The Quest for Accurate Liquid Water Properties from First Principles

The Effect of Surface Oxygen Coverage on the Oxygen Evolution Reaction over a CoFeNiCr High-Entropy Alloy

Developing cost-effective and highly active electrocatalysts for the oxygen evolution reaction (OER) is crucial for advancing sustainable energy applications. High-entropy alloys (HEAs) made from earth-abundant transition metals, thanks to their remarkable stability and electrocatalytic performance, provide a promising alternative to expensive electrocatalysts typically derived from noble metals. While pristine HEA surfaces have been theoretically investigated, and the effect of oxygen coverage on conventional metal electrocatalysts has been examined, the impact of surface oxygen coverage on the electrocatalytic performance of HEAs remains poorly understood. To bridge this gap, we employ density functional theory (DFT) calculations to reconstruct the free energy diagram of OER intermediates on CoFeNiCr HEA surfaces with varying oxygen coverages, evaluating their impact on the rate-limiting step and theoretical overpotential. Our findings reveal that increased oxygen coverage weakens the adsorption of HO* and O*, but not HOO*. As a result, the theoretical overpotential for the OER decreases with higher oxygen coverage, and the rate-limiting step shifts from the third oxidation step (HOO* formation) at low coverage to the first oxidation step (HO* formation) at higher coverage.

To Pair or not to Pair? Machine-Learned Explicitly-Correlated Electronic Structure for NaCl in Water

The extent of ion pairing in solution is an important phenomenon to rationalize transport and thermodynamic properties of electrolytes. A fundamental measure of this pairing is the potential of mean force (PMF) between solvated ions. The relative stabilities of the paired and solvent shared states in the PMF and the barrier between them are highly sensitive to the underlying potential energy surface. However, direct application of accurate electronic structure methods is challenging, since long simulations are required. We develop wave function based machine learning potentials with the random phase approximation (RPA) and second order Møller-Plesset (MP2) perturbation theory for the prototypical system of Na and Cl ions in water. We show both methods in agreement, predicting the paired and solvent shared states to have similar energies (within 0.2 kcal/mol). We also provide the same benchmarks for different DFT functionals as well as insight into the PMF based on simple analyses of the interactions in the system.

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.

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob's ladder

The accurate representation of the structural and dynamical properties of water is essential for simulating the unique behavior of this ubiquitous solvent. Here we assess the current status of describing liquid water using ab initio molecular dynamics, with a special focus on the performance of all the later generation Minnesota functionals. Findings are contextualized within the current knowledge on DFT for describing bulk water under ambient conditions and compared to experimental data. We find that, contrary to the prevalent idea that local and semilocal functionals overstructure water and underestimate dynamical properties, M06-L, revM06-L, and M11-L understructure water, while MN12-L and MN15-L overdistance water molecules due to weak cohesive effects. This can be attributed to a weakening of the hydrogen bond network, which leads to dynamical fingerprints that are over fast. While most of the hybrid Minnesota functionals (M06, M08-HX, M08-SO, M11, MN12-SX, and MN15) also yield understructured water, their dynamical properties generally improve over their semilocal counterparts. It emerges that exact exchange is a crucial component for accurately describing hydrogen bonds, which ultimately leads to corrections in both the dynamical and structural properties. However, an excessive amount of exact exchange strengthens hydrogen bonds and causes overstructuring and slow dynamics (M06-HF). As a compromise, M06-2X is the best performing Minnesota functional for water, and its D3 corrected variant shows very good structural agreement. From previous studies considering nuclear quantum effects (NQEs), the hybrid revPBE0-D3, and the rung-5 RPA (RPA@PBE) have been identified as the only two approximations that closely agree with experiments. Our results suggest that the M06-2X(-D3) functionals have the potential to further improve the reproduction of experimental properties when incorporating NQEs through path integral approaches. This work provides further proof that accurate modeling of water interactions requires the inclusion of both exact exchange and balanced (non-local) correlation, highlighting the need for higher rungs on Jacob's ladder to achieve predictive simulations of complex biological systems in aqueous environments.

First-principles spectroscopy of aqueous interfaces using machine-learned electronic and quantum nuclear effects

Vibrational spectroscopy is a powerful approach to visualising interfacial phenomena. However, extracting structural and dynamical information from vibrational spectra is a challenge that requires first-principles simulations, including non-Condon and quantum nuclear effects. We address this challenge by developing a machine-learning enhanced first-principles framework to speed up predictive modelling of infrared, Raman, and sum-frequency generation spectra. Our approach uses machine learning potentials that encode quantum nuclear effects to generate quantum trajectories using simple molecular dynamics efficiently. In addition, we reformulate bulk and interfacial selection rules to express them unambiguously in terms of the derivatives of polarisation and polarisabilities of the whole system and predict these derivatives efficiently using fully-differentiable machine learning models of dielectric response tensors. We demonstrate our framework's performance by predicting the IR, Raman, and sum-frequency generation spectra of liquid water, ice and the water-air interface by achieving near quantitative agreement with experiments at nearly the same computational efficiency as pure classical methods. Finally, to aid the experimental discovery of new phases of nanoconfined water, we predict the temperature-dependent vibrational spectra of monolayer water across the solid-hexatic-liquid phases transition.

