Structural, electronic, and dynamical properties of liquid water by ab initio molecular dynamics based on SCAN functional within the canonical ensemble

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.

Neutron scattering and neural-network quantum molecular dynamics investigation of the vibrations of ammonia along the solid-to-liquid transition

Vibrational spectroscopy allows us to understand complex physical and chemical interactions of molecular crystals and liquids such as ammonia, which has recently emerged as a strong hydrogen fuel candidate to support a sustainable society. We report inelastic neutron scattering measurement of vibrational properties of ammonia along the solid-to-liquid phase transition with high enough resolution for direct comparisons to ab-initio simulations. Theoretical analysis reveals the essential role of nuclear quantum effects (NQEs) for correctly describing the intermolecular spectrum as well as high energy intramolecular N-H stretching modes. This is achieved by training neural network models using ab-initio path-integral molecular dynamics (PIMD) simulations, thereby encompassing large spatiotemporal trajectories required to resolve low energy dynamics while retaining NQEs. Our results not only establish the role of NQEs in ammonia but also provide general computational frameworks to study complex molecular systems with NQEs.

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.

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.

Core-ionization spectrum of liquid water

We present state-of-the-art calculations of the core-ionization spectrum of water. Despite significant progress in procedures developed to mitigate various experimental complications and uncertainties, the experimental determination of ionization energies of solvated species involves several non-trivial steps such as assessing the effect of the surface potential, electrolytes, and finite escape depths of photoelectrons. This provides a motivation to obtain robust theoretical values of the intrinsic bulk ionization energy and the corresponding solvent-induced shift. Here we develop theoretical protocols based on coupled-cluster theory and electrostatic embedding. Our value of the intrinsic solvent-induced shift of the 1sO ionization energy of water is -1.79 eV. The computed absolute position and the width of the 1sO peak in photoelectron spectrum of water are 538.47 eV and 1.44 eV, respectively, agreeing well with the best experimental values.

Machine Learning Density Functionals from the Random-Phase Approximation

Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in application due to their large computational cost. Here, we use machine learning to map the RPA to a pure Kohn-Sham density functional. The machine learned RPA model (ML-RPA) is a nonlocal extension of the standard gradient approximation. The density descriptors used as ingredients for the enhancement factor are nonlocal counterparts of the local density and its gradient. Rather than fitting only RPA exchange-correlation energies, we also include derivative information in the form of RPA optimized effective potentials. We train a single ML-RPA functional for diamond, its surfaces, and liquid water. The accuracy of ML-RPA for the formation energies of 28 diamond surfaces reaches that of state-of-the-art van der Waals functionals. For liquid water, however, ML-RPA cannot yet improve upon the standard gradient approximation. Overall, our work demonstrates how machine learning can extend the applicability of the RPA to larger system sizes, time scales, and chemical spaces.

Accurate SCC-DFTB Parametrization of Liquid Water with Improved Atomic Charges and Iterative Boltzmann Inversion

This work presents improvements of the description of liquid water within the self-consistent-charge density-functional based tight-binding scheme combining the use of Weighted Mulliken (WMull) charges and optimized O-H repulsive potential through the iterative Boltzmann inversion (IBI) process. The quality of the newly developed models is validated considering pair radial distribution functions (RDFs), as well as other structural, energetic, thermodynamic, and dynamic properties. The use of WMull charges certainly improves the agreement with experimental data, however leading to over-structured RDFs at short distance, that can be further improved by considering an optimized O-H repulsive potential obtained by the IBI process. Three different schemes were used to optimize this potential: (i) optimization including short O-H distances. This led to accurate RDFs as well as improved self-diffusion coefficient and heat of vaporization, while the proton transfer energy barrier is severely deteriorated; (ii) optimization starting at long distance. The proton transfer energy barrier is recovered while the heat of vaporization is deteriorated and the O-H RDF is less accurate at short distance; (iii) optimization within the path-integral molecular dynamics scheme which allows us to exclude nuclear quantum effects from the repulsive potential. The latter potential, in conjunction with the WMull improved atomic charges, provides similar results as (i) for structural, dynamic, and thermodynamic properties while recovering a large part of the proton transfer energy barrier. It therefore offers a good compromise to study both dynamic properties and chemistry within liquid water at a quantum chemical level.

