Phase Diagram of a Deep Potential Water Model

Enhanced deep potential model for fast and accurate molecular dynamics: application to the hydrated electron

In molecular simulations, neural network force fields aim at achieving ab initio accuracy with reduced computational cost. This work introduces enhancements to the Deep Potential network architecture, integrating a message-passing framework and a new lightweight implementation with various improvements. Our model achieves accuracy on par with leading machine learning force fields and offers significant speed advantages, making it well-suited for large-scale, accuracy-sensitive systems. We also introduce a new iterative model for Wannier center prediction, allowing us to keep track of electron positions in simulations of general insulating systems. We apply our model to study the solvated electron in bulk water, an ostensibly simple system that is actually quite challenging to represent with neural networks. Our trained model is not only accurate, but can also transfer to larger systems. Our simulation confirms the cavity model, where the electron's localized state is observed to be stable. Through an extensive run, we accurately determine various structural and dynamical properties of the solvated electron.

Five-Site Water Models for Ice and Liquid Water Generated by a Series-Parallel Machine Learning Strategy

Icing, a common natural phenomenon, always originates from a molecule. Molecular simulation is crucial for understanding the relevant process but still faces a great challenge in obtaining a uniform and accurate description of ice and liquid water with limited model parameters. Here, we propose a series-parallel machine learning (ML) approach consisting of a classification back-propagation neural network (BPNN), parallel regression BPNNs, and a genetic algorithm to establish conventional TIP5P-BG and temperature-dependent TIP5P-BGT models. The established water models exhibit a comprehensive balance among the crucial physical properties (melting point, density, vaporization enthalpy, self-diffusion coefficient, and viscosity) with mean absolute percentage errors of 2.65 and 2.40%, respectively, and excellent predictive performance on the related properties of liquid water. For ice, the simulation results on the critical nucleus size and growth rate are in good accordance with experiments. This work offers a powerful molecular model for phase transition and icing in nanoconfinement and a construction strategy for a complex molecular model in the extreme case.

A machine learning potential construction based on radial distribution function sampling

Sampling reference data is crucial in machine learning potential (MLP) construction. Inadequate coverage of local configurations in reference data may lead to unphysical behaviors in MLP-based molecular dynamics (MLP-MD) simulations. To address this problem, this study proposes a new on-the-fly reference data sampling method called radial distribution function (RDF)-based data sampling for MLP construction. This method detects and extracts anomalous structures from the trajectories of MLP-MD simulations by focusing on the shapes of RDFs. The detected structures are added to the reference data to improve the accuracy of the MLP. This method allows us to realize a reasonable MLP construction for liquid water with minimal additional data. We prepare data from an H2O molecular cluster system and verify whether the constructed MLPs are practical for bulk water systems. MLP-MD simulations without RDF-based data sampling show unphysical behaviors, such as atomic collisions. In contrast, after applying this method, we obtain MLP-MD trajectories with features, such as RDF shapes and angle distributions, that are comparable to those of ab initio MD simulations. Our simulation results demonstrate that the RDF-based data sampling approach is useful for constructing MLPs that are robust to extrapolations from molecular cluster systems to bulk systems without any specialized know-how.

E(n)-Equivariant cartesian tensor message passing interatomic potential

Machine learning potential (MLP) has been a popular topic in recent years for its capability to replace expensive first-principles calculations in some large systems. Meanwhile, message passing networks have gained significant attention due to their remarkable accuracy, and a wave of message passing networks based on Cartesian coordinates has emerged. However, the information of the node in these models is usually limited to scalars, and vectors. In this work, we propose High-order Tensor message Passing interatomic Potential (HotPP), an E(n) equivariant message passing neural network that extends the node embedding and message to an arbitrary order tensor. By performing some basic equivariant operations, high order tensors can be coupled very simply and thus the model can make direct predictions of high-order tensors such as dipole moments and polarizabilities without any modifications. The tests in several datasets show that HotPP not only achieves high accuracy in predicting target properties, but also successfully performs tasks such as calculating phonon spectra, infrared spectra, and Raman spectra, demonstrating its potential as a tool for future research.

Active sparse Bayesian committee machine potential for isothermal-isobaric molecular dynamics simulations

Recent advancements in machine learning potentials (MLPs) have significantly impacted the fields of chemistry, physics, and biology by enabling large-scale first-principles simulations. Among different machine learning approaches, kernel-based MLPs distinguish themselves through their ability to handle small datasets, quantify uncertainties, and minimize over-fitting. Nevertheless, their extensive computational requirements present considerable challenges. To alleviate these, sparsification methods have been developed, aiming to reduce computational scaling without compromising accuracy. In the context of isothermal and isobaric ML molecular dynamics (MD) simulations, achieving precise pressure estimation is crucial for reproducing reliable system behavior under constant pressure. Despite progress, sparse kernel MLPs struggle with precise pressure prediction. Here, we introduce a virial kernel function that significantly enhances the pressure estimation accuracy of MLPs. Additionally, we propose the active sparse Bayesian committee machine (BCM) potential, an on-the-fly MLP architecture that aggregates local sparse Gaussian process regression (SGPR) MLPs. The sparse BCM potential overcomes the steep computational scaling with the kernel size, and a predefined restriction on the size of kernel allows for fast and efficient on-the-fly training. Our advancements facilitate accurate and computationally efficient machine learning-enhanced MD (MLMD) simulations across diverse systems, including ice-liquid coexisting phases, Li10Ge(PS6)2 lithium solid electrolyte, and high-pressure liquid boron nitride.

Toward an ab Initio Description of Adsorbate Surface Dynamics

The advent of machine learning potentials (MLPs) provides a unique opportunity to access simulation time scales and to directly compute physicochemical properties that are typically intractable using density functional theory (DFT). In this study, we use an active learning curriculum to train a generalizable MLP using the DeepMD-kit architecture. By using sufficiently long MLP-based molecular dynamics (MD) simulations, which provide DFT-level accuracy, we investigate the diffusion of key surface-bound adsorbates on a Ag(111) facet. Detailed analysis of the MLP/MD-calculated diffusivities sheds light on the potential shortcomings of using DFT-based nudged elastic band to estimate surface diffusion barriers. More generally, while this study is focused on a specific system, we anticipate that the underlying workflows and the resulting models can be extended to other adsorbates and other materials in the future.

Evidence of ferroelectric features in low-density supercooled water from ab initio deep neural-network simulations

Over the last decade, an increasing body of evidence has emerged, supporting the existence of a metastable liquid-liquid critical point in supercooled water whereby two distinct liquid phases of different densities coexist. Analyzing long molecular dynamics simulations performed using deep neural-network force fields trained to accurate quantum mechanical data, we demonstrate that the low-density liquid phase displays a strong propensity toward spontaneous polarization, as witnessed by large and long-lived collective dipole fluctuations. Our findings suggest that the dynamical stability of the low-density phase, and hence the transition from high-density to low-density liquid, is triggered by a collective process involving an accumulation of rotational angular jumps, which could ignite large dipole fluctuations. This dynamical transition involves subtle changes in the electronic polarizability of water molecules which affects their rotational mobility within the two phases. These findings hold the potential for catalyzing activity in the search for dielectric-based probes of the putative second critical point.

