  Exact (Hartree Fock) exchange is needed to overcome some of the limitations
of local and semilocal approximations of density functional theory (DFT). So
far, however, computational cost has limited the use of exact exchange in plane
wave calculations for extended systems. We show that this difficulty can be
overcome by performing a unitary transformation from Bloch to Maximally
Localized Wannier functions in combination with an efficient technique to
compute real space Coulomb integrals. The resulting scheme scales linearly with
system size. We validate the scheme with representative applications.
