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Updated: Dec 31, 2025

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
Published on: April 12, 2019
Fast multipole method for three-dimensional systems with periodic boundary condition in two directions
Noriyuki Yoshii1,2, Yoshimichi Andoh1, Susumu Okazaki1,2
1Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya, 464-8603, Japan.
Abstract:
We derived a new expression for the electrostatic interaction of three-dimensional charge-neutral systems with two-dimensional periodic boundary conditions (slab geometry) using a fast multipole method (FMM). Contributions from all the image cells are expressed as a sum of real and reciprocal space terms, and a self-interaction term. The reciprocal space contribution consists of two parts: zero and nonzero terms of the absolute value of the reciprocal lattice vector. To test the new expressions, electrostatic interactions were calculated for a randomly placed charge distribution in a cubic box and liquid water produced by molecular dynamics calculation. The accuracy could be controlled by the degree of expansion of the FMM. In the present expression, the computational complexity of the electrostatic interaction of N-particle systems is order N, which is superior to that of the conventional two-dimensional periodic Ewald method for a slab geometry and the particle mesh Ewald method with a large empty space at an interface of the unit cell. © 2020 Wiley Periodicals, Inc.
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