Method for the fast evaluation of Fock exchange for nonlocalized wave functions

We introduce an approach that allows us to significantly reduce the computational cost for the evaluation of the Fock exchange operator when it is applied to an arbitrary periodic wave function in the case of large simulation cells. This method is based on the exponential decay properties of the density matrix and can be applied to systems exhibiting a finite electronic gap. Our scheme does not require the evaluation of Wannier's functions and can be easily implemented in density-functional theory codes based on plane waves. We first validate and benchmark the approach on the isolated benzene molecule, and then we apply it to the isolated tetraphenylporphyrin molecule (C44H30N4) and to a model of bulk Si comprising 512 atoms.