A scalable and accurate algorithm for the computation of Hartree–Fock exchange

Hartree–Fock exchange and hybrid density functionals have recently attracted renewed interest in electronic structure theory for the description of periodic systems, overcoming some of the limitations of local and semi-local approximations of density-functional theory (DFT). However, their use in plane-wave calculations for extended systems remains limited by poor convergence behavior regarding Brillouin-zone sampling and by a high overall computational cost. We present a computational approach that achieves quadratic convergence of exchange integrals with respect to Brillouin zone discretization, while using a compact representation of the exchange operator during non-self-consistent iterations. The computational cost is mitigated by an efficient parallel implementation. The method is applied to computations of Hartree–Fock and hybrid DFT (PBE0) band structures and structural parameters for bulk silicon and diamond.