Relative Resolution: A multipole approximation at appropriate distances

Abstract

Recently, we introduced Relative Resolution (RelRes) as a hybrid formalism for fluid mixtures [Chaimovich et al., J. Chem. Phys. 143, 243107 (2015)]. The essence of this approach is that it switches molecular resolution in terms of relative separation: While nearest neighbors are characterized by a detailed fine-grained model, other neighbors are characterized by a simplified coarse-grained model. Once the two models are analytically connected with each other via energy conservation, RelRes can capture the structural and thermal behavior of various multicomponent and multiphase systems across state space. This current work is a natural continuation of our original communication. Most importantly, we present the comprehensive mathematics of RelRes, casting it as a multipole approximation at appropriate distances; the current set of equations technically applies for any arbitrary system in soft matter (e.g., water). Besides, we continue examining the capability of this multiscale approach in molecular simulations of various (nonpolar) uniform liquids, specifically examining a 2:1 mapping for dumbbell-like molecules, as well as a 6:1 mapping and a 6:2 mapping for butterflylike molecules. In turn, we exhaustively show that RelRes can successfully retrieve for these systems their static and dynamic behavior, given that the fine-grained and coarse-grained potentials are switched at the boundary between the first and second coordination shells, the location at which orientational correlations vanish. We finally conclude by discussing how RelRes is the inherent variant of the "cell-multipole" approach for molecular simulations and, thus, this multiscale framework is especially promising for studying biological systems.

Relative Resolution: A Computationally Efficient Implementation in LAMMPS

“…As mentioned earlier, the main goal of our work is implementing RelRes in LAMMPS, specifically for the LJ potential. Here, we foremost review the theoretical foundation of the RelRes framework, , introducing several practical modifications along the way. We also thoroughly describe all the technical aspects of our implementation in LAMMPS.…”

“…The unique signature of the RelRes approach, as compared with other multiscale strategies, is that the FG and CG interactions are turned on or off depending on these distances: Specifically, nearby sites interact via FG potentials, while faraway sites interact via CG potentials. − We will now define a distance parameter at which interactions switch between the FG potential and the CG potential, and we will specifically call it the “switching distance” r s ; realize that in principle, r s may be distinct for each molecular pair ij , yet we omit these indices for clarity. In the most recent formulation of RelRes, , its FG potential is defined as and its CG potential is defined as In essence, these are just Heaviside functions, with the constants u μν FG ( r s ) and u ij CG ( r s ) respectively providing continuity of the FG and CG potentials at r s . The total energy of the system can be expressed by combining eqs and , while performing the appropriate summation over all sites Notice that with r s → ∞, we obtain a pure FG system, and with r s → 0, we obtain a pure CG system.…”

“…Ever since the advent of molecular simulations, a main goal of the scientific community has been enhancing their computational efficiency, and this has been frequently done by modifying the interactions between the molecules. − These days, multiscale algorithms have become especially popular for such a task: At the most basic level, these schemes link together detailed fine-grained (FG) molecular models and simplified coarse-grained (CG) molecular models. , While there have been various recipes for combining the two models in a single system, − formulations which switch between the FG and CG interactions in terms of a spatial variable have been particularly common. − …”

“…In this work, we specifically focus on the multiscale framework which we call Relative Resolution (RelRes). − The main signature of RelRes is that the molecular model is a function of the relative separation: Given two arbitrary molecules, they are modeled via FG interactions if near to each other yet via CG interactions if far from each other. Such an idea was introduced by Izvekov and Voth in molecular simulations of water, while Shen and Hu employed a reminiscent approach in biomolecular systems .…”

“…Most importantly, while other multiscale approaches typically employ a numerical parametrization between the FG and the CG models, , Chaimovich at al. discovered a crucial benefit of RelRes: It naturally possesses an analytical relation between the FG and the CG potentials, stemming in a multipole approximation. , In fact, by correspondingly employing tabulated potentials in GROMACS, it was shown that RelRes overcomes the transferability and representability issues that hinder most multiscale protocols: , in particular for several nonpolar mixtures, RelRes correctly captures across state space numerous structural correlations and thermal properties of static and dynamic behavior. , …”