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

We have developed a new scheme to install pseudopotentials on a finite real-space grid that significantly reduces unphysical fluctuations of quantities for fractional grid-point shifts in real space. Instead of interpolating the potential on the grid, this scheme chooses a reference position and use a translation method to represent positions of atoms in real space. This translation is exact for integer grid-point shifts and is designed to minimize the "egg box" effect for fractional grid-point shifts. It provides nonlocal but banded representations for local potentials and is compatible with nonlocal pseudopotential operators. As a demonstration, this scheme is tested in one dimension for three types of potentials: a local ionic potential, a local ionic potential plus a nonlocal operator, and a local ionic potential plus the Hartree and exchange-correlation potential. Fluctuations of examined quantities are reduced by four orders, four orders, and three orders, respectively. This scheme does not require the manipulation of grids and can be easily extended to the three-dimensional case.