Addressing the Coulomb potential singularity in exchange-correlation energy integrals with one-electron and two-electron basis sets

Nonlocal functionals for the exchange-correlation energy like the weighted density approximation require evaluating six-dimensional integrals with a Coulomb singularity. The convergence of a straightforward grid-based approach is linear in the number of grid points, because grid points where the integrand’s magnitude exceeds a threshold must be neglected. This slow convergence makes extrapolation to the infinite-grid limit problematic. We …