Isotope effects in liquid water via deep potential molecular dynamics

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.

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.

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.

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.

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.

Revealing Intramolecular Isotope Effects with Chemical-Bond Precision

Isotope substitution of a molecule not only changes its vibrational frequencies but also changes its vibrational distributions in real-space. Quantitatively measuring the isotope effects inside a polyatomic molecule requires both energy and spatial resolutions at the single-bond level, which has been a long-lasting challenge in macroscopic techniques. By achieving ångström resolution in tip-enhanced Raman spectroscopy (TERS), we record the corresponding local vibrational modes of pentacene and its fully deuterated form, enabling us to identify and measure the isotope effect of each vibrational mode. The measured frequency ratio ν_H/ν_D varies from 1.02 to 1.33 in different vibrational modes, indicating different isotopic contributions of H/D atoms, which can be distinguished from TERS maps in real-space and well described by the potential energy distribution simulations. Our study demonstrates that TERS can serve as a non-destructive and highly sensitive methodology for isotope detection and recognition with chemical-bond precision.

Distinct roles of graphene and graphene oxide nanosheets in regulating phospholipid flip-flop

Two-dimensional (2D) nanomaterials, such as graphene nanosheets (GNs) and graphene oxide nanosheets (GOs), could adhere onto or insert into a biological membrane, leading to a change in membrane properties and biological activities. Consequently, GN and GO become potential candidates for mediating interleaflet phospholipid transfer. In this work, molecular dynamics (MD) simulations were employed to investigate the effects of GN and GO on lipid flip-flop behavior and the underlying molecular mechanisms. Of great interest is that GN and GO work in opposite directions. The inserted GN can induce the formation of an ordered nanodomain, which dramatically elevates the free energy barrier of flipping phospholipids from one leaflet to the other, thus leading to a decreased lipid flip-flop rate. In contrast, the embedded GO can catalyze the transport of phospholipids between membrane leaflets by facilitating the formation of water pores. These results suggest that GN may work as an inhibitor of the interleaflet lipid translocation, while GO may play the role of scramblases. These findings are expected to expand promising biomedical applications of 2D nanomaterials.

Routine Molecular Dynamics Simulations Including Nuclear Quantum Effects: From Force Fields to Machine Learning Potentials

We report the implementation of a multi-CPU and multi-GPU massively parallel platform dedicated to the explicit inclusion of nuclear quantum effects (NQEs) in the Tinker-HP molecular dynamics (MD) package. The platform, denoted Quantum-HP, exploits two simulation strategies: the Ring-Polymer Molecular Dynamics (RPMD) that provides exact structural properties at the cost of a MD simulation in an extended space of multiple replicas and the adaptive Quantum Thermal Bath (adQTB) that imposes the quantum distribution of energy on a classical system via a generalized Langevin thermostat and provides computationally affordable and accurate (though approximate) NQEs. We discuss some implementation details, efficient numerical schemes, and parallelization strategies and quickly review the GPU acceleration of our code. Our implementation allows an efficient inclusion of NQEs in MD simulations for very large systems, as demonstrated by scaling tests on water boxes with more than 200,000 atoms (simulated using the AMOEBA polarizable force field). We test the compatibility of the approach with Tinker-HP's recently introduced Deep-HP machine learning potentials module by computing water properties using the DeePMD potential with adQTB thermostatting. Finally, we show that the platform is also compatible with the alchemical free energy estimation capabilities of Tinker-HP and fast enough to perform simulations. Therefore, we study how NQEs affect the hydration free energy of small molecules solvated with the recently developed Q-AMOEBA water force field. Overall, the Quantum-HP platform allows users to perform routine quantum MD simulations of large condensed-phase systems and will help to shed new light on the quantum nature of important interactions in biological matter.

Predicting Structural Properties of Pure Silica Zeolites Using Deep Neural Network Potentials

Machine learning potentials (MLPs) capable of accurately describing complex ab initio potential energy surfaces (PESs) have revolutionized the field of multiscale atomistic modeling. In this work, using an extensive density functional theory (DFT) data set (denoted as Si-ZEO22) consisting of 219 unique zeolite topologies (350,000 unique DFT calculations) found in the International Zeolite Association (IZA) database, we have trained a DeePMD-kit MLP to model the dynamics of silica frameworks. The performance of our model is evaluated by calculating various properties that probe the accuracy of the energy and force predictions. This MLP demonstrates impressive agreement with DFT for predicting zeolite structural properties, energy-volume trends, and phonon density of states. Furthermore, our model achieves reasonable predictions for stress-strain relationships without including DFT stress data during training. These results highlight the ability of MLPs to capture the flexibility of zeolite frameworks and motivate further MLP development for nanoporous materials with near-ab initio accuracy.

