Efficient plane-wave approach to generalized Kohn-Sham density-functional theory of solids with mixed deterministic/stochastic exchange

An efficient mixed deterministic/sparse-stochastic plane-wave approach is developed for bandstructure calculations of large supercell periodic generalized-Kohn-Sham density functional theory, for any hybrid-exchange density functional. The method works for very large elementary cells and supercells, and we benchmark it on covalently bonded solids and molecular crystals with nonbonded interactions, for supercells of up to 33,000 atoms. Memory and CPU requirements scale with supercell size quasi-linearly.