Fast hybrid density-functional computations using plane-wave basis sets

A new, very fast, implementation of the exact (Fock) exchange operator for electronic-structure calculations within the plane-wave pseudopotential method is described and carefully validated. Our method combines the recently proposed adaptively compressed exchange approach, to reduce the number of times the exchange is evaluated in the self-consistent loop, with an orbital localization procedure that reduces the number of exchange integrals to be computed at each evaluation. The new implementation, already available in the Q uantum ESPRESSO distribution, results in a speedup that is never smaller than 3–4 × and that increases with the size of the system, according to various realistic benchmark calculations.