Improving the reliability of machine learned potentials for modeling inhomogeneous liquids

The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical, and biological processes. Classical molecular dynamics simulations have been applied extensively to simulate the response of fluids to inhomogeneities directly, but are limited by the accuracy of the underlying interatomic potentials. Here, we use neural network potentials (NNPs) trained to ab initio simulations to accurately predict the inhomogeneous responses of two distinct fluids: liquid water and molten NaCl. Although NNPs can be readily trained to model complex bulk systems across a range of state points, we show that to appropriately model a fluid's response at an interface, relevant inhomogeneous configurations must be included in the training data. In order to sufficiently sample appropriate configurations of such inhomogeneous fluids, we develop protocols based on molecular dynamics simulations in the presence of external potentials. We demonstrate that NNPs trained on inhomogeneous fluid configurations can more accurately predict several key properties of fluids-including the density response, surface tension and size-dependent cavitation free energies-for liquid water and molten NaCl, compared to both empirical interatomic potentials and NNPs that are not trained on such inhomogeneous configurations. This work therefore provides a first demonstration and framework to extract the response of inhomogeneous fluids from first principles for classical density-functional treatment of fluids free from empirical potentials.

Double-Layer Distribution of Hydronium and Hydroxide Ions in the Air-Water Interface

The acid-base nature of the aqueous interface has long been controversial. Most macroscopic experiments suggest that the air-water interface is basic based on the detection of negative charges at the interface that indicates the enrichment of hydroxides (OH-), whereas microscopic studies mostly support the acidic air-water interface with the observation of hydronium (H3O+) accumulation in the top layer of the interface. It is crucial to clarify the interfacial preference of OH- and H3O+ ions for rationalizing the debate. In this work, we perform deep potential molecular dynamics simulations to investigate the preferential distribution of OH- and H3O+ ions at the aqueous interfaces. The neural network potential energy surface is trained based on density functional theory calculations with the SCAN functional, which can accurately describe the diffusion of these two ions both in the interface and in the bulk water. In contrast to the previously reported single ion enrichment, we show that both OH- and H3O+ surprisingly prefer to accumulate in interfaces but at different interfacial depths, rendering a double-layer ionic distribution within ∼1 nm near the Gibbs dividing surface. The H3O+ preferentially resides in the topmost layer of the interface, but the OH-, which is enriched in the deeper interfacial layer, has a higher equilibrium concentration due to the more negative free energy of interfacial stabilization [-0.90 (OH-) vs -0.56 (H3O+) kcal/mol]. The present finding of the ionic double-layer distribution may qualitatively offer a self-consistent explanation for the long-term controversy about the acid-base nature of the air-water interface.

Hydroxide and Hydronium Ions Modulate the Dynamic Evolution of Nitrogen Nanobubbles in Water

It has been widely recognized that the pH environment influences the nanobubble dynamics and hydroxide ions adsorbed on the surface may be responsible for the long-term survival of the nanobubbles. However, understanding the distribution of hydronium and hydroxide ions in the vicinity of a bulk nanobubble surface at a microscopic scale and the consequent impact of these ions on the nanobubble behavior remains a challenging endeavor. In this study, we carried out deep potential molecular dynamics simulations to explore the behavior of a nitrogen nanobubble under neutral, acidic, and alkaline conditions and the inherent mechanism, and we also conducted a theoretical thermodynamic and dynamic analysis to address constraints related to simulation duration. Our simulations and theoretical analyses demonstrate a trend of nanobubble dissolution similar to that observed experimentally, emphasizing the limited dissolution of bulk nanobubbles in alkaline conditions, where hydroxide ions tend to reside slightly farther from the nanobubble surface than hydronium ions, forming more stable hydrogen bond networks that shield the nanobubble from dissolution. In acidic conditions, the hydronium ions preferentially accumulating at the nanobubble surface in an orderly manner drive nanobubble dissolution to increase the entropy of the system, and the dissolved nitrogen molecules further strengthen the hydrogen bond networks of systems by providing a hydrophobic environment for hydronium ions, suggesting both entropy and enthalpy effects contribute to the instability of nanobubbles under acidic conditions. These results offer fresh insights into the double-layer distribution of hydroxide and hydronium near the nitrogen-water interface that influences the dynamic behavior of bulk nanobubbles.

Nuclear Quantum Effects on the Electronic Structure of Water and Ice

The electronic properties and optical response of ice and water are intricately shaped by their molecular structure, including the quantum mechanical nature of the hydrogen atoms. Despite numerous previous studies, a comprehensive understanding of the nuclear quantum effects (NQEs) on the electronic structure of water and ice at finite temperatures remains elusive. Here, we utilize molecular simulations that harness efficient machine-learning potentials and many-body perturbation theory to assess how NQEs impact the electronic bands of water and hexagonal ice. By comparing path-integral and classical simulations, we find that NQEs lead to a larger renormalization of the fundamental gap of ice, compared to that of water, ultimately yielding similar bandgaps in the two systems, consistent with experimental estimates. Our calculations suggest that the increased quantum mechanical delocalization of protons in ice, relative to water, is a key factor leading to the enhancement of NQEs on the electronic structure of ice.

Proton Collective Quantum Tunneling Induces Anomalous Thermal Conductivity of Ice under Pressure

Proton tunneling is believed to be nonlocal in ice, but its range has been shown to be limited to only a few molecules. Here, we measured the thermal conductivity of ice under pressure up to 50 GPa and found it increases with pressure until 20 GPa but decreases at higher pressures. We attribute this nonmonotonic thermal conductivity to the collective tunneling of protons at high pressures, supported by large-scale quantum molecular dynamics simulations. The collective tunneling loops span several picoseconds in time and are as large as nanometers in space, which match the phonon periods and wavelengths, leading to strong phonon scattering at high pressures. Our results show direct evidence of global quantum motion existing in high-pressure ice and provide a new perspective to understanding the coupling between phonon propagation and atomic tunneling.

Perspectives Toward Damage-Tolerant Nanostructure Ceramics

Advanced ceramic materials and devices call for better reliability and damage tolerance. In addition to their strong bonding nature, there are examples demonstrating superior mechanical properties of nanostructure ceramics, such as damage-tolerant ceramic aerogels that can withstand high deformation without cracking and local plasticity in dense nanocrystalline ceramics. The recent progresses shall be reviewed in this perspective article. Three topics including highly elastic nano-fibrous ceramic aerogels, load-bearing nanoceramics with improved mechanical properties, and implementing machine learning-assisted simulations toolbox in understanding the relationship among structure, deformation mechanisms, and microstructure-properties shall be discussed. It is hoped that the perspectives present here can help the discovery, synthesis, and processing of future structural ceramic materials that are insensitive to processing flaws and local damages in service.