Nonequilibrium Ab Initio Molecular Dynamics Simulation of Water Splitting at Fe2O3-Hematite/Water Interfaces in an External Electric Field

In the exploration of the optimal material for achieving the photoelectrochemical dissociation of water into hydrogen, hematite (α-Fe2O3) emerges as a highly promising candidate for proof-of-concept demonstrations. Recent studies suggest that the concurrent application of external electric fields could enhance the photoelectrochemical (PEC) process. To delve into this, we conducted nonequilibrium ab initio molecular dynamics (NE-AIMD) simulations in this study, focusing on hematite-water interfaces at room temperature under progressively stronger electric fields. Our findings reveal intriguing evidence of water molecule adsorption and dissociation, as evidenced by an analysis of the structural properties of the hydrated layered surface of the hematite-water interface. Additionally, we scrutinized intermolecular structures using radial distribution functions (RDFs) to explore the interaction between the hematite slab and water. Notably, the presence of a Grotthuss hopping mechanism became apparent as the electric field strength increased. A comprehensive discussion based on intramolecular geometry highlighted aspects such as hydrogen-bond lengths, H-bond angles, average H-bond numbers, and the observed correlation existing among the hydrogen-bond strength, bond-dissociation energy, and H-bond lifetime. Furthermore, we assessed the impact of electric fields on the librational, bending, and stretching modes of hydrogen atoms in water by calculating the vibrational density of states (VDOS). This analysis revealed distinct field effects for the three characteristic band modes, both in the bulk region and at the hematite-water interface. We also evaluated the charge density of active elements at the aqueous hematite surface, delving into field-induced electronic charge-density variations through the Hirshfeld charge density analysis of atomic elements. Throughout this work, we drew clear distinctions between parallel and antiparallel field alignments at the hematite-water interface, aiming to elucidate crucial differences in local behavior for each surface direction of the hematite-water interface.

Intra-cluster Charge Migration upon Hydration of Protonated Formic Acid Revealed by Anharmonic Analysis of Cold Ion Vibrational Spectra

The rates of many chemical reactions are accelerated when carried out in micron-sized droplets, but the molecular origin of the rate acceleration remains unclear. One example is the condensation reaction of 1,2-diaminobenzene with formic acid to yield benzimidazole. The observed rate enhancements have been rationalized by invoking enhanced acidity at the surface of methanol solvent droplets with low water content to enable protonation of formic acid to generate a cationic species (protonated formic acid or PFA) formed by attachment of a proton to the neutral acid. Because PFA is the key feature in this reaction mechanism, vibrational spectra of cryogenically cooled, microhydrated PFA·(H2O)n=1-6 were acquired to determine how the extent of charge localization depends on the degree of hydration. Analysis of these highly anharmonic spectra with path integral ab initio molecular dynamics simulations reveals the gradual displacement of the excess proton onto the water network in the microhydration regime at low temperatures with n = 3 as the tipping point for intra-cluster proton transfer.

A Status Report on "Gold Standard" Machine-Learned Potentials for Water

Owing to the central importance of water to life as well as its unusual properties, potentials for water have been the subject of extensive research over the past 50 years. Recently, five potentials based on different machine learning approaches have been reported that are at or near the "gold standard" CCSD(T) level of theory. The development of such high-level potentials enables efficient and accurate simulations of water systems using classical and quantum dynamical approaches. This Perspective serves as a status report of these potentials, focusing on their methodology and applications to water systems across different phases. Their performances on the energies of gas phase water clusters, as well as condensed phase structural and dynamical properties, are discussed.

Collective Proton Transfers in Cyclic Water-Ammonia Tetramers: A Path Integral Machine-Learning Study

We present results from machine-learning-based path integral molecular dynamics simulations that describe isomerization paths articulated via collective proton transfers along mixed, cyclic tetramers combining water and ammonia at cryogenic conditions. The net result of such isomerizations is a reverse of the chirality of the global hydrogen-bonding architecture along the different cyclic moieties. In monocomponent tetramers, the classical free energy profiles associated with these isomerizations present the usual symmetric double-well characteristics whereas the reactive paths exhibit full concertedness among the different intermolecular transfer processes. Contrastingly, in mixed water/ammonia tetramers, the incorporation of a second component introduces imbalances in the strengths of the different hydrogen bonds leading to a partial loss of concertedness, most notably at the vicinity of the transition state. As such, the highest and lowest degrees of progression are registered along OH···N and O···HN coordinations, respectively. These characteristics lead to polarized transition state scenarios akin to solvent-separated ion-pair configurations. The explicit incorporation of nuclear quantum effects promotes drastic depletions in the activation free energies and modifications in the overall shape of the profiles which include central plateau-like stages, indicating the prevalence of deep tunneling regimes. On the other hand, the quantum treatment of the nuclei partially restores the degree of concertedness among the evolutions of the individual transfers.

