Supersampling method for efficient grid-based electronic structure calculations.

Area of Science:

• Computational physics
• Quantum chemistry

Background:

• The egg-box effect causes inaccuracies in grid-based electronic structure calculations.
• This effect arises from discretizing continuous space, leading to spurious energy and force variations.
• Suppressing the egg-box effect is vital for efficient and accurate computational methods.

Purpose of the Study:

• To investigate methods for alleviating the egg-box effect in grid-based calculations.
• To demonstrate the efficacy of the supersampling method for reducing computational errors.
• To identify optimal filtering techniques for mitigating spurious variations.

Main Methods:

• Implementation of the supersampling method to reduce the rapidly varying components of target functions.
• Application of sinc filtering as an ideal low-pass filter.
• Analysis of the impact of grid spacing on computational accuracy.

Main Results:

• The supersampling method significantly reduces the egg-box effect.
• Sinc filtering proved most effective in eliminating high-frequency components.
• The method allows for larger grid spacings without compromising accuracy.

Conclusions:

• Supersampling is a highly effective strategy for mitigating the egg-box effect.
• The use of sinc filtering enhances the performance of supersampling.
• This approach offers a pathway to more accurate and efficient electronic structure calculations.