Interfacial Optimization for AlN/Diamond Heterostructures via Machine Learning Potential Molecular Dynamics Investigation of the Mechanical Properties

AlN/diamond heterostructures hold tremendous promise for the development of next-generation high-power electronic devices due to their ultrawide band gaps and other exceptional properties. However, the poor adhesion at the AlN/diamond interface is a significant challenge that will lead to film delamination and device performance degradation. In this study, the uniaxial tensile failure of the AlN/diamond heterogeneous interfaces was investigated by molecular dynamics simulations based on a neuroevolutionary machine learning potential (NEP) model. The interatomic interactions can be successfully described by trained NEP, the reliability of which has been demonstrated by the prediction of the cleavage planes of AlN and diamond. It can be revealed that the annealing treatment can reduce the total potential energy by enhancing the binding of the C and N atoms at interfaces. The strain engineering of AlN also has an important impact on the mechanical properties of the interface. Furthermore, the influence of the surface roughness and interfacial nanostructures on the AlN/diamond heterostructures has been considered. It can be indicated that the combination of surface roughness reduction, AlN strain engineering, and annealing treatment can effectively result in superior and more stable interfacial mechanical properties, which can provide a promising solution to the optimization of mechanical properties, of ultrawide band gap semiconductor heterostructures.

Accelerating Computation of Acidity Constants and Redox Potentials for Aqueous Organic Redox Flow Batteries by Machine Learning Potential-Based Molecular Dynamics

Due to the increased concern about energy and environmental issues, significant attention has been paid to the development of large-scale energy storage devices to facilitate the utilization of clean energy sources. The redox flow battery (RFB) is one of the most promising systems. Recently, the high cost of transition-metal complex-based RFB has promoted the development of aqueous RFBs with redox-active organic molecules. To expand the working voltage, computational chemistry has been applied to search for organic molecules with lower or higher redox potentials. However, redox potential computation based on implicit solvation models would be challenging due to difficulty in parametrization when considering the complex solvation of supporting electrolytes. Besides, although ab initio molecular dynamics (AIMD) describes the supporting electrolytes with the same level of electronic structure theory as the redox couple, the application is impeded by the high computation costs. Recently, machine learning molecular dynamics (MLMD) has been illustrated to accelerate AIMD by several orders of magnitude without sacrificing the accuracy. It has been established that redox potentials can be computed by MLMD with two separated machine learning potentials (MLPs) for reactant and product states, which is redundant and inefficient. In this work, an automated workflow is developed to construct a universal MLP for both states, which can compute the redox potentials or acidity constants of redox-active organic molecules more efficiently. Furthermore, the predicted redox potentials can be evaluated at the hybrid functional level with much lower costs, which would facilitate the design of aqueous organic RFBs.

Construction of High Accuracy Machine Learning Interatomic Potential for Surface/Interface of Nanomaterials-A Review

The inherent discontinuity and unique dimensional attributes of nanomaterial surfaces and interfaces bestow them with various exceptional properties. These properties, however, also introduce difficulties for both experimental and computational studies. The advent of machine learning interatomic potential (MLIP) addresses some of the limitations associated with empirical force fields, presenting a valuable avenue for accurate simulations of these surfaces/interfaces of nanomaterials. Central to this approach is the idea of capturing the relationship between system configuration and potential energy, leveraging the proficiency of machine learning (ML) to precisely approximate high-dimensional functions. This review offers an in-depth examination of MLIP principles and their execution and elaborates on their applications in the realm of nanomaterial surface and interface systems. The prevailing challenges faced by this potent methodology are also discussed.

The performance of OPC and OPC3 water models in predictions of 2D structures under nanoconfinement

Nanoconfined water plays an important role in broad fields of science and engineering. Classical molecular dynamics (MD) simulations have been widely used to investigate water phases under nanoconfinement. The key ingredient of MD is the force field. In this study, we systematically investigated the performance of a recently introduced family of globally optimal water models, OPC and OPC3, and TIP4P/2005 in describing nanoconfined two-dimensional (2D) water ice. Our studies show that the melting points of the monolayer square ice (MSI) of all three water models are higher than the melting points of the corresponding bulk ice Ih. Under the same conditions, the melting points of MSI of OPC and TIP4P/2005 are the same and are ∼90 K lower than that of the OPC3 water model. In addition, we show that OPC and TIP4P/2005 water models are able to form a bilayer AA-stacked structure and a trilayer AAA-stacked structure, which are not the cases for the OPC3 model. Considering the available experimental data and first-principles simulations, we consider the OPC water model as a potential water model for 2D water ice MD studies.

Many-body interactions and deep neural network potentials for water

We present a detailed assessment of deep neural network potentials developed within the Deep Potential Molecular Dynamics (DeePMD) framework and trained on the MB-pol data-driven many-body potential energy function. Specific focus is directed at the ability of DeePMD-based potentials to correctly reproduce the accuracy of MB-pol across various water systems. Analyses of bulk and interfacial properties as well as many-body interactions characteristic of water elucidate inherent limitations in the transferability and predictive accuracy of DeePMD-based potentials. These limitations can be traced back to an incomplete implementation of the "nearsightedness of electronic matter" principle, which may be common throughout machine learning potentials that do not include a proper representation of self-consistently determined long-range electric fields. These findings provide further support for the "short-blanket dilemma" faced by DeePMD-based potentials, highlighting the challenges in achieving a balance between computational efficiency and a rigorous, physics-based representation of the properties of water. Finally, we believe that our study contributes to the ongoing discourse on the development and application of machine learning models in simulating water systems, offering insights that could guide future improvements in the field.

Layer-by-layer phase transformation in Ti3O5 revealed by machine-learning molecular dynamics simulations

Reconstructive phase transitions involving breaking and reconstruction of primary chemical bonds are ubiquitous and important for many technological applications. In contrast to displacive phase transitions, the dynamics of reconstructive phase transitions are usually slow due to the large energy barrier. Nevertheless, the reconstructive phase transformation from β- to λ-Ti3O5 exhibits an ultrafast and reversible behavior. Despite extensive studies, the underlying microscopic mechanism remains unclear. Here, we discover a kinetically favorable in-plane nucleated layer-by-layer transformation mechanism through metadynamics and large-scale molecular dynamics simulations. This is enabled by developing an efficient machine learning potential with near first-principles accuracy through an on-the-fly active learning method and an advanced sampling technique. Our results reveal that the β-λ phase transformation initiates with the formation of two-dimensional nuclei in the ab-plane and then proceeds layer-by-layer through a multistep barrier-lowering kinetic process via intermediate metastable phases. Our work not only provides important insight into the ultrafast and reversible nature of the β-λ transition, but also presents useful strategies and methods for tackling other complex structural phase transitions.

