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)JCPSA60021-960610.1063/1.4929834]. 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.