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.

Local Molecular Field Theory for Coulomb Interactions in Aqueous Solutions

Coulomb interactions play a crucial role in a wide array of processes in aqueous solutions but present conceptual and computational challenges to both theory and simulations. We review recent developments in an approach addressing these challenges─local molecular field (LMF) theory. LMF theory exploits an exact and physically suggestive separation of intermolecular Coulomb interactions into strong short-range and uniformly slowly varying long-range components. This allows us to accurately determine the averaged effects of the long-range components on the short-range structure using effective single particle fields and analytical corrections, greatly reducing the need for complex lattice summation techniques used in most standard approaches. The simplest use of these ideas in aqueous solutions leads to the short solvent (SS) model, where both solvent-solvent and solute-solvent Coulomb interactions have only short-range components. Here we use the SS model to give a simple description of pairing of nucleobases and biologically relevant ions in water.

Equilibrium and Dynamical Characteristics of Hydrogen Bond Bifurcations in Water-Water and Water-Ammonia Dimers: A Path Integral Molecular Dynamics Study

We present path integral molecular dynamics results that describe the effects of nuclear quantum fluctuations on equilibrium and dynamical characteristics pertaining to bifurcation pathways in hydrogen bonded dimers combining water and ammonia, at cryogenic temperatures of the order of 20 K. Along these isomerizations, the hydrogen atoms in the molecules acting as hydrogen-bond donors interchange their original dangling/connective characters. Our results reveal that the resulting quantum transition paths comprise three stages: the initial and final ones involve overall rotations during which the two protons retain their classical-like characteristics. Effects from quantum fluctuation are clearly manifested in the changes operated at the intermediate passages over transition states, as the spatial extents of the protons stretch over typical lengths comparable to the distances between connective and dangling basins of attractions. Consequently, the classical over-the-hill path is replaced by a tunneling controlled mechanism which, within the path integral perspective, can be cast in terms of concerted inter-basin migrations of polymer beads from dangling-to-connective and from connective-to-dangling, at practically no energy costs. We also estimated the characteristic timescales describing such interconversions within the approximate ring polymer rate theory. Effects derived from full and partial deuteration are also discussed.

Accurate diffusion coefficients of the excess proton and hydroxide in water via extensive ab initio simulations with different schemes

Despite its simple molecular formula, obtaining an accurate in silico description of water is far from straightforward. Many of its very peculiar properties are quite elusive, and in particular, obtaining good estimations of the diffusion coefficients of the solvated proton and hydroxide at a reasonable computational cost has been an unsolved challenge until now. Here, I present extensive results of several unusually long ab initio molecular dynamics (MD) simulations employing different combinations of the Born-Oppenheimer and second-generation Car-Parrinello MD propagation methods with different ensembles (NVE and NVT) and thermostats, which show that these methods together with the RPBE-D3 functional provide a very accurate estimation of the diffusion coefficients of the solvated H₃O⁺ and OH^- ions, together with an extremely accurate description of several properties of neutral water (such as the structure of the liquid and its diffusion and shear viscosity coefficients). In addition, I show that the estimations of D_H3O⁺ and D_OH^- depend dramatically on the simulation length, being necessary to reach timescales in the order of hundreds of picoseconds to obtain reliable results.

Structure and interactions at the Mg(0001)/water interface: An ab initio study

A molecular level understanding of metal/bulk water interface structure is key for a wide range of processes, including aqueous corrosion, which is our focus, but their buried nature makes experimental investigation difficult and we must mainly rely on simulations. We investigate the Mg(0001)/water interface using second generation Car–Parrinello molecular dynamics (MD) to gain structural information, combined with static density functional theory calculations to probe the atomic interactions and electronic structure (e.g., calculating the potential of zero charge). By performing detailed structural analyses of both metal–surface atoms and the near-surface water, we find that, among other insights: (i) water adsorption causes significant surface roughening (the planar distribution for top-layer Mg has two peaks separated by [Formula: see text]), (ii) strongly adsorbed water covers only [Formula: see text] of available surface sites, and (iii) adsorbed water avoids clustering on the surface. Static calculations are used to gain a deeper understanding of the structuring observed in MD. For example, we use an energy decomposition analysis combined with calculated atomic charges to show that adsorbate clustering is unfavorable due to Coulombic repulsion between adsorption site surface atoms. Results are discussed in the context of previous simulations carried out on other metal/water interfaces. The largest differences for the Mg(0001)/water system appear to be the high degree of surface distortion and the minimal difference between the metal work function and metal/water potential of zero charge (at least compared to other interfaces with similar metal–water interaction strengths). The structural information, in this paper, is important for understanding aqueous Mg corrosion, as the Mg(0001)/water interface is the starting point for key reactions. Furthermore, our focus on understanding the driving forces behind this structuring leads to important insights for general metal/water interfaces.

