Harmonic surface mapping algorithm for molecular dynamics simulations of particle systems with planar dielectric interfaces

Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations

Using Brownian dynamics simulations, we investigate the effects of confinement, adsorption on surfaces, and ion-ion interactions on the response of confined electrolyte solutions to oscillating electric fields in the direction perpendicular to the confining walls. Nonequilibrium simulations allows to characterize the transitions between linear and nonlinear regimes when varying the magnitude and frequency of the applied field, but the linear response, characterized by the frequency-dependent conductivity, is more efficiently predicted from the equilibrium current fluctuations. To that end, we (rederive and) use the Green-Kubo relation appropriate for overdamped dynamics, which differs from the standard one for Newtonian or underdamped Langevin dynamics. This expression highlights the contributions of the underlying Brownian fluctuations and of the interactions of the particles between them and with external potentials. Although already known in the literature, this relation has rarely been used to date, beyond the static limit to determine the effective diffusion coefficient or the DC conductivity. The frequency-dependent conductivity always decays from a bulk-like behavior at high frequency to a vanishing conductivity at low frequency due to the confinement of the charge carriers by the walls. We discuss the characteristic features of the crossover between the two regimes, most importantly how the crossover frequency depends on the confining distance and the salt concentration, and the fact that adsorption on the walls may lead to significant changes both at high and low frequencies. Conversely, our results illustrate the possibility to obtain information on diffusion between walls, charge relaxation, and adsorption by analyzing the frequency-dependent conductivity.

Improved Random Batch Ewald Method in Molecular Dynamics Simulations

The random batch Ewald (RBE) is an efficient and accurate method for molecular dynamics (MD) simulations of physical systems at the nano/microscale. The method shows great potential to solve the computational bottleneck of long-range interactions, motivating a necessity to accelerate short-range components of the nonbonded interactions for a further speedup of MD simulations. In this work, we present an improved RBE method for the nonbonding interactions by introducing the random batch idea to constructing neighbor lists for the treatment of both the short-range part of the Ewald splitting and the Lennard-Jones potential. The efficiency that the novel neighbor list algorithm owes to the stochastic minibatch strategy can significantly reduce the total number of neighbors. We obtain the error estimate and convergence by theoretical analysis and implement the improved RBE method in the LAMMPS package. Benchmark simulations are performed to demonstrate the accuracy and stability of the algorithm. Numerical tests on computer performance by conducting large-scaled MD simulations for systems including up to 0.1 billion water molecules are run on massive clusters with up to 50000 CPU cores, demonstrating the attractive features such as the high parallel scalability and memory-saving of the method in comparison to the existing methods.

Superscalability of the random batch Ewald method

Coulomb interaction, following an inverse-square force-law, quantifies the amount of force between two stationary and electrically charged particles. The long-range nature of Coulomb interactions poses a major challenge to molecular dynamics simulations, which are major tools for problems at the nano-/micro-scale. Various algorithms are developed to calculate the pairwise Coulomb interactions to a linear scale, but poor scalability limits the size of simulated systems. Here, we use an efficient molecular dynamics algorithm with the random batch Ewald method on all-atom systems where the complete Fourier components in the Coulomb interaction are replaced by randomly selected mini-batches. By simulating the N-body systems up to 10⁸ particles using 10 000 central processing unit cores, we show that this algorithm furnishes O(N) complexity, almost perfect scalability, and an order of magnitude faster computational speed when compared to the existing state-of-the-art algorithms. Further examinations of our algorithm on distinct systems, including pure water, a micro-phase separated electrolyte, and a protein solution, demonstrate that the spatiotemporal information on all time and length scales investigated and thermodynamic quantities derived from our algorithm are in perfect agreement with those obtained from the existing algorithms. Therefore, our algorithm provides a promising solution on scalability of computing the Coulomb interaction. It is particularly useful and cost-effective to simulate ultra-large systems, which is either impossible or very costly to conduct using existing algorithms, and thus will be beneficial to a broad range of problems at nano-/micro-scales.

Random-batch list algorithm for short-range molecular dynamics simulations

We propose a fast method for the calculation of short-range interactions in molecular dynamics simulations. The so-called random-batch list method is a stochastic version of the classical neighbor-list method to avoid the construction of a full Verlet list, which introduces two-level neighbor lists for each particle such that the neighboring particles are located in core and shell regions, respectively. Direct interactions are performed in the core region. For the shell zone, we employ a random batch of interacting particles to reduce the number of interaction pairs. The error estimate of the algorithm is provided. We investigate the Lennard-Jones fluid by molecular dynamics simulations and show that this novel method can significantly accelerate the simulations with a factor of several fold without loss of the accuracy. This method is simple to implement, can be well combined with any linked cell methods to further speed up and scale up the simulation systems, and can be straightforwardly extended to other interactions, such as Ewald short-range part, and thus it is promising for large-scale molecular dynamics simulations.

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.