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

► Basis set methods are developed for nonlocal exchange-correlation energy functionals. ► Geminal basis sets rapidly converge for 6-dimensional exchange-correlation integrals. ► Potential-type basis functions are used to circumvent the Coulomb singularity. ► Hermite gaussian functions allow explicit and efficient analytic integral evaluation.