Harmonic surface mapping algorithm for molecular dynamics simulations of particle systems with planar dielectric...

Area of Science:

• Computational physics
• Physical chemistry
• Materials science

Background:

• Simulating charged particles near dielectric interfaces is crucial for understanding complex fluids.
• Existing methods often struggle with computational efficiency and accuracy for long-range electrostatic interactions.

Purpose of the Study:

• To develop an accurate and efficient computational method for molecular dynamics simulations of charged particles confined by planar dielectric interfaces.
• To address the challenges of long-range electrostatic interactions in such systems.

Main Methods:

• The algorithm combines the image-charge method for near-field interactions with harmonic surface mapping for far-field contributions.
• Far-field charges are represented by a finite set of charges on an auxiliary sphere, approximated using spherical harmonic expansion.
• Dirichlet-to-Neumann boundary conditions are fitted to determine expansion coefficients.
• Green's second identity transforms the series expansion into a spherical integral, enabling the use of the fast multipole method for O(N) complexity.

Main Results:

• The developed method achieves linear O(N) complexity for summing electrostatic interactions.
• The approach accurately captures the electrostatic potential of charged particles under dielectric confinement.
• The method is validated for its efficiency and accuracy in handling complex systems.

Conclusions:

• The novel algorithm provides an accurate and computationally efficient solution for molecular dynamics simulations of charged systems with dielectric interfaces.
• This method is broadly applicable to various charged complex fluids, advancing simulation capabilities in condensed matter physics and chemistry.