A particle-particle, particle-density algorithm for the calculation of electrostatic interactions of particles with slablike geometry

A fast spectral method for electrostatics in doubly periodic slit channels

We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using Ewald splitting to replace the original Poisson equation for nearly singular sources with a smooth far-field Poisson equation, combined with a localized near-field correction. Unlike existing spectral Ewald methods, which make use of the Fourier transform in the aperiodic direction, we recast the problem as a two-point boundary value problem in the aperiodic direction for each transverse Fourier mode for which exact analytic boundary conditions are available. We solve each of these boundary value problems using a fast, well-conditioned Chebyshev method. In the presence of dielectric jumps, combining Ewald splitting with the classical method of images results in smoothed charge distributions, which overlap the dielectric boundaries themselves. We show how to preserve the spectral accuracy in this case through the use of a harmonic correction, which involves solving a simple Laplace equation with smooth boundary data. We implement our method on graphical processing units and combine our doubly periodic Poisson solver with Brownian dynamics to study the equilibrium structure of double layers in binary electrolytes confined by dielectric boundaries. Consistent with prior studies, we find strong charge depletion near the interfaces due to repulsive interactions with image charges, which points to the need for incorporating polarization effects in understanding confined electrolytes, both theoretically and computationally.

Surface reconstructions and premelting of the (100) CaF2 surface

In this work, surface reconstructions on the (100) surface of CaF2 are comprehensively investigated. The configurations were explored by employing the Minima Hopping Method (MHM) coupled to a machine-learning interatomic potential, that is based on a charge equilibration scheme steered by a neural network (CENT). The combination of these powerful methods revealed about 80 different morphologies for the (100) surface with very similar surface formation energies differing by not more than 0.3 J m-2. To take into account the effect of temperature on the dynamics of this surface as well as to study the solid-liquid transformation, molecular dynamics simulations were carried out in the canonical (NVT) ensemble. By analyzing the atomic mean-square displacements (MSD) of the surface layer in the temperature range of 300-1200 K, it was found that in the surface region the F sublattice is less stable and more diffusive than the Ca sublattice. Based on these results we demonstrate that not only a bulk system, but also a surface can exhibit a sublattice premelting that leads to superionicity. Both the surface sublattice premelting and surface premelting occur at temperatures considerably lower than the bulk values. The complex behaviour of the (100) surface is contrasted with the simpler behavior of other low index crystallographic surfaces.

Communications: The Metropolis Monte Carlo finite element algorithm for electrostatic interactions

The Metropolis Monte Carlo algorithm with the finite element method applied to compute electrostatic interaction energy between charge densities is described in this work. By using the finite element method to integrate numerically Poisson's equation, it is shown that the computing time to obtain the acceptance probability of an elementary trial move does not, in principle, depend on the number of charged particles present in the system.