Development and Validation of Versatile Deep Atomistic Potentials for Metal Oxides

Machine learning interatomic potentials powered by neural networks have been shown to readily model a gradient of compositions in metallic systems. However, their application to date on ionic systems tends to focus on specific compositions and oxidation states owing to their more heterogeneous chemical nature. Herein we show that a deep neural network potential (DNP) can model various properties of metal oxides with different oxidation states without additional charge information. We created and validated DNPs for Ag_xO_y, Cu_xO_y Mg_xO_y, Pt_xO_y, and Zn_xO_y, whereby each system was trained without any limitations on oxidation states. We illustrate how the database can be augmented to enhance the DNP transferability for a new polymorph, surface energies, and thermal expansion. In addition, we show that these potentials can correctly interpolate significant pressure and temperature ranges, exhibit stability over long molecular dynamics simulation time scales, and replicate nonharmonic thermal expansion, consistent with experimental results.

Solvation structures of calcium and magnesium ions in water with the presence of hydroxide: a study by deep potential molecular dynamics

The solvation structures of calcium (Ca²⁺) and magnesium (Mg²⁺) ions with the presence of hydroxide (OH^-) ion in water are essential for understanding their roles in biological and chemical processes but have not been fully explored. Ab initio molecular dynamics (AIMD) is an important tool to address this issue, but two challenges exist. First, an accurate description of OH^- from AIMD needs an appropriate exchange-correlation functional. Second, a long trajectory is needed to reach an equilibrium state for the Ca²⁺-OH^- and Mg²⁺-OH^- ion pairs in aqueous solutions. Herein, we adopt a deep potential molecular dynamics (DPMD) method to simulate 1 ns trajectories for the Ca²⁺-OH^- and Mg²⁺-OH^- ion pairs in water; the DPMD method provides efficient machine-learning-based models that have the accuracy of the SCAN exchange-correlation functional within the framework of density functional theory. The solvation structures of the cations and the OH^- in terms of three different species have been systematically investigated. On the one hand, we find that OH^- have more significant effects on the solvation structure of Ca²⁺ than that of Mg²⁺. We observe that the OH^- substantially affects the orientation angles of water molecules surrounding the cation. Through the time correlation functions, we conclude that the water molecules in the first solvation shell of Ca²⁺ change their preferred orientation faster than those of Mg²⁺. On the other hand, with the presence of the cation in the first solvation shell of OH^-, we find that the hydrogen bonds of OH^- are severely altered, and the adjacent water molecules of OH^- are squeezed. The two cations have substantially different effects on the solvation structure of OH^-. Our work provides new insight into the solvation structures of Ca²⁺ and Mg²⁺ in water with the presence of OH^-.

DP Compress: A Model Compression Scheme for Generating Efficient Deep Potential Models

Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via deep neural networks to predict the energy and atomic forces, resulting in lower running efficiency as compared to the typical empirical force fields. Herein, we report a model compression scheme for boosting the performance of the Deep Potential (DP) model, a deep learning-based PES model. This scheme, we call DP Compress, is an efficient postprocessing step after the training of DP models (DP Train). DP Compress combines several DP-specific compression techniques, which typically speed up DP-based molecular dynamics simulations by an order of magnitude faster and consume an order of magnitude less memory. We demonstrate that DP Compress is sufficiently accurate by testing a variety of physical properties of Cu, H₂O, and Al-Cu-Mg systems. DP Compress applies to both CPU and GPU machines and is publicly available online.

Advances in the OCEAN-3 spectroscopy package

The OCEAN code for calculating valence- and core-level spectra using the Bethe-Salpeter equation is briefly reviewed. OCEAN is capable of calculating optical absorption, near-edge X-ray absorption or non-resonant scattering, and resonant inelastic X-ray scattering, requiring only the structure of the material as input. Improved default behavior and reduced input requirements are detailed as well as new capabilities, such as incorporation of final-state-dependent broadening, finite-temperature dependence, and flexibility in the density-functional theory exchange-correlation potentials. OCEAN is built on top of a plane-wave, pseudopotential, density-functional theory foundation, and calculations are shown for systems ranging in size up to 7 nm³.

