MMM1D: a method for calculating electrostatic interactions in one-dimensional periodic geometries.

Area of Science:

• Computational physics
• Electrostatics
• Materials science

Background:

• Accurate calculation of electrostatic interactions is crucial in condensed matter physics and materials science.
• Periodic boundary conditions are commonly used to model bulk materials, but they pose challenges for electrostatic calculations.
• Existing methods for handling electrostatic sums in periodic systems can be computationally expensive or complex.

Purpose of the Study:

• To introduce a novel and efficient method for computing electrostatic energy and forces in systems with one-dimensional periodic boundary conditions.
• To provide rigorous error bounds for the calculated energies and forces.
• To offer a computationally advantageous alternative to current methods.

Main Methods:

• The Coulomb sum is transformed using a convergence factor.
• This transformation results in a series of fast-decaying functions, analogous to the Lekner method.
• The method's accuracy and error bounds are rigorously derived and numerically validated.

Main Results:

• The new method accurately calculates electrostatic energy and forces for systems with periodic boundary conditions.
• Rigorous error bounds for energies and forces have been derived and numerically confirmed.
• The method demonstrates a computational complexity of O(N^2).

Conclusions:

• The presented method provides an accurate and efficient way to compute electrostatic interactions in periodic systems.
• It offers practical advantages in terms of speed and ease of implementation over existing approaches.
• This method has the potential to accelerate simulations in various fields of computational physics and chemistry.