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.

Radicals in aqueous solution: assessment of density-corrected SCAN functional

We study self-interaction effects in solvated and strongly-correlated cationic molecular clusters, with a focus on the solvated hydroxyl radical. To address the self-interaction issue, we apply the DC-r2SCAN method, with the auxiliary density matrix approach. Validating our method through simulations of bulk liquid water, we demonstrate that DC-r2SCAN maintains the structural accuracy of r2SCAN while effectively addressing spin density localization issues. Extending our analysis to solvated cationic molecular clusters, we find that the hemibonded motif in the [CH3S∴CH3SH]+ cluster is disrupted in the DC-r2SCAN simulation, in contrast to r2SCAN that preserves the (three-electron-two-center)-bonded motif. Similarly, for the [SH∴SH2]+ cluster, r2SCAN restores the hemibonded motif through spin leakage, while DC-r2SCAN predicts a weaker hemibond formation influenced by solvent-solute interactions. Our findings demonstrate the potential of DC-r2SCAN combined with the auxiliary density matrix method to improve electronic structure calculations, providing insights into the properties of solvated cationic molecular clusters. This work contributes to the advancement of self-interaction corrected electronic structure theory and offers a computational framework for modeling condensed phase systems with intricate correlation effects.

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.

Size and Quality of Quantum Mechanical Data Set for Training Neural Network Force Fields for Liquid Water

Molecular dynamics simulations have been used in different scientific fields to investigate a broad range of physical systems. However, the accuracy of calculation is based on the model considered to describe the atomic interactions. In particular, ab initio molecular dynamics (AIMD) has the accuracy of density functional theory (DFT) and thus is limited to small systems and a relatively short simulation time. In this scenario, Neural Network Force Fields (NNFFs) have an important role, since they provide a way to circumvent these caveats. In this work, we investigate NNFFs designed at the level of DFT to describe liquid water, focusing on the size and quality of the training data set considered. We show that structural properties are less dependent on the size of the training data set compared to dynamical ones (such as the diffusion coefficient), and a good sampling (selecting data reference for the training process) can lead to a small sample with good precision.

Hydroxide Diffusion in Functionalized Cylindrical Nanopores as Idealized Models of Anion Exchange Membrane Environments: An Ab Initio Molecular Dynamics Study

Anion exchange membranes (AEMs) have attracted significant interest for their applications in fuel cells and other electrochemical devices in recent years. Understanding water distributions and hydroxide transport mechanisms within AEMs is critical to improving their performance as concerns hydroxide conductivity. Recently, nanoconfined environments have been used to mimic AEM environments. Following this approach, we construct nanoconfined cylindrical pore structures using graphane nanotubes (GNs) functionalized with trimethylammonium cations as models of local AEM morphology. These structures were then used to investigate hydroxide transport using ab initio molecular dynamics (AIMD). The simulations showed that hydroxide transport is suppressed in these confined environments relative to the bulk solution although the mechanism is dominated by structural diffusion. One factor causing the suppressed hydroxide transport is the reduced proton transfer (PT) rates due to changes in hydroxide and water solvation patterns under confinement compared to bulk solution as well as strong interactions between hydroxide ions and the tethered cation groups.

Quantifying the Structure of Water and Hydrated Monovalent Ions by Density Functional Theory-Based Molecular Dynamics

