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

Short-Range Δ-Machine Learning: A Cost-Efficient Strategy to Transfer Chemical Accuracy to Condensed Phase Systems

DFT-based machine-learning potentials (MLPs) are now routinely trained for condensed-phase systems, but surpassing DFT accuracy remains challenging due to the cost or unavailability of periodic reference calculations. Our previous work ( Phys. Rev. Lett. 2022, 129, 226001) demonstrated that high-accuracy periodic MLPs can be trained within the CCMD framework using extended yet finite reference calculations. Here, we introduce short-range Δ-Machine Learning (srΔML), a method that starts from a baseline MLP trained on low-level periodic data and adds a Δ-MLP correction based on high-level cluster calculations at the CC level. Applied to liquid water, srΔML reduces the required cluster size from (H2O)64 to (H2O)15 and significantly lowers the number of clusters needed, resulting in a 50-200× reduction in computational cost. The resulting potential closely reproduces the target CC potential and accurately captures both two- and three-body structural descriptors.

From Grotthuss Transfer to Conductivity: Machine Learning Molecular Dynamics of Aqueous KOH

Accurate conductivity predictions of KOH(aq) are crucial for electrolysis applications. OH- is transferred in water by the Grotthuss transfer mechanism, thereby increasing its mobility compared to that of other ions. Classical and ab initio molecular dynamics struggle to capture this enhanced mobility due to limitations in computational costs or in capturing chemical reactions. Most studies to date have provided only qualitative descriptions of the structure during Grotthuss transfer, without quantitative results for the transfer rate and the resulting transport properties. Here, machine learning molecular dynamics is used to investigate 50,000 transfer events. Analysis confirmed earlier works that Grotthuss transfer requires a reduction in accepted and a slight increase in donated hydrogen bonds to the hydroxide, indicating that hydrogen-bond rearrangements are rate-limiting. The computed self-diffusion coefficients and electrical conductivities are consistent with experiments for a wide temperature range, outperforming classical interatomic force fields and earlier AIMD simulations.

Neural Network-Based Molecular Dynamics Simulation of Water Assisted by Active Learning

In our study, we combined classical molecular dynamics (MD) simulations with the simulated annealing (SA) method to explore the conformational landscape of water molecules. By using the K-means clustering method, we processed the MD simulation data to extract representative samples of water molecular structures used to train a deep potential (DP) model. Our DeePMD method showed accuracy in predicting water structural properties compared to DFT-MD results. Meanwhile, this approach achieves a balanced prediction of water density and self-diffusion coefficients compared with earlier DeePMD simulations. These results highlight the essential role of representative sampling techniques in training the DP model. Furthermore, we demonstrated the effectiveness of combining the DeePMD simulation with the centroid molecular dynamics (CMD) approach, which incorporates nuclear quantum effects (NQEs). This approach successfully reproduced the shoulder feature at 3250 cm-1 in the Raman spectra for the O-H stretch. Incorporating the path integral method into the DeePMD simulations underscores the importance of considering NQEs in understanding water molecules' structural and dynamic behaviors.

Projected Wave Function Extrapolation Scheme to Accelerate Plane-Wave Hybrid Functional-Based Born-Oppenheimer Molecular Dynamics Simulations

Born-Oppenheimer molecular dynamics (BOMD) simulations are of great interest for the dynamic properties of molecular and solid systems. However, BOMD simulations necessitate not only an extensive period of dynamical evolution but also costly self-consistent-field (SCF) electronic structure calculations, especially for hybrid functional-based BOMD (H-BOMD) simulations within plane-wave basis sets. Here, we propose an improved always stable predictor-corrector (ASPC) method for the wave function extrapolation to accelerate the plane-wave H-BOMD simulations, named projected ASPC (PASPC), yielding a wave function closer to the actual solution space and efficiently reducing the number of SCF iterations at each MD step. We investigated the convergence properties of different extrapolation schemes for molecular and solid systems. Numerical results demonstrate that plane-wave H-BOMD simulations can be significantly faster than conventional cases by combining the accelerated algorithms with the PASPC method. The energy drift is also evaluated, showing that PASPC produces energy drift with smaller oscillations and can simulate a larger time step for systems containing heavy atoms, demonstrating the accuracy of the extrapolation schemes. Furthermore, H-BOMD simulations showcase more accurate power and infrared spectra of silicon dioxide and liquid water that are comparable to those of experimental measurements.

