Efficient Computation of the Hartree–Fock Exchange in Real-Space with Projection Operators

We describe an efficient projection-based real-space implementation of the nonlocal single-determinant exchange operator. Through a matrix representation of the projected operator, we show that this scheme works equally well for both occupied and virtual states. Our scheme reaches a speedup of 2 orders of magnitude and has no significant loss of accuracy compared to an implementation of the full nonlocal single-determinant exchange operator. We find excellent agreement upon comparing Hartree–Fock eigenvalues, dipoles, and polarizabilities of selected molecules calculated using our method to values in the literature. To illustrate the efficiency of this scheme we perform calculations on systems with up to 240 carbon atoms.