The accurate description of the structures of water and hydrated ions is important in electrochemical desalination, ion separation, and supercapacitors. In this work, we present an ab initio atomistic simulation-based study to explore the structure of water and hydrated monovalent ions (Li⁺, Na⁺, K⁺, Rb⁺, F^-, and Cl^-) at ambient conditions using generalized gradient approximation (GGA)-based methods with and without van der Waals correction (PBE, PBE + D3, and revPBE + D3) and recently developed strongly constrained and appropriately normed (SCAN) meta-GGA. We find that both revPBE + D3 and SCAN can well capture the structure of bulk water with +30 K artificial high temperature in contrast to overstructuring water using PBE and PBE + D3. However, being the same as PBE + D3, revPBE + D3 overestimates the structure of the hydration shell, especially for monovalent cations. Surprisingly, SCAN can well match the experimental results of hydrated monovalent ions. Detailed structure analyzes of entropy reveal that the hydration shell under the level of PBE + D3 and revPBE + D3 is more disordered and looser than SCAN. The successful prediction of the flexible SCAN functional could facilitate the exploration of complex ionic processes in the aqueous phase, the interactions of hydrated ions with surfaces, and solvation states in nanopores at an accurate, efficient, predictive, and ab initio level.

How Good Is the Density-Corrected SCAN Functional for Neutral and Ionic Aqueous Systems, and What Is So Right about the Hartree-Fock Density?

Density functional theory (DFT) is the most widely used electronic structure method, due to its simplicity and cost effectiveness. The accuracy of a DFT calculation depends not only on the choice of the density functional approximation (DFA) adopted but also on the electron density produced by the DFA. SCAN is a modern functional that satisfies all known constraints for meta-GGA functionals. The density-driven errors, defined as energy errors arising from errors of the self-consistent DFA electron density, can hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree-Fock level of theory due to its relatively low computational cost. In this work, we present extensive calculations aimed at determining the accuracy of the DC-SCAN functional for various aqueous systems. DC-SCAN (SCAN@HF) shows remarkable consistency in reproducing reference data obtained at the coupled cluster level of theory, with minimal loss of accuracy. Density-driven errors in the description of ionic aqueous clusters are thoroughly investigated. By comparison with the orbital-optimized CCD density in the water dimer, we find that the self-consistent SCAN density transfers a spurious fraction of an electron across the hydrogen bond to the hydrogen atom (H^*, covalently bound to the donor oxygen atom) from the acceptor (O_A) and donor (O_D) oxygen atoms, while HF makes a much smaller spurious transfer in the opposite direction, consistent with DC-SCAN (SCAN@HF) reduction of SCAN overbinding due to delocalization error. While LDA seems to be the conventional extreme of density delocalization error, and HF the conventional extreme of (usually much smaller) density localization error, these two densities do not quite yield the conventional range of density-driven error in energy differences. Finally, comparisons of the DC-SCAN results with those obtained with the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method show that DC-SCAN represents a more accurate approach to reducing density-driven errors in SCAN calculations of ionic aqueous clusters. While the HF density is superior to that of SCAN for noncompact water clusters, the opposite is true for the compact water molecule with exactly 10 electrons.

EXAFS spectroscopy measurements and ab initio molecular dynamics simulations reveal the hydration structure of the radium(II) ion

Radium is refocused from the viewpoint of an environmental pollutant and cancer therapy using alpha particles, where it mainly exists as a hydrated ion. We investigated the radium hydration structure and the dynamics of water molecules by extended X-ray absorption fine structure (EXAFS) spectroscopy and ab initio molecular dynamics (AIMD) simulation. The EXAFS experiment showed that the coordination number and average distance between radium ion and the oxygen atoms in the first hydration shell are 9.2 ± 1.9 and 2.87 ± 0.06 Å, respectively. They are consistent with those obtained from the AIMD simulations, 8.4 and 2.88 Å. The AIMD simulations also revealed that the water molecules in the first hydration shell of radium are less structured and more mobile than those of barium, which is an analogous element of radium. Our results indicate that radium can be more labile than barium in terms of interactions with water.