Toward High-level Machine Learning Potential for Water Based on Quantum Fragmentation and Neural Networks

Accurate and efficient simulation of liquids, such as water and salt solutions, using high-level wave function theories is still a formidable task for computational chemists owing to the high computational costs. In this study, we develop a deep machine learning potential based on fragment-based second-order Møller-Plesset perturbation theory (DP-MP2) for water through neural networks. We show that the DP-MP2 potential predicts the structural, dynamical, and thermodynamic properties of liquid water in better agreement with the experimental data than previous studies based on density functional theory (DFT). The nuclear quantum effects (NQEs) on the properties of liquid water are also examined, which are noticeable in affecting the structural and dynamical properties of liquid water under ambient conditions. This work provides a general framework for quantitative predictions of the properties of condensed-phase systems with the accuracy of high-level wave function theory while achieving significant computational savings compared to ab initio simulations.

Assessing the Interplay between Functional-Driven and Density-Driven Errors in DFT Models of Water

We investigate the interplay between functional-driven and density-driven errors in different density functional approximations within density functional theory (DFT) and the implications of these errors for simulations of water with DFT-based data-driven potentials. Specifically, we quantify density-driven errors in two widely used dispersion-corrected functionals derived within the generalized gradient approximation (GGA), namely BLYP-D3 and revPBE-D3, and two modern meta-GGA functionals, namely strongly constrained and appropriately normed (SCAN) and B97M-rV. The effects of functional-driven and density-driven errors on the interaction energies are first assessed for the water clusters of the BEGDB dataset. Further insights into the nature of functional-driven errors are gained from applying the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) to the interaction energies, which demonstrates that functional-driven errors are strongly correlated with the nature of the interactions. We discuss cases where density-corrected DFT (DC-DFT) models display higher accuracy than the original DFT models and cases where reducing the density-driven errors leads to larger deviations from the reference energies due to the presence of large functional-driven errors. Finally, molecular dynamics simulations are performed with data-driven many-body potentials derived from DFT and DC-DFT data to determine the effect that minimizing density-driven errors has on the description of liquid water. Besides rationalizing the performance of widely used DFT models of water, we believe that our findings unveil fundamental relations between the shortcomings of some common DFT approximations and the requirements for accurate descriptions of molecular interactions, which will aid the development of a consistent, DFT-based framework for the development of data-driven and machine-learned potentials for simulations of condensed-phase systems.

Static and Dynamic Correlations in Water: Comparison of Classical Ab Initio Molecular Dynamics at Elevated Temperature with Path Integral Simulations at Ambient Temperature

It is a common practice in ab initio molecular dynamics (AIMD) simulations of water to use an elevated temperature to overcome the overstructuring and slow diffusion predicted by most current density functional theory (DFT) models. The simulation results obtained in this distinct thermodynamic state are then compared with experimental data at ambient temperature based on the rationale that a higher temperature effectively recovers nuclear quantum effects (NQEs) that are missing in the classical AIMD simulations. In this work, we systematically examine the foundation of this assumption for several DFT models as well as for the many-body MB-pol model. We find for the cases studied that a higher temperature does not correctly mimic NQEs at room temperature, which is especially manifest in significantly different three-molecule correlations as well as hydrogen bond dynamics. In many of these cases, the effects of NQEs are the opposite of the effects of carrying out the simulations at an elevated temperature.

Density Functional Theory of Water with the Machine-Learned DM21 Functional

The delicate interplay between functional-driven and density-driven errors in density functional theory (DFT) has hindered traditional density functional approximations (DFAs) from providing an accurate description of water for over 30 years. Recently, the deep-learned DeepMind 21 (DM21) functional has been shown to overcome the limitations of traditional DFAs as it is free of delocalization error. To determine if DM21 can enable a molecular-level description of the physical properties of aqueous systems within Kohn-Sham DFT, we assess the accuracy of the DM21 functional for neutral, protonated, and deprotonated water clusters. We find that the ability of DM21 to accurately predict the energetics of aqueous clusters varies significantly with cluster size. Additionally, we introduce the many-body MB-DM21 potential derived from DM21 data within the many-body expansion of the energy and use it in simulations of liquid water as a function of temperature at ambient pressure. We find that size-dependent functional-driven errors identified in the analysis of the energetics of small clusters calculated with the DM21 functional result in the MB-DM21 potential systematically overestimating the hydrogen-bond strength and, consequently, predicting a more ice-like local structure of water at room temperature.

