Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

Area of Science:

• Theoretical Chemistry
• Computational Electrostatics
• Physical Chemistry

Background:

• Continuum electrostatics models are crucial for understanding molecular interactions.
• Nonlocal effects in solvents, particularly water, are significant for accurate molecular simulations.
• Existing models often require approximations or high computational cost.

Purpose of the Study:

• To present an exact, infinite-series solution for Lorentz nonlocal continuum electrostatics.
• To apply this method to spherical solutes with arbitrary charge distributions.
• To provide a computationally efficient approach for nonlocal model analysis.

Main Methods:

• Reformulating the partial differential equation (PDE) problem using boundary-integral equations.
• Diagonalizing boundary-integral operators via eigenfunctions (surface spherical harmonics).
• Re-deriving Kirkwood's results for a protein in a Stern layer and electrolyte using the linearized Poisson-Boltzmann equation.

Main Results:

• An exact solution for nonlocal electrostatics in separable geometries was achieved.
• The eigenfunction-expansion approach offers computational efficiency for nonlocal models.
• The study estimates the plausible range for the nonlocal length-scale parameter (λ).

Conclusions:

• Nonlocal solvent response may decrease the necessity of high dielectric constants for pH-dependent protein behavior.
• The developed method provides a framework for testing nonlocal model implications.
• Further research with more advanced nonlocal models is needed for comprehensive understanding.