Effect of Interlayer Bonding on Superlubric Sliding of Graphene Contacts: A Machine-Learning Potential Study

Surface defects and their mutual interactions are anticipated to affect the superlubric sliding of incommensurate layered material interfaces. Atomistic understanding of this phenomenon is limited due to the high computational cost of ab initio simulations and the absence of reliable classical force-fields for molecular dynamics simulations of defected systems. To address this, we present a machine-learning potential (MLP) for bilayer defected graphene, utilizing state-of-the-art graph neural networks trained against many-body dispersion corrected density functional theory calculations under iterative configuration space exploration. The developed MLP is utilized to study the impact of interlayer bonding on the friction of bilayer defected graphene interfaces. While a mild effect on the sliding dynamics of aligned graphene interfaces is observed, the friction coefficients of incommensurate graphene interfaces are found to significantly increase due to interlayer bonding, nearly pushing the system out of the superlubric regime. The methodology utilized herein is of general nature and can be adapted to describe other homogeneous and heterogeneous defected layered material interfaces.

Homogeneous water vapor condensation with a deep neural network potential model

Molecular-level nucleation has not been clearly understood due to the complexity of multi-body potentials and the stochastic, rare nature of the process. This work utilizes molecular dynamics (MD) simulations, incorporating a first-principles-based deep neural network (DNN) potential model, to investigate homogeneous water vapor condensation. The nucleation rates and critical nucleus sizes predicted by the DNN model are compared against commonly used semi-empirical models, namely extended simple point charge (SPC/E), TIP4P, and OPC, in addition to classical nucleation theory (CNT). The nucleation rates from the DNN model are comparable with those from the OPC model yet surpass the rates from the SPC/E and TIP4P models, a discrepancy that could mainly arise from the overestimated bulk free energy by SPC/E and TIP4P. The surface free energy predicted by CNT is lower than that in MD simulations, while its bulk free energy is higher than that in MD simulations, irrespective of the potential model used. Further analysis of cluster properties with the DNN model unveils pronounced variations of O-H bond length and H-O-H bond angle, along with averaged bond lengths and angles that are enlarged during embryonic cluster formation. Properties such as cluster surface free energy and liquid-to-vapor density transition profiles exhibit significant deviations from CNT assumptions.

Deep-potential enabled multiscale simulation of gallium nitride devices on boron arsenide cooling substrates

High-efficient heat dissipation plays critical role for high-power-density electronics. Experimental synthesis of ultrahigh thermal conductivity boron arsenide (BAs, 1300 W m-1K-1) cooling substrates into the wide-bandgap semiconductor of gallium nitride (GaN) devices has been realized. However, the lack of systematic analysis on the heat transfer across the GaN-BAs interface hampers the practical applications. In this study, by constructing the accurate and high-efficient machine learning interatomic potentials, we perform multiscale simulations of the GaN-BAs heterostructures. Ultrahigh interfacial thermal conductance of 260 MW m-2K-1 is achieved, which lies in the well-matched lattice vibrations of BAs and GaN. The strong temperature dependence of interfacial thermal conductance is found between 300 to 450 K. Moreover, the competition between grain size and boundary resistance is revealed with size increasing from 1 nm to 1000 μm. Such deep-potential equipped multiscale simulations not only promote the practical applications of BAs cooling substrates in electronics, but also offer approach for designing advanced thermal management systems.

Comparing machine learning potentials for water: Kernel-based regression and Behler-Parrinello neural networks

In this paper, we investigate the performance of different machine learning potentials (MLPs) in predicting key thermodynamic properties of water using RPBE + D3. Specifically, we scrutinize kernel-based regression and high-dimensional neural networks trained on a highly accurate dataset consisting of about 1500 structures, as well as a smaller dataset, about half the size, obtained using only on-the-fly learning. This study reveals that despite minor differences between the MLPs, their agreement on observables such as the diffusion constant and pair-correlation functions is excellent, especially for the large training dataset. Variations in the predicted density isobars, albeit somewhat larger, are also acceptable, particularly given the errors inherent to approximate density functional theory. Overall, this study emphasizes the relevance of the database over the fitting method. Finally, this study underscores the limitations of root mean square errors and the need for comprehensive testing, advocating the use of multiple MLPs for enhanced certainty, particularly when simulating complex thermodynamic properties that may not be fully captured by simpler tests.

Local-environment-guided selection of atomic structures for the development of machine-learning potentials

Machine learning potentials (MLPs) have attracted significant attention in computational chemistry and materials science due to their high accuracy and computational efficiency. The proper selection of atomic structures is crucial for developing reliable MLPs. Insufficient or redundant atomic structures can impede the training process and potentially result in a poor quality MLP. Here, we propose a local-environment-guided screening algorithm for efficient dataset selection in MLP development. The algorithm utilizes a local environment bank to store unique local environments of atoms. The dissimilarity between a particular local environment and those stored in the bank is evaluated using the Euclidean distance. A new structure is selected only if its local environment is significantly different from those already present in the bank. Consequently, the bank is then updated with all the new local environments found in the selected structure. To demonstrate the effectiveness of our algorithm, we applied it to select structures for a Ge system and a Pd13H2 particle system. The algorithm reduced the training data size by around 80% for both without compromising the performance of the MLP models. We verified that the results were independent of the selection and ordering of the initial structures. We also compared the performance of our method with the farthest point sampling algorithm, and the results show that our algorithm is superior in both robustness and computational efficiency. Furthermore, the generated local environment bank can be continuously updated and can potentially serve as a growing database of feature local environments, aiding in efficient dataset maintenance for constructing accurate MLPs.

Computational Design of Peptides for Biomaterials Applications

Computer-aided molecular design and protein engineering emerge as promising and active subjects in bioengineering and biotechnological applications. On one hand, due to the advancing computing power in the past decade, modeling toolkits and force fields have been put to use for accurate multiscale modeling of biomolecules including lipid, protein, carbohydrate, and nucleic acids. On the other hand, machine learning emerges as a revolutionary data analysis tool that promises to leverage physicochemical properties and structural information obtained from modeling in order to build quantitative protein structure-function relationships. We review recent computational works that utilize state-of-the-art computational methods to engineer peptides and proteins for various emerging biomedical, antimicrobial, and antifreeze applications. We also discuss challenges and possible future directions toward developing a roadmap for efficient biomolecular design and engineering.

