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

Area of Science:

• Computational Physics
• Materials Science
• Quantum Chemistry

Background:

• Pseudopotential representations on real-space grids can suffer from the "egg box" effect, leading to unphysical oscillations.
• This effect arises from the interpolation of electron-ion potentials onto discrete grid points.

Purpose of the Study:

• To develop a new scheme for representing pseudopotentials on finite real-space grids.
• To significantly reduce or eliminate the "egg box" effect in computed quantities.

Main Methods:

• A novel scheme is proposed that avoids direct interpolation of the electron-ion potential.
• The method uses a weighted sum of translation operators from a reference position to account for atomic positions.
• The scheme generates a nonlocal but banded representation compatible with existing operators.

Main Results:

• The new scheme reduces fluctuations by at least three orders of magnitude.
• Demonstrated effectiveness in one dimension for local, nonlocal, and self-consistent potentials.
• The approach is compatible with various pseudopotential types and computational methods.

Conclusions:

• The proposed real-space grid scheme effectively mitigates the "egg box" effect.
• This method offers a more accurate and stable representation of pseudopotentials.
• The approach is generalizable to three dimensions without modification.