Structures of liquid and aqueous water isotopologues at ambient temperature from ab initio path integral simulations

The heavy hydrogen isotopes D and T are found in trace amounts in water, and when their concentration increases they can play an intricate role in modulating the physical properties of the liquid. We present an analysis of the microscopic structures of ambient light water (H₂O(l)), heavy water (D₂O(l)), T₂O(l), HDO(aq) and HTO(aq) studied by ab initio path integral molecular dynamics (PIMD). Unlike previous ab initio PIMD investigations of H₂O(l) and D₂O(l) [Chen et al., Phys. Rev. Lett., 2003, 91, 215503] [Machida et al., J. Chem. Phys., 2017, 148, 102324] we find that D₂O(l) is more structured than H₂O(l), as is predicted by the experiment. The agreement between the experiment and our simulation for H₂O(l) and D₂O(l) allows us to accurately predict the intra- and intermolecular structures of T₂O(l) HDO(aq) and HTO(aq). T₂O(l) is found to have a similar intermolecular structure to that of D₂O(l), while the intramolecular structure is more compact, giving rise to a smaller dipole moment than those of H₂O(l) and D₂O(l). For the mixed isotope species, HDO(aq) and HTO(aq), we find smaller dipole moments and fewer hydrogen bonds when compared with the pure species H₂O and D₂O. We can attribute this effect to the relative compactness of the mixed isotope species, which results in a lower dipole moment than that of the pure species.

E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials

This work presents Neural Equivariant Interatomic Potentials (NequIP), an E(3)-equivariant neural network approach for learning interatomic potentials from ab-initio calculations for molecular dynamics simulations. While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs E(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of atomic environments. The method achieves state-of-the-art accuracy on a challenging and diverse set of molecules and materials while exhibiting remarkable data efficiency. NequIP outperforms existing models with up to three orders of magnitude fewer training data, challenging the widely held belief that deep neural networks require massive training sets. The high data efficiency of the method allows for the construction of accurate potentials using high-order quantum chemical level of theory as reference and enables high-fidelity molecular dynamics simulations over long time scales.

Electrocatalysis in Alkaline Media and Alkaline Membrane-Based Energy Technologies

Hydrogen energy-based electrochemical energy conversion technologies offer the promise of enabling a transition of the global energy landscape from fossil fuels to renewable energy. Here, we present a comprehensive review of the fundamentals of electrocatalysis in alkaline media and applications in alkaline-based energy technologies, particularly alkaline fuel cells and water electrolyzers. Anion exchange (alkaline) membrane fuel cells (AEMFCs) enable the use of nonprecious electrocatalysts for the sluggish oxygen reduction reaction (ORR), relative to proton exchange membrane fuel cells (PEMFCs), which require Pt-based electrocatalysts. However, the hydrogen oxidation reaction (HOR) kinetics is significantly slower in alkaline media than in acidic media. Understanding these phenomena requires applying theoretical and experimental methods to unravel molecular-level thermodynamics and kinetics of hydrogen and oxygen electrocatalysis and, particularly, the proton-coupled electron transfer (PCET) process that takes place in a proton-deficient alkaline media. Extensive electrochemical and spectroscopic studies, on single-crystal Pt and metal oxides, have contributed to the development of activity descriptors, as well as the identification of the nature of active sites, and the rate-determining steps of the HOR and ORR. Among these, the structure and reactivity of interfacial water serve as key potential and pH-dependent kinetic factors that are helping elucidate the origins of the HOR and ORR activity differences in acids and bases. Additionally, deliberately modulating and controlling catalyst-support interactions have provided valuable insights for enhancing catalyst accessibility and durability during operation. The design and synthesis of highly conductive and durable alkaline membranes/ionomers have enabled AEMFCs to reach initial performance metrics equal to or higher than those of PEMFCs. We emphasize the importance of using membrane electrode assemblies (MEAs) to integrate the often separately pursued/optimized electrocatalyst/support and membranes/ionomer components. Operando/in situ methods, at multiscales, and ab initio simulations provide a mechanistic understanding of electron, ion, and mass transport at catalyst/ionomer/membrane interfaces and the necessary guidance to achieve fuel cell operation in air over thousands of hours. We hope that this Review will serve as a roadmap for advancing the scientific understanding of the fundamental factors governing electrochemical energy conversion in alkaline media with the ultimate goal of achieving ultralow Pt or precious-metal-free high-performance and durable alkaline fuel cells and related technologies.

