Anomalous waterlike behavior in spherically-symmetric water models optimized with the relative entropy

Abstract

Recent efforts have attempted to understand many of liquid water's anomalous properties in terms of effective spherically-symmetric pairwise molecular interactions entailing two characteristic length scales (so-called "core-softened" potentials). In this work, we examine the extent to which such simple descriptions of water are representative of the true underlying interactions by extracting coarse-grained potential functions that are optimized to reproduce the behavior of an all-atom model. To perform this optimization, we use a novel procedure based upon minimizing the relative entropy, a quantity that measures the extent to which a coarse-grained configurational ensemble overlaps with a reference all-atom one. We show that the optimized spherically-symmetric water models exhibit notable variations with the state conditions at which they were optimized, reflecting in particular the shifting accessibility of networked hydrogen bonding interactions. Moreover, we find that water's density and diffusivity anomalies are only reproduced when the effective coarse-grained potentials are allowed to vary with state. Our results therefore suggest that no state-independent spherically-symmetric potential can fully capture the interactions responsible for water's unique behavior; rather, the particular way in which the effective interactions vary with temperature and density contributes significantly to anomalous properties.

From Atomistic to Systematic Coarse-Grained Models for Molecular Systems

“…is the RE (or Kullback-Leibler divergence) between the microscopic Gibbs measure µ(q) and and a back-mapping µ ✓ (q) of the approximate CG measureμ ✓ (Q) / exp( Ū eff (Q; ✓)), [16,4]. E µ [·] denotes averages with respect to the probability measure dµ(q).…”

“…Methods such as inverse Monte Carlo [1], inverse Boltzmann [2], force matching [3], relative entropy [4], provide parameterizations of coarse-grained effective potentials at equilibrium by minimizing a fitting functional over a parameter space. Then, we further extend these studies using path-space methods (relative entropy rate) for coarse-graining and uncertainty quantification for non-equilibrium processes, [5,6,7,8].…”

Computer Simulations of Soft Matter: Linking the Scales

“…Recently a different coarse-graining strategy has been developed, namely the Relative Entropy method [131][132][133], which relies on a quantitative measure of the loss of information that follows from the description of a system in terms of different interaction potentials and/or different resolution. Remarkably, it is possible to demonstrate that the information function employed in this strategy connects Relative Entropy, IBI and Force Matching together.…”

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“…The latter two parameters may depend directly on the probe radius. 30,33 Hydra, Hy, is the recently introduced parameter quantifying the fraction of hydrophobic surface area. Hy < 0 indicates a hydrophobic interaction with a water depletion layer at the extended interface.…”