A Local Structural Basis to Resolve Amorphous Ices

TL;DR

The paper addresses how to distinguish amorphous ice phases (LDA vs HDA) using local structural information. It introduces an interpretable probabilistic framework that combines atom-centered symmetry functions and bond-orientational order descriptors with mutual-information feature selection and a calibrated Naive Bayes classifier to assign phase identity and detect out-of-distribution states. The authors show that phase discrimination is encoded within the first coordination shell, dominated by interstitial hydrogen density, and that the LDA→HDA transition proceeds by redistribution of local motifs with no intermediates, exhibiting hysteresis and first-order-like behavior across two water models. The approach provides a general, model-agnostic tool for probing local structure in disordered materials and for comparing different interatomic potentials at the environment level, with broad implications for linking microstructure to macroscopic phase behavior.

Abstract

Phases with distinct thermodynamic properties must differ in their underlying distributions of microscopic structures. While ordered phases are readily distinguished by unit cells and space groups, the local structural basis differentiating amorphous phases is less apparent. Here, using a new probabilistic data-driven framework applied to molecular simulation data on water, we identify local collective variables that discriminate low-density and high-density amorphous (LDA and HDA) ices and characterize pressure-induced transitions between these phases. As expected, descriptors related to local density capably distinguish LDA and HDA; however, phase identity is surprisingly encoded within the first coordination shell. Furthermore, LDA transitions to HDA by a simple redistribution of LDA- and HDA-like environments with no evident intermediate structures, in accordance with a first-order-like transition that contrasts with the gradual evolution observed in other amorphous systems such as metallic glasses. These findings are robust across force fields, which themselves exhibit structural differences, and exemplify how other systems lacking obvious distinguishing features can be characterized.

Figures (13)

• Figure 1: Overview of the probabilistic classification framework. (1) Local atomic environments are sampled from MD simulations and represented using ACSF and BOO descriptors. (2) A two-stage feature-selection procedure removes redundant descriptors and identifies those most informative for distinguishing LDA and HDA. (3) For each selected descriptor and class, one-dimensional probability densities are estimated using Gaussian kernel density estimation. (4) The joint probability for each class is computed as the product of the descriptor-wise probabilities, providing an interpretable probabilistic classification and enabling explicit detection of out-of-distribution configurations.
• Figure 2: Predicted LDA log-probabilities for true LDA environments (blue) and hexagonal ice Ih (red) for (A) BOO-NN, (B) PointNet, (C) AE–GMM, and (D) present work. 'Density*' refers to probability densities that are normalized so that their maximum value is 1.0.
• Figure 3: Mutual information of descriptors selected for LDA/HDA classification. Features with higher mutual information are considered more useful for LDA/HDA classification.
• Figure 4: Select order parameters distinguishing LDA and HDA environments. (A) The functional form of the $f_c(R_{ij})$ cutoff function used to compute the most informative descriptor. (B-F) The distribution of configurations from HDA (blue) and HDA (red) characterized by various local descriptors, ranked from most to the fifth-most informative. 'Density' refers to the normalized probability density for each descriptor.
• Figure 5: Sensitivity of classification accuracy to environment size. (A) Classification accuracy as a function of atomic environment size, where size is the number of neighboring water molecules. Means and standard deviations are obtained from five-fold cross validation. (B) Function form of distance-dependent contributions to $G_\text{H}^{3}$. Distributions from HDA and LDA environments characterized by (C) $G_\text{H}^{3}(\kappa=1.5)$ using environments of size 3, (D) $G_\text{H}^{3}(\kappa=1.5)$ using environments of size 16, and (E) $G_\text{H}^{1}$ using environments of size 3.