Efficient Computation of Hartree-Fock Exchange Using Recursive Subspace Bisection

We use a recursive subspace bisection approach introduced in Phys. Rev. Lett. 2009, 102, 166406 to accelerate the computation of the Hartree-Fock exchange operator in plane-wave pseudopotential electronic structure calculations. Recursive subspace bisection allows for an unbiased localization of orbitals in domains of varying size and a truncation of orbitals that preserves accuracy in a controlled manner. This representation is used to accelerate the computation of the Hartree-Fock exchange operator, which in turn makes first-principles molecular dynamics simulations based on hybrid density functionals feasible for larger systems than previously possible. We describe a parallel implementation of the method and a load balancing algorithm. The efficiency and accuracy of this approach are demonstrated in electronic structure calculations of a chloride ion solvated in liquid water and calculations of the vacancy formation energy in a 512-atom silicon crystal using the PBE0 hybrid exchange-correlation functional.