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory-Based Ab Initio Molecular Dynamics II: Extensions to the Isobaric-Isoenthalpic and Isobaric-Isothermal Ensembles

In the previous paper of this series [Ko, H.-Y. et al. J. Chem. Theory Comput. 2020, 16, 3757-3785], we presented a theoretical and algorithmic framework based on a localized representation of the occupied space that exploits the inherent sparsity in the real-space evaluation of the exact exchange (EXX) interaction in finite-gap systems. This was accompanied by a detailed description of exx, a massively parallel hybrid message-passing interface MPI/OpenMP implementation of this approach in Quantum ESPRESSO (QE) that enables linear scaling hybrid density functional theory (DFT)-based ab initio molecular dynamics (AIMD) in the microcanonical/canonical (NVE/NVT) ensembles of condensed-phase systems containing 500-1000 atoms (in fixed orthorhombic cells) with a wall time cost comparable to semi-local DFT. In this work, we extend the current capabilities of exx to enable hybrid DFT-based AIMD simulations of large-scale condensed-phase systems with general and fluctuating cells in the isobaric-isoenthalpic/isobaric-isothermal (NpH/NpT) ensembles. The theoretical extensions to this approach include an analytical derivation of the EXX contribution to the stress tensor for systems in general simulation cells with a computational complexity that scales linearly with system size. The corresponding algorithmic extensions to exx include optimized routines that (i) handle both static and fluctuating simulation cells with non-orthogonal lattice symmetries, (ii) solve Poisson's equation in general/non-orthogonal cells via an automated selection of the auxiliary grid directions in the Natan-Kronik representation of the discrete Laplacian operator, and (iii) evaluate the EXX contribution to the stress tensor. Using this approach, we perform a case study on a variety of condensed-phase systems (including liquid water, a benzene molecular crystal polymorph, and semi-conducting crystalline silicon) and demonstrate that the EXX contributions to the energy and stress tensor simultaneously converge with an appropriate choice of exx parameters. This is followed by a critical assessment of the computational performance of the extended exx module across several different high-performance computing architectures via case studies on (i) the computational complexity due to lattice symmetry during NpT simulations of three different ice polymorphs (i.e., ice Ih, II, and III) and (ii) the strong/weak parallel scaling during large-scale NpT simulations of liquid water. We demonstrate that the robust and highly scalable implementation of this approach in the extended exx module is capable of evaluating the EXX contribution to the stress tensor with negligible cost (<1%) as well as all other EXX-related quantities needed during NpT simulations of liquid water (with a very tight 150 Ry planewave cutoff) in ≈5.2 s ((H₂O)₁₂₈) and ≈6.8 s ((H₂O)₂₅₆) per AIMD step. As such, the extended exx module presented in this work brings us another step closer to routinely performing hybrid DFT-based AIMD simulations of sufficient duration for large-scale condensed-phase systems across a wide range of thermodynamic conditions.

Modeling Liquid Water by Climbing up Jacob's Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials

Within the framework of Kohn-Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob's ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric-isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

Phase Diagram of a Deep Potential Water Model

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII^{''} and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments.

Machine learning phase space quantum dynamics approaches

Derived from phase space expressions of the quantum Liouville theorem, equilibrium continuity dynamics is a category of trajectory-based phase space dynamics methods, which satisfies the two critical fundamental criteria: conservation of the quantum Boltzmann distribution for the thermal equilibrium system and being exact for any thermal correlation functions (even of nonlinear operators) in the classical and harmonic limits. The effective force and effective mass matrix are important elements in the equations of motion of equilibrium continuity dynamics, where only the zeroth term of an exact series expansion of the phase space propagator is involved. We introduce a machine learning approach for fitting these elements in quantum phase space, leading to a much more efficient integration of the equations of motion. Proof-of-concept applications to realistic molecules demonstrate that machine learning phase space dynamics approaches are possible as well as competent in producing reasonably accurate results with a modest computation effort.