Mechanism of Charge Transport in Lithium Thiophosphate

Lithium ortho-thiophosphate (Li3PS4) has emerged as a promising candidate for solid-state electrolyte batteries, thanks to its highly conductive phases, cheap components, and large electrochemical stability range. Nonetheless, the microscopic mechanisms of Li-ion transport in Li3PS4 are far from being fully understood, the role of PS4 dynamics in charge transport still being controversial. In this work, we build machine learning potentials targeting state-of-the-art DFT references (PBEsol, r2SCAN, and PBE0) to tackle this problem in all known phases of Li3PS4 (α, β, and γ), for large system sizes and time scales. We discuss the physical origin of the observed superionic behavior of Li3PS4: the activation of PS4 flipping drives a structural transition to a highly conductive phase, characterized by an increase in Li-site availability and by a drastic reduction in the activation energy of Li-ion diffusion. We also rule out any paddle-wheel effects of PS4 tetrahedra in the superionic phases-previously claimed to enhance Li-ion diffusion-due to the orders-of-magnitude difference between the rate of PS4 flips and Li-ion hops at all temperatures below melting. We finally elucidate the role of interionic dynamical correlations in charge transport, by highlighting the failure of the Nernst-Einstein approximation to estimate the electrical conductivity. Our results show a strong dependence on the target DFT reference, with PBE0 yielding the best quantitative agreement with experimental measurements not only for the electronic band gap but also for the electrical conductivity of β- and α-Li3PS4.

A first-principles machine-learning force field for heterogeneous ice nucleation on microcline feldspar

The formation of ice in the atmosphere affects precipitation and cloud properties, and plays a key role in the climate of our planet. Although ice can form directly from liquid water under deeply supercooled conditions, the presence of foreign particles can aid ice formation at much warmer temperatures. Over the past decade, experiments have highlighted the remarkable efficiency of feldspar minerals as ice nuclei compared to other particles present in the atmosphere. However, the exact mechanism of ice formation on feldspar surfaces has yet to be fully understood. Here, we develop a first-principles machine-learning model for the potential energy surface aimed at studying ice nucleation at microcline feldspar surfaces. The model is able to reproduce with high-fidelity the energies and forces derived from density-functional theory (DFT) based on the SCAN exchange and correlation functional. Our training set includes configurations of bulk supercooled water, hexagonal and cubic ice, microcline, and fully-hydroxylated feldspar surfaces exposed to a vacuum, liquid water, and ice. We apply the machine-learning force field to study different fully-hydroxylated terminations of the (100), (010), and (001) surfaces of microcline exposed to a vacuum. Our calculations suggest that terminations that do not minimize the number of broken bonds are preferred in a vacuum. We also study the structure of supercooled liquid water in contact with microcline surfaces, and find that water density correlations extend up to around 10 Å from the surfaces. Finally, we show that the force field maintains a high accuracy during the simulation of ice formation at microcline surfaces, even for large systems of around 30 000 atoms. Future work will be directed towards the calculation of nucleation free-energy barriers and rates using the force field developed herein, and understanding the role of different microcline surfaces in ice nucleation.

Accuracy of TIP4P/2005 and SPC/Fw Water Models

Water is used as the main solvent in model systems containing bioorganic molecules. Choosing the right water model is an important step in the study of the biophysical and biochemical processes that occur in cells. In the present work, we perform molecular dynamics simulations using two distinct force fields for water: the rigid model TIP4P/2005, where only intermolecular interactions are considered, and the flexible model SPC/Fw, where intramolecular interactions are also taken into account. The simulations aim to determine the effect of the inclusion of intramolecular interactions on the accuracy of calculated properties of bulk water (density and thermal expansion coefficient, self-diffusion coefficients, shear viscosity, radial distribution functions, and dielectric constant), as compared to experimental results, over a temperature range between 250 and 370 K. We find that the results of the rigid model present the smallest deviations relative to experiments for most of the calculated quantities, except for the shear viscosity of supercooled water and the water dielectric constant, where the flexible model presents better agreement with experiments.

Implementation and Validation of an OpenMM Plugin for the Deep Potential Representation of Potential Energy

Machine learning potentials, particularly the deep potential (DP) model, have revolutionized molecular dynamics (MD) simulations, striking a balance between accuracy and computational efficiency. To facilitate the DP model's integration with the popular MD engine OpenMM, we have developed a versatile OpenMM plugin. This plugin supports a range of applications, from conventional MD simulations to alchemical free energy calculations and hybrid DP/MM simulations. Our extensive validation tests encompassed energy conservation in microcanonical ensemble simulations, fidelity in canonical ensemble generation, and the evaluation of the structural, transport, and thermodynamic properties of bulk water. The introduction of this plugin is expected to significantly expand the application scope of DP models within the MD simulation community, representing a major advancement in the field.

DP/MM: A Hybrid Model for Zinc-Protein Interactions in Molecular Dynamics

Zinc-containing proteins are vital for many biological processes, yet accurately modeling them using classical force fields is hindered by complicated polarization and charge transfer effects. This study introduces DP/MM, a hybrid force field scheme that utilizes a deep potential model to correct the atomic forces of zinc ions and their coordinated atoms, elevating them from MM to QM levels of accuracy. Trained on the difference between MM and QM atomic forces across diverse zinc coordination groups, the DP/MM model faithfully reproduces structural characteristics of zinc coordination during simulations, such as the tetrahedral coordination of Cys4 and Cys3His1 groups. Furthermore, DP/MM allows water exchange in the zinc coordination environment. With its unique blend of accuracy, efficiency, flexibility, and transferability, DP/MM serves as a valuable tool for studying structures and dynamics of zinc-containing proteins and also represents a pioneering approach in the evolving landscape of machine learning potentials for molecular modeling.

Applications and Advances in Machine Learning Force Fields

Force fields (FFs) form the basis of molecular simulations and have significant implications in diverse fields such as materials science, chemistry, physics, and biology. A suitable FF is required to accurately describe system properties. However, an off-the-shelf FF may not be suitable for certain specialized systems, and researchers often need to tailor the FF that fits specific requirements. Before applying machine learning (ML) techniques to construct FFs, the mainstream FFs were primarily based on first-principles force fields (FPFF) and empirical FFs. However, the drawbacks of FPFF and empirical FFs are high cost and low accuracy, respectively, so there is a growing interest in using ML as an effective and precise tool for reconciling this trade-off in developing FFs. In this review, we introduce the fundamental principles of ML and FFs in the context of machine learning force fields (MLFF). We also discuss the advantages and applications of MLFF compared to traditional FFs, as well as the MLFF toolkits widely employed in numerous applications.