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Extended X-ray absorption fine structure (EXAFS) measurement revealed the hydration structure of radium ion

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Ab initio molecular dynamics (AIMD) simulation brought consistent results

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AIMD revealed the structural and dynamic properties of the water molecules

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The hydration structure of radium ion is more labile than that of barium ion

Structural and Dynamic Properties of Solvated Hydroxide and Hydronium Ions in Water from Ab Initio Modeling

Predicting the asymmetric structure and dynamics of solvated hydroxide and hydronium in water has been a challenging task from ab initio molecular dynamics (AIMD). The difficulty mainly comes from a lack of accurate and efficient exchange-correlation functional in elucidating the amphiphilic nature and the ubiquitous proton transfer behaviors of the two ions. By adopting the strongly-constrained and appropriately normed (SCAN) meta-GGA functional in AIMD simulations, we systematically examine the amphiphilic properties, the solvation structures, the electronic structures, and the dynamic properties of the two water ions. In particular, we compare these results to those predicted by the PBE0-TS functional, which is an accurate yet computationally more expensive exchange-correlation functional. We demonstrate that the general-purpose SCAN functional provides a reliable choice in describing the two water ions. Specifically, in the SCAN picture of water ions, the appearance of the fourth and fifth hydrogen bonds near hydroxide stabilizes the pot-like shape solvation structure and suppresses the structural diffusion, while the hydronium stably donates three hydrogen bonds to its neighbors. We apply a detailed analysis of the proton transfer mechanism of the two ions and find the two ions exhibit substantially different proton transfer patterns. Our AIMD simulations indicate hydroxide diffuses slower than hydronium in water, which is consistent with the experiments.

Connection between water's dynamical and structural properties: Insights from ab initio simulations

SignificanceFirst-principles calculations, which explicitly account for the electronic structure of matter, can shed light on the molecular structure and dynamics of water in its supercooled state. In this work, we use density functional theory, which relies on a functional to describe electronic exchange and correlations, to evaluate which functional best describes the temperature evolution of bulk water transport coefficients. We also assess the validity of the Stokes-Einstein relation for all the functionals in the temperature range studied, and explore the link between structure and dynamics. Based on these results, we show how transport coefficients can be computed from structural descriptors, which require shorter simulation times to converge, and we point toward strategies to develop better functionals.

Self-consistent determination of long-range electrostatics in neural network potentials

Machine learning has the potential to revolutionize the field of molecular simulation through the development of efficient and accurate models of interatomic interactions. Neural networks can model interactions with the accuracy of quantum mechanics-based calculations, but with a fraction of the cost, enabling simulations of large systems over long timescales. However, implicit in the construction of neural network potentials is an assumption of locality, wherein atomic arrangements on the nanometer-scale are used to learn interatomic interactions. Because of this assumption, the resulting neural network models cannot describe long-range interactions that play critical roles in dielectric screening and chemical reactivity. Here, we address this issue by introducing the self-consistent field neural network — a general approach for learning the long-range response of molecular systems in neural network potentials that relies on a physically meaningful separation of the interatomic interactions — and demonstrate its utility by modeling liquid water with and without applied fields.

Machine learning-based neural network potentials often cannot describe long-range interactions. Here the authors present an approach for building neural network potentials that can describe the electronic and nuclear response of molecular systems to long-range electrostatics.

Structural characteristics of low-density environments in liquid water

The existence of two structural forms in liquid water has been a point of discussion for a long time. A phase transition between these two forms of liquid water has been proposed based on evidence from molecular simulations, and experiments have also been very recently able to track the proposed transition of the low-density liquid form to the high-density liquid form. We propose to use the average angle an oxygen atom makes with its neighbors to describe the structural environment of a water molecule. The distribution of this order parameter is observed to have two peaks with one peak at ∼109.5^{∘}, corresponding to the internal angle of a regular tetrahedron, indicating tetrahedral arrangement. The other peak corresponds to an environment with a tighter arrangement of neighboring molecules. The distribution of O-O-O angles is decomposed into two skewed distributions to estimate the fractions of the two liquid forms in water. A good similarity is observed between the temperature and pressure trends of fractions of locally favored tetrahedral structure (LFTS) form estimated using the new order parameter and the reports in the literature, over a range of temperatures and pressures. We also compare the structural environments indicated by different order parameters and find that the order parameter proposed in this paper captures the structure of first solvation shell of the LFTS accurately.

