Rigorous Error Bounds for Ewald Summation of Electrostatics at Planar Interfaces

Area of Science:

• Computational physics
• Materials science
• Electrostatics

Background:

• Evaluating electrostatic interactions in periodic systems is crucial for materials science.
• Existing Ewald summation methods can be computationally intensive.
• Accurate treatment of interfaces and finite systems requires specialized corrections.

Purpose of the Study:

• To develop a rigorous and efficient Ewald summation formula for 2D periodic planar interfaces in 3D systems.
• To unify electrostatic layer and boundary corrections within a single framework.
• To provide precise error bounds for the summation method.

Main Methods:

• Rewriting the Fourier part of the Ewald2D summation to a closed-form Fourier integral.
• Deriving electrostatic layer and boundary corrections from a rigorous trapezoidal summation.
• Utilizing contour integrals to define exact corrections and error bounds.
• Performing numerical calculations of Madelung constants in slab model ionic crystals.

Main Results:

• A novel Ewald summation formula for 2D periodic planar interfaces is presented.
• Electrostatic layer and boundary corrections naturally emerge from the new formulation.
• The method offers precise error bounds based on system parameters.
• Analytical results are validated by numerical computations on model ionic crystals.

Conclusions:

• The presented Ewald summation formula offers a rigorous and efficient approach to calculating electrostatic interactions in complex systems.
• The unified treatment of corrections simplifies analysis and improves accuracy.
• This work provides a valuable tool for computational materials science and condensed matter physics.