Bridging the Gap-Thermofluidic Designs for Precision Bioelectronics

Bioelectronics, the merging of biology and electronics, can monitor and modulate biological behaviors across length and time scales with unprecedented capability. Current bioelectronics research largely focuses on devices' mechanical properties and electronic designs. However, the thermofluidic control is often overlooked, which is noteworthy given the discipline's importance in almost all bioelectronics processes. It is believed that integrating thermofluidic designs into bioelectronics is essential to align device precision with the complexity of biofluids and biological structures. This perspective serves as a mini roadmap for researchers in both fields to introduce key principles, applications, and challenges in both bioelectronics and thermofluids domains. Important interdisciplinary opportunities for the development of future healthcare devices and precise bioelectronics will also be discussed.

From ab initio to continuum: Linking multiple scales using deep-learned forces

We develop a deep learning-based algorithm, called DeepForce, to link ab initio physics with the continuum theory to predict concentration profiles of confined water. We show that the deep-learned forces can be used to predict the structural properties of water confined in a nanochannel with quantum scale accuracy by solving the continuum theory given by Nernst-Planck equation. The DeepForce model has an excellent predictive performance with a relative error less than 7.6% not only for confined water in small channel systems (L < 6 nm) but also for confined water in large channel systems (L = 20 nm) which are computationally inaccessible through the high accuracy ab initio molecular dynamics simulations. Finally, we note that classical Molecular dynamics simulations can be inaccurate in capturing the interfacial physics of water in confinement (L < 4.0 nm) when quantum scale physics are neglected.

Probing the self-ionization of liquid water with ab initio deep potential molecular dynamics

The chemical equilibrium between self-ionized and molecular water dictates the acid-base chemistry in aqueous solutions, yet understanding the microscopic mechanisms of water self-ionization remains experimentally and computationally challenging. Herein, Density Functional Theory (DFT)-based deep neural network (DNN) potentials are combined with enhanced sampling techniques and a global acid-base collective variable to perform extensive atomistic simulations of water self-ionization for model systems of increasing size. The explicit inclusion of long-range electrostatic interactions in the DNN potential is found to be crucial to accurately reproduce the DFT free energy profile of solvated water ion pairs in small (64 and 128 H2O) cells. The reversible work to separate the hydroxide and hydronium to a distance [Formula: see text] is found to converge for simulation cells containing more than 500 H2O, and a distance of [Formula: see text] 8 Å is the threshold beyond which the work to further separate the two ions becomes approximately zero. The slow convergence of the potential of mean force with system size is related to a restructuring of water and an increase of the local order around the water ions. Calculation of the dissociation equilibrium constant illustrates the key role of long-range electrostatics and entropic effects in the water autoionization process.

Consistent density functional theory-based description of ion hydration through density-corrected many-body representations

Delocalization error constrains the accuracy of density functional theory in describing molecular interactions in ion-water systems. Using Na+ and Cl- in water as model systems, we calculate the effects of delocalization error in the SCAN functional for describing ion-water and water-water interactions in hydrated ions, and demonstrate that density-corrected SCAN (DC-SCAN) predicts n-body and interaction energies with an accuracy approaching coupled cluster theory. The performance of DC-SCAN is size-consistent, maintaining an accurate description of molecular interactions well beyond the first solvation shell. Molecular dynamics simulations at ambient conditions with many-body MB-SCAN(DC) potentials, derived from the many-body expansion, predict the solvation structure of Na+ and Cl- in quantitative agreement with reference data, while simultaneously reproducing the structure of liquid water. Beyond rationalizing the accuracy of density-corrected models of ion hydration, our findings suggest that our unified density-corrected MB formalism holds great promise for efficient DFT-based simulations of condensed-phase systems with chemical accuracy.

Ab Initio Molecular Dynamics Investigation of the Solvation States of Hydrated Ions in Confined Water

Ionic transport in nanoscale channels with a critical size comparable to that of ions and solutes exhibits exceptional performance in water desalination, ion separation, electrocatalysts, and supercapacitors. However, the solvation states (SSs), i.e., the hydration structures and probability distribution, of hydrated ions in nanochannels differ from those in the bulk and the perspective of continuum theory. In this work, we conduct ab initio enhanced-sampling atomistic simulations to investigate the ion-specific SSs of monovalent ions (including Li+, Na+, K+, F-, Cl-, and I-) in the graphene channel with a width of 1 nm. Our findings highlight that the SSs of those ions are primarily determined by ion-water hydration, where ion-wall interactions play a minor role. The distribution of ions in layered confined water is a result of ion-specific hydration, which arises from the synergy of entropy and enthalpy. The free energy barriers for transitions between SSs are on the order of 1kBT, allowing for modulation through applying external fields or modifying surface properties. As the ion-wall interaction strengthens, as observed in vermiculite and carbides and nitrides of transition metal channels, the probability of near-wall SSs increases. These results help to improve the performance of nanofluidic devices and provide crucial insights for developing accurate force fields of molecular simulations or advanced theoretical approaches for ion dynamics in confined channels.

Thermal dependence of the hydrated proton and optimal proton transfer in the protonated water hexamer

Water is a key ingredient for life and plays a central role as solvent in many biochemical reactions. However, the intrinsically quantum nature of the hydrogen nucleus, revealing itself in a large variety of physical manifestations, including proton transfer, gives rise to unexpected phenomena whose description is still elusive. Here we study, by a combination of state-of-the-art quantum Monte Carlo methods and path-integral molecular dynamics, the structure and hydrogen-bond dynamics of the protonated water hexamer, the fundamental unit for the hydrated proton. We report a remarkably low thermal expansion of the hydrogen bond from zero temperature up to 300 K, owing to the presence of short-Zundel configurations, characterised by proton delocalisation and favoured by the synergy of nuclear quantum effects and thermal activation. The hydrogen bond strength progressively weakens above 300 K, when localised Eigen-like configurations become relevant. Our analysis, supported by the instanton statistics of shuttling protons, reveals that the near-room-temperature range from 250 K to 300 K is optimal for proton transfer in the protonated water hexamer.

High-Throughput Aqueous Electrolyte Structure Prediction Using IonSolvR and Equivariant Graph Neural Network Potentials

Neural network potentials have recently emerged as an efficient and accurate tool for accelerating ab initio molecular dynamics (AIMD) in order to simulate complex condensed phases such as electrolyte solutions. Their principal limitation, however, is their requirement for sufficiently large and accurate training sets, which are often composed of Kohn-Sham density functional theory (DFT) calculations. Here we examine the feasibility of using existing density functional tight-binding (DFTB) molecular dynamics trajectory data available in the IonSolvR database in order to accelerate the training of E(3)-equivariant graph neural network potentials. We show that the solvation structure of Na+ and Cl- in aqueous NaCl solutions can be accurately reproduced with remarkably small amounts of data (i.e., 100 MD frames). We further show that these predictions can be systematically improved further via an embarrassingly parallel resampling approach.

