Exact Coulomb cutoff technique for supercell calculations

We present a new reciprocal space analytical method to cutoff the long range interactions in supercell calculations for systems that are infinite and periodic in 1 or 2 dimensions, extending previous works for finite systems. The proposed cutoffs are functions in Fourier space, that are used as a multiplicative factor to screen the bare Coulomb interaction. The functions are analytic everywhere but in a sub-domain of the Fourier space that depends on the periodic dimensionality. We show that the divergences that lead to the non-analytical behaviour can be exactly cancelled when both the ionic and the Hartree potential are properly screened. This technique is exact, fast, and very easy to implement in already existing supercell codes. To illustrate the performance of the new scheme, we apply it to the case of the Coulomb interaction in systems with reduced periodicity (as one-dimensional chains and layers). For those test cases we address the impact of the cutoff in different relevant quantities for ground and excited state properties, namely: the convergence of the ground state properties, the static polarisability of the system, the quasiparticle corrections in the GW scheme and in the binding energy of the excitonic states in the Bethe-Salpeter equation. The results are very promising.