Mining of effective local order parameters for classifying crystal structures: A machine learning study

Distinguish microphase-separated structures of diblock copolymers using local order parameters

The microphase-separated structures of block copolymers are inherently highly ordered local structures, commonly characterized by differences in domain width and curvature. By focusing on diblock copolymers, we propose local order parameters (LOPs) that accurately distinguish between adjacent microphase-separated structures on the phase diagram. We used the Molecular Assembly structure Learning package for Identifying Order parameters (MALIO) to evaluate the structure classification performance of 186 candidate LOPs. MALIO calculates the numerical values of all candidate LOPs for the input microphase-separated structures to create a dataset, and then performs supervised machine learning to select the best LOPs quickly and systematically. We evaluated the robustness of the selected LOPs in terms of classification accuracy against variations in miscibility and fraction of block. The minimum local area size required for LOPs to achieve their classification performances is closely related to the characteristic sizes of the microphase-separated structures. The proposed LOPs are potentially applicable over a large area on the phase diagram.

Numerical evidence for the existence of three different stable liquid water structures as indicated by local order parameter

Structures of liquid water are controversial not only in supercooled polyamorphism but also in stable bulk liquids in the high temperature and pressure range. Several experimental studies in bulk liquid have assumed the existence of three different liquid water structures. If indeed the three liquid water structures are different, they should be clearly distinguished by some measure other than density that characterizes the difference in structural order. In this study, whether the three different bulk liquid water structures are real or not is numerically verified based on molecular simulations using a reliable water molecular model. Since these liquid water structures have been suggested to be related to three different crystal structures (i.e., ice Ih, III, and V), liquid structures are sampled from the vicinity of the ice Ih-liquid coexistence point, the ice III-V-liquid triple point, and the ice V-VI-liquid triple point, respectively. An attempt is made to introduce local order parameters (LOPs) as an indicator to distinguish these structures. A fast and exhaustive LOP search is performed by the molecular assembly structure learning package for Identifying order parameters. The selected LOP distinguishes the molecular structures of three different stable liquid waters with high accuracy, providing numerical evidence that these structural orders differ from each other. Furthermore, regions of the liquid water structures are drawn on a phase diagram using the LOP, demonstrating their consistency with experimental studies.

Graph-Neural-Network-Based Unsupervised Learning of the Temporal Similarity of Structural Features Observed in Molecular Dynamics Simulations

Classification of molecular structures is a crucial step in molecular dynamics (MD) simulations to detect various structures and phases within systems. Molecular structures, which are commonly identified using order parameters, were recently identified using machine learning (ML), that is, the ML models acquire structural features using labeled crystals or phases via supervised learning. However, these approaches may not identify unlabeled or unknown structures, such as the imperfect crystal structures observed in nonequilibrium systems and interfaces. In this study, we proposed the use of a novel unsupervised learning framework, denoted temporal self-supervised learning (TSSL), to learn structural features and design their parameters. In TSSL, the ML models learn that the structural similarity is learned via contrastive learning based on minor short-term variations caused by perturbations in MD simulations. This learning framework is applied to a sophisticated architecture of graph neural network models that use bond angle and length data of the neighboring atoms. TSSL successfully classifies water and ice crystals based on high local ordering, and furthermore, it detects imperfect structures typical of interfaces such as the water-ice and ice-vapor interfaces.

Molecular cluster analysis using local order parameters selected by machine learning

Accurately extracting local molecular structures is essential for understanding the mechanisms of phase and structural transitions. A promising method to characterize the local molecular structure is defining the value of the local order parameter (LOP) for each particle. This work develops the Molecular Assembly structure Learning package for Identifying Order parameters (MALIO), a machine learning package that can propose an optimal (set of) LOP(s) quickly and automatically for a huge number of LOP species and various methods of selecting neighboring particles for the calculation. We applied this package to distinguish between the nematic and smectic phases of uniaxial liquid crystal molecules, and selected candidate LOPs that could be used to precisely observe the nematic-smectic phase transition. The LOP candidates were used to observe the nucleation and subsequent percolation transition, and the effect of the choice of LOP species and neighboring particles on the statistics of local molecular structures (clusters) was examined. The procedure revealed the time evolution of the number of clusters and the dependence of the percolation curve on the number of neighboring particles for each LOP species. The LOP species with the lowest dependence on the number of neighboring particles was the best-performing LOP species in the MALIO screening strategy. These results not only show that machine learning can powerfully screen a huge number of LOP species and suggest only a few promising candidates, but also indicate that MALIO can select the best LOP species.

Screening toward the Development of Fingerprints of Atomic Environments Using Bond-Orientational Order Parameters

A combination of atomic numbers and bond-orientational order parameters is considered a candidate for a simple representation that involves information on both the atomic species and their positional relation. The 504 candidates are applied as the fingerprint of the molecules stored in QM9, a data set of computed geometric, energetic, electronic, and thermodynamic properties for 133 885 stable small organic molecules made up of carbon, hydrogen, oxygen, nitrogen, and fluorine atoms. To screen the fingerprints, a regression analysis of the atomic charges given by Open Babel was performed by supervised machine learning. The regression results indicate that the 60 fingerprints successfully estimate Open Babel charges. The results of the dipole moments, an example of a property expressed by charge and position, also had a high accuracy in comparison with the values computed from Open Babel charges. Therefore, the screened 60 fingerprints have the potential to precisely describe the chemical and structural information on the atomic environment of molecules.

Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics

Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process and correctly calculating the relative free energies of different polymorphs. Here, we demonstrate, for the prototypical case of urea nucleation from the melt, how one can learn such a one-dimensional reaction coordinate as a function of prespecified order parameters and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of the generic thermodynamic and structural order parameters using the "spectral gap optimization of order parameters (SGOOP)" approach [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. U.S.A. (2016)] and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insights into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes an accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. We believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.