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.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Elevating density functional theory to chemical accuracy for water simulations through a density-corrected many-body formalism

Density functional theory (DFT) has been extensively used to model the properties of water. Albeit maintaining a good balance between accuracy and efficiency, no density functional has so far achieved the degree of accuracy necessary to correctly predict the properties of water across the entire phase diagram. Here, we present density-corrected SCAN (DC-SCAN) calculations for water which, minimizing density-driven errors, elevate the accuracy of the SCAN functional to that of "gold standard" coupled-cluster theory. Building upon the accuracy of DC-SCAN within a many-body formalism, we introduce a data-driven many-body potential energy function, MB-SCAN(DC), that quantitatively reproduces coupled cluster reference values for interaction, binding, and individual many-body energies of water clusters. Importantly, molecular dynamics simulations carried out with MB-SCAN(DC) also reproduce the properties of liquid water, which thus demonstrates that MB-SCAN(DC) is effectively the first DFT-based model that correctly describes water from the gas to the liquid phase.

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.

Thermophysical properties of water using reactive force fields

The widescale importance and rich phenomenology of water continue to motivate the development of computational models. ReaxFF force fields incorporate many characteristics desirable for modeling aqueous systems: molecular flexibility, polarization, and chemical reactivity (bond formation and breaking). However, their ability to model the general properties of water has not been evaluated in detail. We present comprehensive benchmarks of the thermophysical properties of water for two ReaxFF models, the water-2017 and CHON-2017_weak force fields. These include structural, electrostatic, vibrational, thermodynamic, coexistence, and transport properties at ambient conditions (300 K and 0.997 g cm^-3) and along the standard pressure (1 bar) isobar. Overall, CHON-2017_weak predicts more accurate thermophysical properties than the water-2017 force field. Based on our results, we recommend potential avenues for improvement: the dipole moment to quadrupole moment ratio, the self-diffusion coefficient, especially for water-2017, and the gas phase vibrational frequencies with the aim to improve the vibrational properties of liquid water.

Photo-induced hydrophilicity at the ZnO(112̄0) surface: an evolutionary algorithm-aided density functional theory study

Evolutionary algorithm-aided density functional theory calculations were utilized to determine the stable adsorption structures of H₂O at ZnO(112̄0) extensively under different coverages. By decomposing the adsorption energetics, we illustrate that H₂O dissociation to a large extent is actually hampered by the barrier for induced distortion of the ZnO surface, and once the surface becomes less difficult to be distorted it will exhibit higher hydrophilicity or even superhydrophilicity. Specifically, photo-stimulation modelling suggests that the surface Zn-O bonds can be weakened by photo-excitation, and the layer of fully dissociated H₂O can be then facilitated to form. Accordingly, a novel mechanism for photo-induced superhydrophilicity is proposed.

A transferable active-learning strategy for reactive molecular force fields

Predictive molecular simulations require fast, accurate and reactive interatomic potentials. Machine learning offers a promising approach to construct such potentials by fitting energies and forces to high-level quantum-mechanical data, but doing so typically requires considerable human intervention and data volume. Here we show that, by leveraging hierarchical and active learning, accurate Gaussian Approximation Potential (GAP) models can be developed for diverse chemical systems in an autonomous manner, requiring only hundreds to a few thousand energy and gradient evaluations on a reference potential-energy surface. The approach uses separate intra- and inter-molecular fits and employs a prospective error metric to assess the accuracy of the potentials. We demonstrate applications to a range of molecular systems with relevance to computational organic chemistry: ranging from bulk solvents, a solvated metal ion and a metallocage onwards to chemical reactivity, including a bifurcating Diels-Alder reaction in the gas phase and non-equilibrium dynamics (a model SN2 reaction) in explicit solvent. The method provides a route to routinely generating machine-learned force fields for reactive molecular systems.

Nuclear Quantum Effect and Its Temperature Dependence in Liquid Water from Random Phase Approximation via Artificial Neural Network

We report structural and dynamical properties of liquid water described by the random phase approximation (RPA) correlation together with the exact exchange energy (EXX) within density functional theory. By utilizing thermostated ring polymer molecular dynamics, we examine the nuclear quantum effects and their temperature dependence. We circumvent the computational limitation of performing direct first-principles molecular dynamics simulation at this high level of electronic structure theory by adapting an artificial neural network model. We show that the EXX+RPA level of theory accurately describes liquid water in terms of both dynamical and structural properties.