Simulating the isotropic Raman spectra of O-H stretching mode in liquid H2O based on a machine learning potential: the influence of vibrational couplings

In this study, we trained a deep potential (DP) for H2O, an accurate machine learning (ML) potential. We performed molecular dynamics (MD) simulations of liquid water using the DP model (or DeePMD simulations). Our results showed that the DP model exhibits DFT-level accuracy, and the DeePMD simulation is a promising approach for modeling the structural properties of liquid water. Based on the DeePMD simulation trajectories, we calculated the isotropic Raman spectra of the O-H stretching mode using the surface-specific velocity-velocity correlation function (ssVVCF), showing that the DeePMD/ssVVCF approach can correctly capture the bimodal characteristics of the experimental Raman spectra, with one peak located near 3400 cm-1 and the other near 3250 cm-1. The success of the DeePMD/ssVVCF approach should be credited to (1) the DFT-level accuracy of the DP model for H2O, (2) the ssVVCF formulation considering the coupling between vibrational modes, and (3) non-Condon effects. Furthermore, the DeePMD simulations revealed that the anharmonic interactions between the coupled water molecules in the first and second hydration shells should play an essential role in the strong mixing of the H-O-H bending mode and the O-H stretching mode, leading to the delocalization of the O-H stretching band. In particular, increasing the strength of hydrogen bonds would enhance the bend-stretch coupling, leading to the red-shifting of the O-H vibrational spectra and the increase in the intensity of the shoulder around 3250 cm-1.

Flow through Deformed Carbon Nanotubes Predicted by Rigid and Flexible Water Models

In this study, using nonequilibrium molecular dynamics simulation, the flow of water in deformed carbon nanotubes is studied for two water models TIP4P/2005 and simple point charge/FH (SPC/FH). The results demonstrated a nonuniform dependence of the flow on the tube deformation and the flexibility imposed on the water molecules, leading to an unexpected increase in the flow in some cases. The effects of the tube diameter and pressure gradient are investigated to explain the abnormal flow behavior with different degrees of structural deformation.

Collective motion in hcp-Fe at Earth's inner core conditions

Earth's inner core is predominantly composed of solid iron (Fe) and displays intriguing properties such as strong shear softening and an ultrahigh Poisson's ratio. Insofar, physical mechanisms to explain these features coherently remain highly debated. Here, we have studied longitudinal and shear wave velocities of hcp-Fe (hexagonal close-packed iron) at relevant pressure-temperature conditions of the inner core using in situ shock experiments and machine learning molecular dynamics (MLMD) simulations. Our results demonstrate that the shear wave velocity of hcp-Fe along the Hugoniot in the premelting condition, defined as T/Tm (Tm: melting temperature of iron) above 0.96, is significantly reduced by ~30%, while Poisson's ratio jumps to approximately 0.44. MLMD simulations at 230 to 330 GPa indicate that collective motion with fast diffusive atomic migration occurs in premelting hcp-Fe primarily along [100] or [010] crystallographic direction, contributing to its elastic softening and enhanced Poisson's ratio. Our study reveals that hcp-Fe atoms can diffusively migrate to neighboring positions, forming open-loop and close-loop clusters in the inner core conditions. Hcp-Fe with collective motion at the inner core conditions is thus not an ideal solid previously believed. The premelting hcp-Fe with collective motion behaves like an extremely soft solid with an ultralow shear modulus and an ultrahigh Poisson's ratio that are consistent with seismic observations of the region. Our findings indicate that premelting hcp-Fe with fast diffusive motion represents the underlying physical mechanism to help explain the unique seismic and geodynamic features of the inner core.

Characterization of the Hydrogen-Bond Network in High-Pressure Water by Deep Potential Molecular Dynamics

The hydrogen-bond (H-bond) network of high-pressure water is investigated by neural-network-based molecular dynamics (MD) simulations with first-principles accuracy. The static structure factors (SSFs) of water at three densities, i.e., 1, 1.115, and 1.24 g/cm3, are directly evaluated from 512 water MD trajectories, which are in quantitative agreement with the experiments. We propose a new method to decompose the computed SSF and identify the changes in the SSF with respect to the changes in H-bond structures. We find that a larger water density results in a higher probability for one or two non-H-bonded water molecules to be inserted into the inner shell, explaining the changes in the tetrahedrality of water under pressure. We predict that the structure of the accepting end of water molecules is more easily influenced by the pressure than by the donating end. Our work sheds new light on explaining the SSF and H-bond properties in related fields.

DeePMD-kit v2: A software package for deep potential models

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

Melting curves of ice polymorphs in the vicinity of the liquid-liquid critical point

The possible existence of a liquid-liquid critical point in deeply supercooled water has been a subject of debate due to the challenges associated with providing definitive experimental evidence. The pioneering work by Mishima and Stanley [Nature 392, 164-168 (1998)] sought to shed light on this problem by studying the melting curves of different ice polymorphs and their metastable continuation in the vicinity of the expected liquid-liquid transition and its associated critical point. Based on the continuous or discontinuous changes in the slope of the melting curves, Mishima [Phys. Rev. Lett. 85, 334 (2000)] suggested that the liquid-liquid critical point lies between the melting curves of ice III and ice V. We explore this conjecture using molecular dynamics simulations with a machine learning model based on ab initio quantum-mechanical calculations. We study the melting curves of ices III, IV, V, VI, and XIII and find that all of them are supercritical and do not intersect the liquid-liquid transition locus. We also find a pronounced, yet continuous, change in the slope of the melting lines upon crossing of the liquid locus of maximum compressibility. Finally, we analyze the literature in light of our findings and conclude that the scenario in which the melting curves are supercritical is favored by the most recent computational and experimental evidence. Although the preponderance of evidence is consistent with the existence of a second critical point in water, the behavior of ice polymorph melting lines does not provide strong evidence in support of this viewpoint, according to our calculations.

Thermal Conductivity of Water at Extreme Conditions

Measuring the thermal conductivity (κ) of water at extreme conditions is a challenging task, and few experimental data are available. We predict κ for temperatures and pressures relevant to the conditions of the Earth mantle, between 1,000 and 2,000 K and up to 22 GPa. We employ close to equilibrium molecular dynamics simulations and a deep neural network potential fitted to density functional theory data. We then interpret our results by computing the equation of state of water on a fine grid of points and using a simple model for κ. We find that the thermal conductivity is weakly dependent on temperature and monotonically increases with pressure with an approximate square-root behavior. In addition, we show how the increase of κ at high pressure, relative to ambient conditions, is related to the corresponding increase in the sound velocity. Although the relationships between the thermal conductivity, pressure and sound velocity established here are not rigorous, they are sufficiently accurate to allow for a robust estimate of the thermal conductivity of water in a broad range of temperatures and pressures, where experiments are still difficult to perform.