Mining of Effective Local Order Parameters to Classify Ice Polymorphs

Order parameters make it possible to quantify the degree of structural ordering in a material and thus to apply as the reaction coordinates during the free-energy analysis of phase or structure transitions. Furthermore, order parameters are useful in determining the local structures of molecular groups during transition stages. However, identifying or developing local order parameters (LOPs) that are sensitive for specific materials and phases is a non-trivial task. In this study, the ability of LOPs to classify the solid and liquid structures of water at coexistence or triple points is investigated with the aid of supervised machine learning. The classification accuracy of a total of 179,738,433 combinations of 493 LOPs is automatically and systematically compared for water structures at the ice Ih-Ic-liquid coexistence point and the ice III-V-liquid and ice V-VI-liquid triple points. The optimal sets of two LOPs are found for each point, and sets of three LOPs are suggested for better accuracy.

Multistep nucleation of anisotropic molecules

Phase transition of anisotropic materials is ubiquitously observed in physics, biology, materials science, and engineering. Nevertheless, how anisotropy of constituent molecules affects the phase transition dynamics is still poorly understood. Here we investigate numerically the phase transition of a simple model system composed of anisotropic molecules, and report on our discovery of multistep nucleation of nuclei with layered positional ordering (smectic ordering), from a fluid-like nematic phase with orientational order only (no positional order). A trinity of molecular dynamics simulation, machine learning, and molecular cluster analysis yielding free energy landscapes unambiguously demonstrates the dynamics of multistep nucleation process involving characteristic metastable clusters that precede supercritical smectic nuclei and cannot be accounted for by the classical nucleation theory. Our work suggests that molecules of simple shape can exhibit rich and complex nucleation processes, and our numerical approach will provide deeper understanding of phase transitions and resulting structures in anisotropic materials such as biological systems and functional materials.

The seven deadly sins: When computing crystal nucleation rates, the devil is in the details

The formation of crystals has proven to be one of the most challenging phase transformations to quantitatively model-let alone to actually understand-be it by means of the latest experimental technique or the full arsenal of enhanced sampling approaches at our disposal. One of the most crucial quantities involved with the crystallization process is the nucleation rate, a single elusive number that is supposed to quantify the average probability for a nucleus of critical size to occur within a certain volume and time span. A substantial amount of effort has been devoted to attempt a connection between the crystal nucleation rates computed by means of atomistic simulations and their experimentally measured counterparts. Sadly, this endeavor almost invariably fails to some extent, with the venerable classical nucleation theory typically blamed as the main culprit. Here, we review some of the recent advances in the field, focusing on a number of perhaps more subtle details that are sometimes overlooked when computing nucleation rates. We believe it is important for the community to be aware of the full impact of aspects, such as finite size effects and slow dynamics, that often introduce inconspicuous and yet non-negligible sources of uncertainty into our simulations. In fact, it is key to obtain robust and reproducible trends to be leveraged so as to shed new light on the kinetics of a process, that of crystal nucleation, which is involved into countless practical applications, from the formulation of pharmaceutical drugs to the manufacturing of nano-electronic devices.

Effect of chemical design of grafted polymers on the self-assembled morphology of polymer-tethered nanoparticles in nanotubes

There is a clear relationship between the self-assembling architecture of nanoparticles (NPs) and their physical properties, and they are currently used in a variety of applications, including optical sensors. Polymer-tethered NPs, which are created by grafting polymers onto NPs to control the self-assembly of NPs, have attracted considerable attention. Recent synthetic techniques have made it possible to synthesize a wide variety of polymers and thereby create NPs with many types of surfaces. However, self-assembled structures have not been systematically classified because of the large number of tuning parameters such as the polymer length and graft density. In this study, by using coarse-grained molecular simulation, we investigated the changes in the self-assembled structure of polymer-tethered NP solutions confined in nanotubes due to the chemical properties of polymers. Three types of tethered polymer NP models were examined: homo hydrophilic, diblock hydrophilic-hydrophobic (HI-HO), and diblock hydrophobic-hydrophilic. Under strong confinement, the NPs were dispersed in single file at low axial pressure. As the pressure increased, multilayered lamellar was observed in the HI-HO model. In contrast, under weak confinement, the difference in the pressure at which the phases emerge, depending on the model, was significant. By changing the chemical properties of the grafted polymer, the thermodynamic conditions (the axial pressure in this study) under which the phases appear is altered, although the coordination of NPs remains almost unchanged. Our simulation offers a theoretical guide for controlling the morphologies of self-assembled polymer-tethered NPs, a novel system that may find applications in nanooptical devices or for nanopatterning.

Searching for local order parameters to classify water structures at triple points

The diversity of ice polymorphs is of interest in condensed-matter physics, engineering, astronomy, and biosphere and climate studies. In particular, their triple points are critical to elucidate the formation of each phase and transitions among phases. However, an approach to distinguish their molecular structures is lacking. When precise molecular geometries are given, order parameters are often computed to quantify the degree of structural ordering and to classify the structures. Many order parameters have been developed for specific or multiple purposes, but their capabilities have not been exhaustively investigated for distinguishing ice polymorphs. Here, 493 order parameters and their combinations are considered for two triple points involving the ice polymorphs ice III-V-liquid and ice V-VI-liquid. Supervised machine learning helps automatic and systematic searching of the parameters. For each triple point, the best set of two order parameters was found that distinguishes three structures with high accuracy. A set of three order parameters is also suggested for better accuracy.