Linear Combination of Atomic Dipoles to Calculate the Bond and Molecular Dipole Moments of Molecules and Molecular Liquids

We report a linear combination of atomic dipole (LCAD) method for calculating the bond dipole moments of molecules. We show that the LCAD method reproduces the known molecular dipole moments of small to large molecules with a small error with respect to experimental and benchmark ab initio calculations, and molecular dipole distributions of bulk water that agree with maximally localized Wannier functions. The bond dipole moments derived from LCAD are also chemically interpretable in terms of the trend in bond ionicity in going from neutral to charged molecules. Moreover, the LCAD method accurately captures the influence of electric fields, supported by the correct trend in the change of the dipole moment under a uniform external electric field. The better grounding of bond dipole calculations indicates that it should also serve as a useful approach to bond dipole-field models used in catalysis or to reconstruct the small dipole of a H-terminated graphene flake.

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.

Approaching the basis set limit in Gaussian-orbital-based periodic calculations with transferability: Performance of pure density functionals for simple semiconductors

Simulating solids with quantum chemistry methods and Gaussian-type orbitals (GTOs) has been gaining popularity. Nonetheless, there are few systematic studies that assess the basis set incompleteness error (BSIE) in these GTO-based simulations over a variety of solids. In this work, we report a GTO-based implementation for solids and apply it to address the basis set convergence issue. We employ a simple strategy to generate large uncontracted (unc) GTO basis sets that we call the unc-def2-GTH sets. These basis sets exhibit systematic improvement toward the basis set limit as well as good transferability based on application to a total of 43 simple semiconductors. Most notably, we found the BSIE of unc-def2-QZVP-GTH to be smaller than 0.7 mEh per atom in total energies and 20 meV in bandgaps for all systems considered here. Using unc-def2-QZVP-GTH, we report bandgap benchmarks of a combinatorially designed meta-generalized gradient approximation (mGGA) functional, B97M-rV, and show that B97M-rV performs similarly (a root-mean-square-deviation of 1.18 eV) to other modern mGGA functionals, M06-L (1.26 eV), MN15-L (1.29 eV), and Strongly Constrained and Appropriately Normed (SCAN) (1.20 eV). This represents a clear improvement over older pure functionals such as local density approximation (1.71 eV) and Perdew-Burke-Ernzerhof (PBE) (1.49 eV), although all these mGGAs are still far from being quantitatively accurate. We also provide several cautionary notes on the use of our uncontracted bases and on future research on GTO basis set development for solids.

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.

Molecular Properties and Chemical Transformations Near Interfaces

The properties of bulk water and aqueous solutions are known to change in the vicinity of an interface and/or in a confined environment, including the thermodynamics of ion selectivity at interfaces, transition states and pathways of chemical reactions, and nucleation events and phase growth. Here we describe joint progress in identifying unifying concepts about how air, liquid, and solid interfaces can alter molecular properties and chemical reactivity compared to bulk water and multicomponent solutions. We also discuss progress made in interfacial chemistry through advancements in new theory, molecular simulation, and experiments.

Water Breakup at Fe2O3-Hematite/Water Interfaces: Influence of External Electric Fields from Nonequilibrium Ab Initio Molecular Dynamics

The dynamical properties of physically and chemically adsorbed water molecules at pristine hematite-(001) surfaces have been studied by means of nonequilibrium ab initio molecular dynamics (NE-AIMD) in the NVT ensemble at room temperature, in the presence of externally applied, uniform static electric fields of increasing intensity. The dissociation of water molecules to form chemically adsorbed species was scrutinized, in addition to charge redistribution and Grotthus proton hopping between water molecules. Dynamical properties of the adsorbed water molecules and OH- and H3O+ ions were gauged, such as the hydrogen bonds between protons in water molecules and the bridging oxygen atoms at the hematite surface, as well as the interactions between oxygen atoms in adsorbed water molecules and iron atoms at the hematite surface. The development of Helmholtz charge layers via water breakup at Fe2O3-hematite/water interfaces is also an interesting feature, with the development of protonic conduction on the surface and more bulk-like water.

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.

Toward a First-Principles Framework for Predicting Collective Properties of Electrolytes

