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We present a robust strategy to numerically sample the Coulomb potential in reciprocal space for periodic Born–von Karman cells of general shape. Our approach tackles two common issues of plane-wave based implementations of Coulomb integrals under periodic boundary conditions: the treatment of the singularity at the Brillouin-zone center and discretization errors, which can cause severe convergence problems in anisotropic cells, necessary for the calculation of low-dimensional systems. We apply our strategy to the Hartree–Fock and coupled cluster (CC) theories and discuss the consequences of different sampling strategies on different theories. We show that sampling the Coulomb potential via the widely used probe-charge Ewald method is unsuitable for CC calculations in anisotropic cells. To demonstrate the applicability of our developed approach, we study two representative, low-dimensional use cases: the infinite carbon chain, for which we report the first periodic CCSD(T) potential energy surface, and a surface slab of lithium hydride, for which we demonstrate the impact of different sampling strategies for calculating surface energies. We find that our Coulomb sampling strategy serves as a vital solution, addressing the critical need for improved accuracy in plane-wave based CC calculations for low-dimensional systems. 

Abstract Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schrödinger equation are crucial for computational materials science. Methods such as coupled cluster theory show potential for widespread adoption if computational cost bottlenecks can be removed. For example, extremely densek-point grids are required to model long-range electronic correlation effects, particularly for metals. Although these grids can be made more effective by averaging calculations over an offset (or twist angle), the resultant cost in time for coupled cluster theory is prohibitive. We show here that a single special twist angle can be found using the transition structure factor, which provides the same benefit as twist averaging with one or two orders of magnitude reduction in computational time. We demonstrate that this not only works for metal systems but also is applicable to a broader range of materials, including insulators and semiconductors.