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Fast multipole method for three‐dimensional systems with periodic boundary condition in two directions
Author(s) -
Yoshii Noriyuki,
Andoh Yoshimichi,
Okazaki Susumu
Publication year - 2020
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.26141
Subject(s) - multipole expansion , fast multipole method , periodic boundary conditions , boundary (topology) , boundary value problem , mathematics , mathematical analysis , computer science , physics , quantum mechanics
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.