Given the universal importance of electrolyte solutions, it is natural to expect that we have a nearly complete understanding of the fundamental properties of these solutions (e.g., the chemical potential) and that we can therefore explain, predict, and control the phenomena occurring in them. In fact, reality falls short of these expectations. But, recent advances in the simulation and modeling of electrolyte solutions indicate that it should soon be possible to make progress toward these goals. In this Account, we will discuss the use of first-principles interaction potentials based in quantum mechanics (QM) to enhance our understanding of electrolyte solutions. Specifically, we will focus on the use of quantum density functional theory (DFT) combined with molecular dynamics simulation (DFT-MD) as the foundation for our approach. The overarching concept is to understand and accurately reproduce the balance between local or short-ranged (SR) structural details and long-range (LR) correlations, allowing the prediction of the thermodynamics of both single ions in solution as well as the collective interactions characterized by activity/osmotic coefficients. In doing so, relevant collective motions and driving forces characterized by chemical potentials can be determined.In this Account, we will make the case that understanding electrolyte solutions requires a faithful QM representation of the SR nature of the ion-ion, ion-water, and water-water interactions. However, the number of molecules that is required for collective behavior makes the direct application of high-level QM methods that contain the best SR physics untenable, making methods that balance accuracy and efficiency a practical goal. Alternatives such as continuum solvent models (CSMs) and empirically based classical molecular dynamics have been extensively employed to resolve this problem but without yet overcoming the fundamental issue of SR accuracy. We will demonstrate that accurately describing the SR interaction is imperative for predicting both intrinsic properties, namely, at infinite dilution, and collective properties of electrolyte solutions.DFT has played an important role in our understanding of condensed phase systems, e.g., bulk liquid water, the air-water interface, ions in bulk, and at the air-water interface. This approach holds huge promise to provide benchmark calculations of electrolyte solution properties that will allow for the development and improvement of more efficient methods, as well as an enhanced understanding of fundamental phenomena. However, the standard protocol using the generalized gradient approximation with van der Waals (vdW) correction requires improvement in order to achieve a high level of quantitative accuracy. Simply simulating with higher level DFT functionals may not be the best route considering the significant computational cost. Alternative methods of incorporating information from higher levels of QM should be explored; e.g., using force matching techniques on small clusters, where high level benchmark calculations are possible, to develop ideal correction terms to the DFT functional is a promising possibility. We argue that DFT with statistical mechanics is becoming an increasingly useful framework enabling the prediction of collective electrolyte properties.

Dynamics & Spectroscopy with Neutrons-Recent Developments & Emerging Opportunities

This work provides an up-to-date overview of recent developments in neutron spectroscopic techniques and associated computational tools to interrogate the structural properties and dynamical behavior of complex and disordered materials, with a focus on those of a soft and polymeric nature. These have and continue to pave the way for new scientific opportunities simply thought unthinkable not so long ago, and have particularly benefited from advances in high-resolution, broadband techniques spanning energy transfers from the meV to the eV. Topical areas include the identification and robust assignment of low-energy modes underpinning functionality in soft solids and supramolecular frameworks, or the quantification in the laboratory of hitherto unexplored nuclear quantum effects dictating thermodynamic properties. In addition to novel classes of materials, we also discuss recent discoveries around water and its phase diagram, which continue to surprise us. All throughout, emphasis is placed on linking these ongoing and exciting experimental and computational developments to specific scientific questions in the context of the discovery of new materials for sustainable technologies.

Persistent Homology Metrics Reveal Quantum Fluctuations and Reactive Atoms in Path Integral Dynamics

Nuclear quantum effects (NQEs) are known to impact a number of features associated with chemical reactivity and physicochemical properties, particularly for light atoms and at low temperatures. In the imaginary time path integral formalism, each atom is mapped onto a "ring polymer" whose spread is related to the quantum mechanical uncertainty in the particle's position, i.e., its thermal wavelength. A number of metrics have previously been used to investigate and characterize this spread and explain effects arising from quantum delocalization, zero-point energy, and tunneling. Many of these shape metrics consider just the instantaneous structure of the ring polymers. However, given the significant interest in methods such as centroid molecular dynamics and ring polymer molecular dynamics that link the molecular dynamics of these ring polymers to real time properties, there exists significant opportunity to exploit metrics that also allow for the study of the fluctuations of the atom delocalization in time. Here we consider the ring polymer delocalization from the perspective of computational topology, specifically persistent homology, which describes the 3-dimensional arrangement of point cloud data, (i.e. atomic positions). We employ the Betti sequence probability distribution to define the ensemble of shapes adopted by the ring polymer. The Wasserstein distances of Betti sequences adjacent in time are used to characterize fluctuations in shape, where the Fourier transform and associated principal components provides added information differentiating atoms with different NQEs based on their dynamic properties. We demonstrate this methodology on two representative systems, a glassy system consisting of two atom types with dramatically different de Broglie thermal wavelengths, and ab initio molecular dynamics simulation of an aqueous 4 M HCl solution where the H-atoms are differentiated based on their participation in proton transfer reactions.

Nuclear quantum effects on the thermodynamic, structural, and dynamical properties of water

We perform path-integral molecular dynamics (PIMD) simulations of H2O and D2O using the q-TIP4P/F model. Simulations are performed at P = 1 bar and over a wide range of temperatures that include the equilibrium (T≥ 273 K) and supercooled (210 ≤T < 273 K) liquid states of water. The densities of both H2O and D2O calculated from PIMD simulations are in excellent agreement with experiments in the equilibrium and supercooled regimes. We also evaluate important thermodynamic response functions, specifically, the thermal expansion coefficient αP(T), isothermal compressibility κT(T), isobaric heat capacity CP(T), and static dielectric constant ε(T). While these properties are in excellent [αP(T) and κT(T)] or semi-quantitative agreement [CP(T) and ε(T)] with experiments in the equilibrium regime, they are increasingly underestimated upon further cooling. It follows that the inclusion of nuclear quantum effects in PIMD simulations of (q-TIP4P/F) water is not sufficient to reproduce the anomalous large fluctuations in density, entropy, and electric dipole moment characteristic of supercooled water. It has been hypothesized that water may exhibit a liquid-liquid critical point (LLCP) in the supercooled regime at P > 1 bar and that such a LLCP generates a maximum in CP(T) and κT(T) at 1 bar. Consistent with this hypothesis and in particular, with experiments, we find a maximum in the κT(T) of q-TIP4P/F light and heavy water at T≈ 230-235 K. No maximum in CP(T) could be detected down to T≥ 210 K. We also calculate the diffusion coefficient D(T) of H2O and D2O using the ring-polymer molecular dynamics (RPMD) technique and find that computer simulations are in remarkable good agreement with experiments at all temperatures studied. The results from RPMD/PIMD simulations are also compared with the corresponding results obtained from classical MD simulations of q-TIP4P/F water where atoms are represented by single interacting sites. Surprisingly, we find minor differences in most of the properties studied, with CP(T), D(T), and structural properties being the only (expected) exceptions.

