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We present a robust strategy to numerically sample the Coulomb potential inreciprocal space for periodic Born-von Karman cells of general shape. Ourapproach tackles two common issues of plane-wave based implementations ofCoulomb integrals under periodic boundary conditions, the treatment of thesingularity at the Brillouin-zone center, as well as quadrature errors, whichcan cause severe convergence problems in anisotropic cells, necessary for thecalculation of low-dimensional systems. We apply our strategy to theHartree-Fock (HF) and coupled cluster (CC) theory and discuss the consequencesof different sampling strategies on the different theories. We show thatsampling the Coulomb potential via the widely used probe-charge Ewald method isunsuitable for CC calculations in anisotropic cells. To demonstrate theapplicability of our developed approach, we study two representative,low-dimensional use cases: the infinite carbon chain, for which we report thefirst periodic CCSD(T) potential energy surface, as well as a surface slab oflithium hydride, for which we demonstrate the impact of different samplingstrategies for calculating surface energies. We find that our Coulomb samplingstrategy serves as a vital solution, addressing the critical need for improvedaccuracy in plane-wave based CC calculations for low-dimensional systems.

Sampling the reciprocal Coulomb potential in finite and anisotropic cells