General Approach for Reducing Continuous Translational Symmetry Errors in Finite Difference Real-Space Calculations.

We provide a new scheme for representing pseudopotentials on a finite real-space grid, designed to significantly reduce the "egg box" (also known as the "egg carton") effect, i.e., unphysical fluctuations of computed quantities upon real-space translation. Instead of interpolating the electron-ion potential onto the grid, our scheme starts at a reference position and then uses a weighted sum of translation operators to account for the positions of atoms in real space. This results in a nonlocal but banded representation (even for local potentials) which is fully compatible with nonlocal pseudopotential operators. As a demonstration, this scheme is tested in one dimension for three types of potentials: a local pseudopotential, a nonlocal pseudopotential, and a local pseudopotential with self-consistent Hartree and exchange-correlation potentials. This scheme is found to reduce fluctuations of examined quantities by at least three orders of magnitude. The approach requires neither grid adaptation nor pseudopotential modification and can be readily extended to the three-dimensional case.