Catalytic Principles from Natural Enzymes and Translational Design Strategies for Synthetic Catalysts

As biocatalysts, enzymes are characterized by their high catalytic efficiency and strong specificity but are relatively fragile by requiring narrow and specific reactive conditions for activity. Synthetic catalysts offer an opportunity for more chemical versatility operating over a wider range of conditions but currently do not reach the remarkable performance of natural enzymes. Here we consider some new design strategies based on the contributions of nonlocal electric fields and thermodynamic fluctuations to both improve the catalytic step and turnover for rate acceleration in arbitrary synthetic catalysts through bioinspired studies of natural enzymes. With a focus on the enzyme as a whole catalytic construct, we illustrate the translational impact of natural enzyme principles to synthetic enzymes, supramolecular capsules, and electrocatalytic surfaces.

An isolated water droplet in the aqueous solution of a supramolecular tetrahedral cage

Water under nanoconfinement at ambient conditions has exhibited low-dimensional ice formation and liquid-solid phase transitions, but with structural and dynamical signatures that map onto known regions of water's phase diagram. Using terahertz (THz) absorption spectroscopy and ab initio molecular dynamics, we have investigated the ambient water confined in a supramolecular tetrahedral assembly, and determined that a dynamically distinct network of 9 ± 1 water molecules is present within the nanocavity of the host. The low-frequency absorption spectrum and theoretical analysis of the water in the Ga₄L₆ ^12- host demonstrate that the structure and dynamics of the encapsulated droplet is distinct from any known phase of water. A further inference is that the release of the highly unusual encapsulated water droplet creates a strong thermodynamic driver for the high-affinity binding of guests in aqueous solution for the Ga₄L₆ ^12- supramolecular construct.

Fragment-based quantum mechanical approach to biomolecules, molecular clusters, molecular crystals and liquids

To study large molecular systems beyond the system size that the current state-of-the-art ab initio electronic structure methods could handle, fragment-based quantum mechanical (QM) approaches have been developed over the past years, and proved to be efficient in dealing with large molecular systems at various ab initio levels. According to the fragmentation approach, a large molecular system can be divided into subsystems (fragments), and subsequently the property of the whole system can be approximately obtained by taking a proper combination of the corresponding terms of individual fragments. Therefore, the standard QM calculation of a large system could be circumvented by carrying out a series of calculations on small fragments, which significantly promotes computational efficiency. The electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method is one of the fragment-based QM approaches which has been developed by our research group in recent years. This Perspective presents the theoretical framework of this fragmentation method and its applications in biomolecules, molecular clusters, molecular crystals and liquids, including total energy calculation, protein-ligand/protein binding affinity prediction, geometry optimization, vibrational spectrum simulation, ab initio molecular dynamics simulation, and prediction of excited-state properties.

Quantum kinetic energy and isotope fractionation in aqueous ionic solutions

At room temperature, the quantum contribution to the kinetic energy of a water molecule exceeds the classical contribution by an order of magnitude. The quantum kinetic energy (QKE) of a water molecule is modulated by its local chemical environment and leads to uneven partitioning of isotopes between different phases in thermal equilibrium, which would not occur if the nuclei behaved classically. In this work, we use ab initio path integral simulations to show that QKEs of the water molecules and the equilibrium isotope fractionation ratios of the oxygen and hydrogen isotopes are sensitive probes of the hydrogen bonding structures in aqueous ionic solutions. In particular, we demonstrate how the QKE of water molecules in path integral simulations can be decomposed into translational, rotational and vibrational degrees of freedom, and use them to determine the impact of solvation on different molecular motions. By analyzing the QKEs and isotope fractionation ratios, we show how the addition of the Na⁺, Cl^- and HPO₄^2- ions perturbs the competition between quantum effects in liquid water and impacts their local solvation structures.

