects

The random-phase approximation (RPA) is a promising approximation to the exchange-correlation energy of density functional theory, since it contains the van der Waals (vdW) interaction and yields a potential with the correct band gap. However, its calculation is computationally very demanding. We apply a range-separation concept to RPA and demonstrate how it drastically speeds up the calculations without loss of accuracy. The scheme is then successfully applied to a layered system subjected to weak vdW attraction and is used to address the controversy of the self-diffusion in silicon. We calculate the formation and migration energies of self-interstitials and vacancies taking into account atomic relaxations. The obtained activation energies deviate significantly from the earlier calculations and challenge some of the experimental interpretations: the diffusion of vacancies and interstitials has almost the same activation energy.