Kohn-Sham approach for fast hybrid density functional calculations in real-space numerical grid methods

Real-space methods have not been suitable for hybrid density functional calculations due to high cost coming from the nonlocality of Fock operator. Here we propose a practical approach for fast computation. The key is to use a strictly local Kohn-Sham potential that can be deduced from any hybrid functional using the optimized effective potential method. This new approach improved the computation speed of the global and range-separated hybrid methods up to 30 and 80 times, respectively. As a result, accurate prediction of the size-dependent excitonic spectra of Si quantum dots became feasible.