Ewaldsomatie

Ewaldsomatie is a computational technique used to calculate long-range electrostatic interactions in periodic systems, such as crystals, liquids, or biomolecules, where charges interact across an infinite lattice. The method was introduced by Paul Peter Ewald in 1921 to overcome the slow convergence of direct lattice sums. In Dutch-language literature, the term Ewaldsomatie is commonly used to refer to this approach or its standard implementations.

The core idea is to split the Coulomb potential into two rapidly convergent parts by introducing a damping parameter alpha. The real-space part, which decays quickly, handles short-range interactions, while the reciprocal-space part, computed in Fourier space, accounts for long-range contributions. A self-interaction correction removes the unphysical interaction of a charge with its own smeared distribution. The split is typically written in terms of erfc and erf functions, which control how much of the interaction is treated in real space versus reciprocal space. The method assumes periodic boundary conditions and requires careful choice of parameters (alpha and real/reciprocal-space cutoffs) to balance accuracy and efficiency.

Variants of the Ewald approach have been developed to improve performance. The traditional Ewald summation scales roughly as O(N^3/2), whereas particle-mmesh methods, such as Particle Mesh Ewald (PME) and Smooth PME, reduce scaling to near O(N log N) for large systems. Ewaldsomatie remains widely used in molecular dynamics, materials science, and computational chemistry due to its accuracy in treating long-range electrostatics, though it requires careful parameter selection and, for charged or non-neutral systems, finite-size correction.