Nuclear Quantum Effects from the Analysis of Smoothed Trajectories: Pilot Study for Water

Nuclear quantum effects have significant contributions to thermodynamic quantities and structural properties; furthermore, very expensive methods are necessary for their accurate computation. In most calculations, these effects, for instance, zero-point energies, are simply neglected or only taken into account within the quantum harmonic oscillator approximation. Herein, we present a new method, Generalized Smoothed Trajectory Analysis, to determine nuclear quantum effects from molecular dynamics simulations. The broad applicability is demonstrated with the examples of a harmonic oscillator and different states of water. Ab initio molecular dynamics simulations have been performed for ideal gas up to the temperature of 5000 K. Classical molecular dynamics have been carried out for hexagonal ice, liquid water, and vapor at atmospheric pressure. With respect to the experimental heat capacity, our method outperforms previous calculations in the literature in a wide temperature range at lower computational cost than other alternatives. Dynamic and structural nuclear quantum effects of water are also discussed.

Prediction of aqueous free energies of solvation using coupled QM and MM explicit solvent simulations

A method based on molecular dynamics simulations which employ two distinct levels of theory is proposed and tested for the prediction of Gibbs free energies of solvation for non-ionic solutes in water. The method consists of two additive contributions: (i) an evaluation of the free energy of solvation predicted by a computationally efficient molecular mechanics (MM) method; and (ii) an evaluation of the free energy difference between the potential energy surface of the MM method and that of a more computationally intensive first-principles quantum-mechanical (QM) method. The latter is computed by a thermodynamic integration method based on a series of shorter molecular dynamics simulations that employ weighted averages of the QM and MM force evaluations. The combined computational approach is tested against the experimental free energies of aqueous solvation for four solutes. For solute-solvent interactions that are found to be described qualitatively well by the MM method, the QM correction makes a modest improvement in the predicted free energy of aqueous solvation. However, for solutes that are found to not be adequately described by the MM method, the QM correction does not improve agreement with experiment. These preliminary results provide valuable insights into the novel concept of implementing thermodynamic integration between two model chemistries, suggesting that it is possible to use QM methods to improve upon the MM predictions of free energies of aqueous solvation.

Interplay of water and a supramolecular capsule for catalysis of reductive elimination reaction from gold

Supramolecular assemblies have gained tremendous attention due to their ability to catalyze reactions with the efficiencies of natural enzymes. Using ab initio molecular dynamics, we identify the origin of the catalysis by the supramolecular capsule Ga₄L₆^12- on the reductive elimination reaction from gold complexes and assess their similarity to natural enzymes. By comparing the free energies of the reactants and transition states for the catalyzed and uncatalyzed reactions, we determine that an encapsulated water molecule generates electric fields that contributes the most to the reduction in the activation free energy. Although this is unlike the biomimetic scenario of catalysis through direct host-guest interactions, the electric fields from the nanocage also supports the transition state to complete the reductive elimination reaction with greater catalytic efficiency. However it is also shown that the nanocage poorly organizes the interfacial water, which in turn creates electric fields that misalign with the breaking bonds of the substrate, thus identifying new opportunities for catalytic design improvements in nanocage assemblies.

Diels-Alder Reactions in Water Are Determined by Microsolvation

Nanoconfined aqueous environments and the recent advent of accelerated chemistry in microdroplets are increasingly being investigated for catalysis. The mechanisms underlying the enhanced reactivity in alternate solvent environments and whether the enhanced reactivity due to nanoconfinement is a universal phenomenon are not fully understood. Here, we use ab initio molecular dynamics simulations to characterize the free energy of a retro-Diels-Alder reaction in bulk water at very different densities and in water nanoconfined by parallel graphene sheets. We find that the broadly different global solvation environments accelerate the reactions to a similar degree with respect to the gas-phase reaction, with activation free energies that do not differ by more than k_bT from each other. The reason for the same acceleration factor in the extremely different solvation environments is that it is the microsolvation of the dienophile's carbonyl group that governs the transition-state stabilization and mechanism, which is not significantly disrupted by either the lower density in bulk water or the strong nanoconfinement conditions used here. Our results also suggest that significant acceleration of Diels-Alder reactions in microdroplets or on-water conditions cannot arise from local microsolvation when water is present but instead must come from highly altered reaction environments that drastically change the reaction mechanisms.

First-Principles Modeling of Electronic Stopping in Complex Matter under Ion Irradiation

Electronic stopping refers to the dynamical energy-transfer process to electrons in matter from highly energetic charged particles such as high-velocity protons. We discuss recent progress in theoretical studies of electronic stopping in condensed matter under ion irradiation, focusing on modern electronic structure theory's role in enabling the study of electronic excitation dynamics that result from the energy transfer. In the last few decades, first-principles simulation approaches based on real-time time-dependent density functional theory have greatly advanced the field. While linear response theory is widely used to study electronic stopping processes, especially for simple solids, novel first-principles dynamics approaches now allow us to study chemically complex systems and also yield detailed descriptions of electronic excitations at the molecular scale. Outstanding challenges for further advancement of electronic stopping modeling are also discussed from the viewpoint of electronic structure theory.

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.