Transferability evaluation of the deep potential model for simulating water-graphene confined system

Machine learning potentials (MLPs) are poised to combine the accuracy of ab initio predictions with the computational efficiency of classical molecular dynamics (MD) simulation. While great progress has been made over the last two decades in developing MLPs, there is still much to be done to evaluate their model transferability and facilitate their development. In this work, we construct two deep potential (DP) models for liquid water near graphene surfaces, Model S and Model F, with the latter having more training data. A concurrent learning algorithm (DP-GEN) is adopted to explore the configurational space beyond the scope of conventional ab initio MD simulation. By examining the performance of Model S, we find that an accurate prediction of atomic force does not imply an accurate prediction of system energy. The deviation from the relative atomic force alone is insufficient to assess the accuracy of the DP models. Based on the performance of Model F, we propose that the relative magnitude of the model deviation and the corresponding root-mean-square error of the original test dataset, including energy and atomic force, can serve as an indicator for evaluating the accuracy of the model prediction for a given structure, which is particularly applicable for large systems where density functional theory calculations are infeasible. In addition to the prediction accuracy of the model described above, we also briefly discuss simulation stability and its relationship to the former. Both are important aspects in assessing the transferability of the MLP model.

Temperature-pressure phase diagram of confined monolayer water/ice at first-principles accuracy with a machine-learning force field

Understanding the phase behaviour of nanoconfined water films is of fundamental importance in broad fields of science and engineering. However, the phase behaviour of the thinnest water film - monolayer water - is still incompletely known. Here, we developed a machine-learning force field (MLFF) at first-principles accuracy to determine the phase diagram of monolayer water/ice in nanoconfinement with hydrophobic walls. We observed the spontaneous formation of two previously unreported high-density ices, namely, zigzag quasi-bilayer ice (ZZ-qBI) and branched-zigzag quasi-bilayer ice (bZZ-qBI). Unlike conventional bilayer ices, few inter-layer hydrogen bonds were observed in both quasi-bilayer ices. Notably, the bZZ-qBI entails a unique hydrogen-bonding network that consists of two distinctive types of hydrogen bonds. Moreover, we identified, for the first time, the stable region for the lowest-density [Formula: see text] monolayer ice (LD-48MI) at negative pressures (<-0.3 GPa). Overall, the MLFF enables large-scale first-principle-level molecular dynamics (MD) simulations of the spontaneous transition from the liquid water to a plethora of monolayer ices, including hexagonal, pentagonal, square, zigzag (ZZMI), and hexatic monolayer ices. These findings will enrich our understanding of the phase behaviour of the nanoconfined water/ices and provide a guide for future experimental realization of the 2D ices.

High-Throughput Condensed-Phase Hybrid Density Functional Theory for Large-Scale Finite-Gap Systems: The SeA Approach

High-throughput electronic structure calculations (often performed using density functional theory (DFT)) play a central role in screening existing and novel materials, sampling potential energy surfaces, and generating data for machine learning applications. By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal DFT and furnish a more accurate description of the underlying electronic structure, albeit at a computational cost that often prohibits such high-throughput applications. To address this challenge, we have constructed a robust, accurate, and computationally efficient framework for high-throughput condensed-phase hybrid DFT and implemented this approach in the PWSCF module of Quantum ESPRESSO (QE). The resulting SeA approach (SeA = SCDM + exx + ACE) combines and seamlessly integrates: (i) the selected columns of the density matrix method (SCDM, a robust noniterative orbital localization scheme that sidesteps system-dependent optimization protocols), (ii) a recently extended version of exx (a black-box linear-scaling EXX algorithm that exploits sparsity between localized orbitals in real space when evaluating the action of the standard/full-rank V^xx operator), and (iii) adaptively compressed exchange (ACE, a low-rank V^xx approximation). In doing so, SeA harnesses three levels of computational savings: pair selection and domain truncation from SCDM + exx (which only considers spatially overlapping orbitals on orbital-pair-specific and system-size-independent domains) and low-rank V^xx approximation from ACE (which reduces the number of calls to SCDM + exx during the self-consistent field (SCF) procedure). Across a diverse set of 200 nonequilibrium (H₂O)₆₄ configurations (with densities spanning 0.4-1.7 g/cm³), SeA provides a 1-2 order-of-magnitude speedup in the overall time-to-solution, i.e., ≈8-26× compared to the convolution-based PWSCF(ACE) implementation in QE and ≈78-247× compared to the conventional PWSCF(Full) approach, and yields energies, ionic forces, and other properties with high fidelity. As a proof-of-principle high-throughput application, we trained a deep neural network (DNN) potential for ambient liquid water at the hybrid DFT level using SeA via an actively learned data set with ≈8,700 (H₂O)₆₄ configurations. Using an out-of-sample set of (H₂O)₅₁₂ configurations (at nonambient conditions), we confirmed the accuracy of this SeA-trained potential and showcased the capabilities of SeA by computing the ground-truth ionic forces in this challenging system containing >1,500 atoms.

Realistic phase diagram of water from "first principles" data-driven quantum simulations

Since the experimental characterization of the low-pressure region of water's phase diagram in the early 1900s, scientists have been on a quest to understand the thermodynamic stability of ice polymorphs on the molecular level. In this study, we demonstrate that combining the MB-pol data-driven many-body potential for water, which was rigorously derived from "first principles" and exhibits chemical accuracy, with advanced enhanced-sampling algorithms, which correctly describe the quantum nature of molecular motion and thermodynamic equilibria, enables computer simulations of water's phase diagram with an unprecedented level of realism. Besides providing fundamental insights into how enthalpic, entropic, and nuclear quantum effects shape the free-energy landscape of water, we demonstrate that recent progress in "first principles" data-driven simulations, which rigorously encode many-body molecular interactions, has opened the door to realistic computational studies of complex molecular systems, bridging the gap between experiments and simulations.

A Deep Potential model for liquid-vapor equilibrium and cavitation rates of water

Computational studies of liquid water and its phase transition into vapor have traditionally been performed using classical water models. Here, we utilize the Deep Potential methodology-a machine learning approach-to study this ubiquitous phase transition, starting from the phase diagram in the liquid-vapor coexistence regime. The machine learning model is trained on ab initio energies and forces based on the SCAN density functional, which has been previously shown to reproduce solid phases and other properties of water. Here, we compute the surface tension, saturation pressure, and enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K and evaluate the Deep Potential model performance against experimental results and the semiempirical TIP4P/2005 classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier and nucleation rate at negative pressures for the isotherm of 296.4 K. We find that the nucleation rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005 water model due to an underestimation in the surface tension from the Deep Potential model. From analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water model, which is (0.091 ± 0.008) nm at 296.4 K. Finally, we identify that water molecules display a preferential orientation in the liquid-vapor interface, in which H atoms tend to point toward the vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behavior is more pronounced for planar interfaces than for the curved interfaces in bubbles. This work represents the first application of Deep Potential models to the study of liquid-vapor coexistence and water cavitation.