Machine-Learning-Driven Simulations on Microstructure and Thermophysical Properties of MgCl2-KCl Eutectic

Theoretical studies on the MgCl₂-KCl eutectic heavily rely on ab initio calculations based on density functional theory (DFT). However, neither large-scale nor long-time calculations are feasible in the framework of the ab initio method, which makes it challenging to accurately predict some properties. To address this issue, a scheme based on ab initio calculation, deep neural networks, and machine learning is introduced. By training on high-quality data sets generated by ab initio calculations, a deep potential (DP) is constructed to describe the interaction between atoms. This work shows that the DP enables higher efficiency and similar accuracy relative to DFT. By performing molecular dynamics simulations with DP, the microstructure and thermophysical properties of the MgCl₂-KCl eutectic (32:68 mol %) are investigated. The structural evolution with temperature is analyzed through partial radial distribution functions, coordination numbers, angular distribution functions, and structural factors. Meanwhile, the estimated thermophysical properties are discussed, including density, thermal expansion coefficient, shear viscosity, self-diffusion coefficient, and specific heat capacity. It reveals that the Mg²⁺ ions in this system have a distorted tetrahedral geometry rather than an octahedral one (with vacancies). The microstructure of the MgCl₂-KCl eutectic shows the feature of medium-range order, and this feature will be enhanced at a higher temperature. All predicted thermophysical properties are in good agreement with the experimental results. The hydrodynamic radius determined from the shear viscosity and self-diffusion coefficient shows that the Mg²⁺ ions have a strong local structure and diffuse as if with an intact coordination shell. Overall, this work provides a thorough understanding of the microstructure and enriches the data of the thermophysical properties of the MgCl₂-KCl eutectic.

Faster exact exchange in periodic systems using single-precision arithmetic

Density-functional theory simplifies many-electron calculations by approximating the exchange and correlation interactions with a one-electron operator that is a functional of the density. Hybrid functionals incorporate some amount of exact exchange, improving agreement with measured electronic and structural properties. However, calculations with hybrid functionals require substantial computational resources, limiting their use. By calculating the exchange interaction of periodic systems with single-precision arithmetic, the computation time is cut nearly in half with a negligible loss in accuracy. This improvement makes exact exchange calculations quicker and more feasible, especially for high-throughput calculations. Example hybrid density-functional theory calculations of band energies, forces, and x-ray absorption spectra show that this single-precision implementation maintains accuracy with significantly reduced runtime and memory requirements.

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based Ab Initio Molecular Dynamics. 1. Theory, Algorithm, and Performance

By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal density functional theory (DFT) and thereby furnish a more accurate and reliable description of the underlying electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we describe a linear-scaling approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions (MLWFs)) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems of interest at the hybrid DFT level. We focus our theoretical discussion on the integration of this approach into the framework of Car-Parrinello AIMD, and highlight the central role played by the MLWF-product potential (i.e., the solution of Poisson's equation for each corresponding MLWF-product density) in the evaluation of the EXX energy and wave function forces. We then provide a comprehensive description of the exx algorithm implemented in the open-source Quantum ESPRESSO program, which employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the high-performance computing (HPC) resources available on current- and next-generation supercomputer architectures. This is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when AIMD simulations of liquid water are performed in the canonical (NVT) ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT-based AIMD simulations of condensed-phase systems containing 500-1000 atoms (e.g., (H₂O)₂₅₆) with a wall time cost that is comparable to that of semilocal DFT. In doing so, exx takes us one step closer to routinely performing AIMD simulations of complex and large-scale condensed-phase systems for sufficiently long time scales at the hybrid DFT level of theory.

Free energy of proton transfer at the water-TiO2 interface from ab initio deep potential molecular dynamics

TiO₂ is a widely used photocatalyst in science and technology and its interface with water is important in fields ranging from geochemistry to biomedicine. Yet, it is still unclear whether water adsorbs in molecular or dissociated form on TiO₂ even for the case of well-defined crystalline surfaces. To address this issue, we simulated the TiO₂-water interface using molecular dynamics with an ab initio-based deep neural network potential. Our simulations show a dynamical equilibrium of molecular and dissociative adsorption of water on TiO₂. Water dissociates through a solvent-assisted concerted proton transfer to form a pair of short-lived hydroxyl groups on the TiO₂ surface. Molecular adsorption of water is ΔF = 8.0 ± 0.9 kJ mol^-1 lower in free energy than the dissociative adsorption, giving rise to a 5.6 ± 0.5% equilibrium water dissociation fraction at room temperature. Due to the relevance of surface hydroxyl groups to the surface chemistry of TiO₂, our model might be key to understanding phenomena ranging from surface functionalization to photocatalytic mechanisms.