The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, emph{charge re
gulation}, in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient charge regulation Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the LAMMPS molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of charge regulation on the nature of the polyelectrolyte coil--globule transition and on the effective interaction between oppositely charged nanoparticles.
We implement two recently developed fast Coulomb solvers, HSMA3D [J. Chem. Phys. 149 (8) (2018) 084111] and HSMA2D [J. Chem. Phys. 152 (13) (2020) 134109], into a new user package HSMA for molecular dynamics simulation engine LAMMPS. The HSMA package
is designed for efficient and accurate modeling of electrostatic interactions in 3D and 2D periodic systems with dielectric effects at the O(N) cost. The implementation is hybrid MPI and OpenMP parallelized and compatible with existing LAMMPS functionalities. The vectorization technique following AVX512 instructions is adopted for acceleration. To establish the validity of our implementation, we have presented extensive comparisons to the widely used particle-particle particle-mesh (PPPM) algorithm in LAMMPS and other dielectric solvers. With the proper choice of algorithm parameters and parallelization setup, the package enables calculations of electrostatic interactions that outperform the standard PPPM in speed for a wide range of particle numbers.
A modified 3D-Ewald summation is presented for accurately simulating the ion-dipole mixture under dielectric confinement. The method is based on the combination of image charges and image dipoles with the conventional Ewald summation and has a scalin
g O(^3/2). The accuracy and efficiency of our algorithm are examined through numerical examples.
Two main treatments within classical simulations for modeling a charged surface are using explicit, discrete charges and continuous, uniform charges. The computational cost can be substantially reduced if, instead of discrete surface charges, one use
s an electric field to represent continuous surface charges. In addition, many electrolyte theories, including the Poisson--Boltzmann theory, are developed on the assumption of uniform surface charge. However, recent simulations have demonstrated with discrete surface charges, one observes much stronger charge reversal, compared to the surfaces with continuous surface charges, when the lattice constant becomes notably larger than the ion diameter. These examples show that the two treatments for modeling a charged dielectric interface can lead to substantially different results. In this short note, we calculate the electrostatic force for a single point charge above an infinite plane, and compare the differences between discrete and continuous representations of surface charges. Our results show that while the continuous, uniform surface charge model gives a quite simple picture, the discrete surface charge model can offer several different cases even for such a simple problem, depending on the respective values of ion size versus lattice spacing and a self-image interaction parameter.
