High-Dimensional Fluctuations in Liquid Water: Combining Chemical Intuition with Unsupervised Learning

Abstract

The microscopic description of the local structure of water remains an open challenge. Here, we adopt an agnostic approach to understanding water’s hydrogen bond network using data harvested from molecular dynamics simulations of an empirical water model. A battery of state-of-the-art unsupervised data-science techniques are used to characterize the free-energy landscape of water starting from encoding the water environment using local atomic descriptors, through dimensionality reduction and finally the use of advanced clustering techniques. Analysis of the free energy under ambient conditions was found to be consistent with a rough single basin and independent of the choice of the water model. We find that the fluctuations of the water network occur in a high-dimensional space, which we characterize using a combination of both atomic descriptors and chemical-intuition-based coordinates. We demonstrate that a combination of both types of variables is needed in order to adequately capture the complexity of the fluctuations in the hydrogen bond network at different length scales both at room temperature and also close to the critical point of water. Our results provide a general framework for examining fluctuations in water under different conditions.

Charge Gradients around Dendritic Voids Cause Nanoscale Inhomogeneities in Liquid Water

“…The extent of the high and low density regions undergoes its most significant changes upon supercooling. , A recent theoretical study by the Goddard group refers to liquid water as a “dynamic polydisperse polymer” consisting of water molecules with only two intact hydrogen bonds . Molecular dynamics simulation studies by others, however, severely contest these interpretations and insist that water is a homogeneous liquid. ,,, To understand the structure of water on the molecular and nanoscale level, there is a need for alternative experimental techniques that can probe the water structure over nanometric length scales and, correspondingly, on time scales comparable to the femtosecond restructuring time of the hydrogen bond network of water. However, although there are many spectroscopic techniques to probe the water structure, − nearly all methods are sensitive to the hydration shell (subnanometric length scales involving at most a few layers of water) and spatiotemporal structural averaging, severely limiting our understanding of the nanometric length and femtosecond time scales on which water structures and transforms …”

DADApy: Distance-based analysis of data-manifolds in Python

“…Another key difference between k NN and PA k estimators is that k NN assumes the density to be exactly constant in the neighborhood of each point, while PA k possesses an additional free parameter that allows to describe small density variations. The PA k density estimator can be used to reconstruct free energy surfaces, especially in high-dimensional spaces, 18 , 20 , 21 , 22 and it can also be used for a detailed analysis of the data, as in Offei-Danso et al., 23 where a distinct analysis of the data points with different densities lead to some physical insight about the system under study.…”

Dimensionality reduction of local structure in glassy binary mixtures

“…The cost is a reduced interpretability of the descriptor and a larger hyper-parameter space to explore. Indeed, structural analysis using the SOAP descriptor must be combined with chemical and physical intuition to grasp the key results 24 . In this section, we summarize the few robust trends we have identified, as well as the shortcomings of this kind of analysis.…”

“…As we shall see in the next section, the SOAP descriptor also provides a good fit to dynamic heterogeneity, from purely structural information. Its application in the context of unsupervised learning of disordered materials is more recent and focused so far on systems with highly directional correlations, such as amorphous carbon 16,22 , or normal and supercooled liquid water 23,24 . Even in such systems with low coordination numbers and sharp orientational correlations, interpreting the results requires some physical and chemical intuition.…”

“…This approach has been recently applied, for instance, to crystal structure identification in colloidal suspensions 17,18 and the study of partially ordered systems 16,19 . Recent studies have also tackled challenging problems of structural analysis in bulk disordered materials, such as simple models of supercooled liquids and glasses 20,21 , amorphous carbon 16,22 , and liquid water in normal and supercooled conditions 23,24 . However, some of these extensions employ high-dimensional structural descriptors, which are not always easy to interpret, and involve non-linear reduction methods, which mostly act as black boxes.…”