Fast calculation of the electrostatic potential in ionic crystals by direct summation method

Area of Science:

• Solid State Physics
• Computational Materials Science
• Crystallography

Background:

• The Madelung potential is crucial for understanding the electrostatic properties of ionic crystals.
• Existing methods like Ewald summation are computationally intensive.
• Real-space methods offer an alternative but often face convergence challenges.

Purpose of the Study:

• To develop a novel, efficient real-space method for Madelung potential calculation.
• To demonstrate exponential convergence in series summation for ionic crystals.
• To provide a computationally efficient alternative to traditional methods.

Main Methods:

• Extension of Evjen's method for real-space potential evaluation.
• Analysis of series convergence based on canceled multipolar moments.
• Utilizes simple algebraic functions for calculations.

Main Results:

• Achieved exponential convergence rate for Madelung potential series.
• The method's efficiency is comparable to the established Ewald's method.
• Demonstrated the use of simple algebraic functions, simplifying computation.

Conclusions:

• The proposed real-space method provides an efficient and accurate way to compute Madelung potentials.
• Offers a computationally advantageous alternative using basic algebraic operations.
• Significant implications for materials science simulations and theoretical crystallography.