Effects of applied voltage on water at a gold electrode interface from ab initio molecular dynamics

Electrode–water interfaces under voltage bias demonstrate anomalous electrostatic and structural properties that are influential in their catalytic and technological applications. Mean-field and empirical models of the electrical double layer (EDL) that forms in response to an applied potential do not capture the heterogeneity that polarizable, liquid-phase water molecules engender. To illustrate the inhomogeneous nature of the electrochemical interface, Born–Oppenheimer ab initio molecular dynamics calculations of electrified Au(111) slabs interfaced with liquid water were performed using a combined explicit–implicit solvent approach. The excess charges localized on the model electrode were held constant and the electrode potentials were computed at frequent simulation times. The electrode potential in each trajectory fluctuated with changes in the atomic structure, and the trajectory-averaged potentials converged and yielded a physically reasonable differential capacitance for the system. The effects of the average applied voltages, both positive and negative, on the structural, hydrogen bonding, dynamical, and vibrational properties of water were characterized and compared to literature where applicable. Controlled-potential simulations of the interfacial solvent dynamics provide a framework for further investigation of more complex or reactive species in the EDL and broadly for understanding electrochemical interfaces in situ.

Ab initio molecular dynamics of an aqueous electrode interface reveal the electrostatic, structural, and dynamic effects of quantifiable voltage biases on water.

Born–Oppenheimer molecular dynamics simulations on structures of high-density and low-density water: a comparison of the SCAN meta-GGA and PBE GGA functionals

Using Born–Oppenheimer ab initio molecular dynamics (BOAIMD) simulations, the high-density water (HDW) and low-density water (LDW) structures based on SCAN meta-GGA are compared with those based on PBE GGA.

Accurate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation

The recently proposed rSCAN functional [ J. Chem. Phys. 2019 150, 161101] is a regularized form of the SCAN functional [ Phys. Rev. Lett. 2015 115, 036402] that improves SCAN's numerical performance at the expense of breaking constraints known from the exact exchange-correlation functional. We construct a new meta-generalized gradient approximation by restoring exact constraint adherence to rSCAN. The resulting functional maintains rSCAN's numerical performance while restoring the transferable accuracy of SCAN.

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.

First-Principles Calculation of Water pKa Using the Newly Developed SCAN Functional

Acid/base chemistry is an intriguing topic that still constitutes a challenge for computational chemistry. While estimating the acid dissociation constant (or pK_a) could shed light on many chemistry processes, especially in the fields of biochemistry and geochemistry, evaluating the relative stability between protonated and nonprotonated species is often very difficult. Indeed, a prerequisite for calculating the pK_a of any molecule is an accurate description of the energetics of water dissociation. Here, we applied constrained molecular dynamics simulations, a noncanonical sampling technique, to investigate the water deprotonation process by selecting the OH distance as the reaction coordinate. The calculation is based on density functional theory and the newly developed SCAN functional, which has shown excellent performance in describing water structure. This first benchmark of SCAN on a chemical reaction shows that this functional accurately models the energetics of proton transfer reactions in an aqueous environment. After taking Coulomb long-range corrections and nuclear quantum effects into account, the estimated water pK_a is only 1.0 pK_a unit different from the target experimental value. Our results show that the combination of SCAN and constrained MD successfully reproduces the chemistry of water and constitutes a good framework for calculating the free energy of chemical reactions of interest.

Similarities and differences between potassium and ammonium ions in liquid water: a first-principles study

Understanding ion solvation in liquid water is critical in optimizing materials for a wide variety of emerging technologies, including water desalination and purification.

Quantifying the hydration structure of sodium and potassium ions: taking additional steps on Jacob's Ladder

The ability to reproduce the experimental structure of water around the sodium and potassium ions is a key test of the quality of interaction potentials due to the central importance of these ions in a wide range of important phenomena.