The homogeneity condition: A simple way to derive isotropic periodic sum potentials for efficient calculation of long-range interactions in molecular simulation

Non-Ewald methods for evaluating the electrostatic interactions of charge systems: similarity and difference

In molecular simulations, it is essential to properly calculate the electrostatic interactions of particles in the physical system of interest. Here we consider a method called the non-Ewald method, which does not rely on the standard Ewald method with periodic boundary conditions, but instead relies on the cutoff-based techniques. We focus on the physicochemical and mathematical conceptual aspects of the method in order to gain a deeper understanding of the simulation methodology. In particular, we take into account the reaction field (RF) method, the isotropic periodic sum (IPS) method, and the zero-multipole summation method (ZMM). These cutoff-based methods are based on different physical ideas and are completely distinguishable in their underlying concepts. The RF and IPS methods are "additive" methods that incorporate information outside the cutoff region, via dielectric medium and isotropic boundary condition, respectively. In contrast, the ZMM is a "subtraction" method that tries to remove the artificial effects, generated near the boundary, from the cutoff sphere. Nonetheless, we find physical and/or mathematical similarities between these methods. In particular, the modified RF method can be derived by the principle of neutralization utilized in the ZMM, and we also found a direct relationship between IPS and ZMM.

Determination of van der Waals Parameters Using a Double Exponential Potential for Nonbonded Divalent Metal Cations in TIP3P Solvent

A double exponential (DE) functional form for Lennard-Jones (LJ) interactions, proposed in our previous study, has many advantages over LJ potentials including a natural softcore characteristic for the convenience of the pathway-based free-energy calculations, fast convergence, and flexibility in use. In this work, we put the first step on the application of the DE functional form by identifying a DE potential, coined DE-TIP3P, for molecular simulations using the TIP3P water model. The developed DE-TIP3 potential was better than LJ potential in reproducing the experimental water properties. Afterward, we developed the nonbonded models of 15 divalent metal ions, which frequently appear and play vital roles in biological systems, to be consistent with the DE-TIP3P potential and TIP3P water model. Our nonbonded models were as good as the complicated nonbonded dummy cationic models by Jiang et al. and the nonbonded 12-6-4 LJ models by Li and Merz in reproducing the experimental properties of those ions. Moreover, our nonbonded models achieved a better performance than the compromise (CM) LJ models and 12-6-4 LJ models, developed by Li and Merz, in reproducing the properties of MgCl₂ in aqueous solution.

Reaction-field electrostatics in molecular dynamics simulations: development of a conservative scheme compatible with an atomic cutoff

Shifting and switching schemes are developed to enable strict energy conservation in molecular dynamics simulations relying on reaction-field electrostatic (as well as Lennard-Jones) interactions with an atom-based cutoff truncation.

Periodic Coulomb Tree Method: An Alternative to Parallel Particle Mesh Ewald

Particle mesh Ewald (PME) is generally the method of choice for handling electrostatics in simulations with periodic boundary conditions. The excellent efficiency of PME on low processor counts is largely due to the use of the fast Fourier transform (FFT). However, due to the FFT's high communication cost, PME scales poorly in parallel. We develop a periodic Coulomb tree (PCT) method for electrostatic interactions in periodic boundary conditions as an alternative to PME in parallel simulations. We verify the accuracy of PCT by comparison of structural and dynamical properties of three different systems obtained via MD simulations using PME and PCT and provide parallel timing comparisons of the two methods on up to 1024 cores.