Simulations of non-neutral slab systems with long-range electrostatic interactions in two-dimensional periodic boundary conditions

Abstract

We introduce a regularization procedure to define electrostatic energies and forces in a slab system of thickness h that is periodic in two dimensions and carries a net charge. The regularization corresponds to a neutralization of the system by two charged walls and can be viewed as the extension to the two-dimensional (2D)+h geometry of the neutralization by a homogeneous background in the standard three-dimensional Ewald method. The energies and forces can be computed efficiently by using advanced methods for systems with 2D periodicity, such as MMM2D or P3M/ELC, or by introducing a simple background-charge correction to the Yeh-Berkowitz approach of slab systems. The results are checked against direct lattice sum calculations on simple systems. We show, in particular, that the Madelung energy of a 2D square charge lattice in a uniform compensating background is correctly reproduced to high accuracy. A molecular dynamics simulation of a sodium ion close to an air/water interface is performed to demonstrate that the method does indeed provide consistent long-range electrostatics. The mean force on the ion reduces at large distances to the image-charge interaction predicted by macroscopic electrostatics. This result is used to determine precisely the position of the macroscopic dielectric interface with respect to the true molecular surface.

Efficient Algorithms for Electrostatic Interactions Including Dielectric Contrasts

“…Note that it is also possible to consider systems that are not charge neutral. Formally, one assumes two equally charged plates at the positions of the dielectric interfaces that cancel the total charge [28]. The field of a charged plate is, however, exactly what the |z|/(2ε m L 2 ) term represents, so that the above considerations for this term still hold.…”

Interfacial Tension Does Not Drive Asymmetric Nanoscale Electrowetting on Graphene

“…Since the simulation box is not periodic in the z-direction, the Coulomb force and potential are corrected in this direction to have a pseudo-2D Ewald summation. [36][37] The cutoff radius for the non-bonded interactions is 1.0 nm for the pure water and the salt solution. 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 12 the density distributions are averaged over 20 ps.…”

Long ranged interactions in computer simulations and for quasi-2D systems

“…[161] and more recently, the authors of Ref. [162] used also two charged walls to define correctly electrostatic energies and forces.…”