Random Sampling Versus Active Learning Algorithms for Machine Learning Potentials of Quantum Liquid Water

Training accurate machine learning potentials requires electronic structure data comprehensively covering the configurational space of the system of interest. As the construction of this data is computationally demanding, many schemes for identifying the most important structures have been proposed. Here, we compare the performance of high-dimensional neural network potentials (HDNNPs) for quantum liquid water at ambient conditions trained to data sets constructed using random sampling as well as various flavors of active learning based on query by committee. Contrary to the common understanding of active learning, we find that for a given data set size, random sampling leads to smaller test errors for structures not included in the training process. In our analysis, we show that this can be related to small energy offsets caused by a bias in structures added in active learning, which can be overcome by using instead energy correlations as an error measure that is invariant to such shifts. Still, all HDNNPs yield very similar and accurate structural properties of quantum liquid water, which demonstrates the robustness of the training procedure with respect to the training set construction algorithm even when trained to as few as 200 structures. However, we find that for active learning based on preliminary potentials, a reasonable initial data set is important to avoid an unnecessary extension of the covered configuration space to less relevant regions.

Nuclear Quantum Effects in Liquid Water Are Marginal for Its Average Structure but Significant for Dynamics

Isotopic substitution, which can be realized in both experiment and computer simulations, is a direct approach to assess the role of nuclear quantum effects on the structure and dynamics of matter. However, the impact of nuclear quantum effects on the structure of liquid water as probed in experiment by comparing normal to heavy water has remained controversial. To settle this issue, we employ a highly accurate machine-learned high-dimensional neural network potential to perform converged coupled cluster-quality path integral simulations of liquid H2O versus D2O at ambient conditions. We find substantial H/D quantum effects on the rotational and translational dynamics of water, in close agreement with the experimental benchmarks. However, in stark contrast to the role for dynamics, H/D quantum effects turn out to be small, on the order of 1/1000 Å, on both average intramolecular and H-bonding structures of water. The most probable structure of water remains nearly unaffected by nuclear quantum effects, but effects on fluctuations away from average are appreciable, rendering H2O substantially more "liquid" than D2O.

The Dynamic Diversity and Invariance of Ab Initio Water

Comprehending water dynamics is crucial in various fields, such as water desalination, ion separation, electrocatalysis, and biochemical processes. While ab initio molecular dynamics (AIMD) accurately portray water's structure, computing its dynamic properties over nanosecond time scales proves cost-prohibitive. This study employs machine learning potentials (MLPs) to accurately determine the dynamic properties of liquid water with ab initio accuracy. Our findings reveal diversity in the calculated diffusion coefficient (D) and viscosity of water (η) across different methodologies. Specifically, while the GGA, meta-GGA, and hybrid functional methods struggle to predict dynamic properties under ambient conditions, methods on the higher level of Jacob's ladder of DFT approximation perform significantly better. Intriguingly, we discovered that both D and η adhere to the established Stokes-Einstein (SE) relation for all of the ab initio water. The diversity observed across different methods can be attributed to distinct structural entropy, affirming the applicability of excess entropy scaling relations across all functionals. The correlation between D and η provides valuable insights for identifying the ideal temperature to accurately replicate the dynamic properties of liquid water. Furthermore, our findings can validate the rationale behind employing artificially high temperatures in the simulation of water via AIMD. These outcomes not only pave the path to designing better functionals for water but also underscore the significance of water's many-body characteristics.

The heterogeneity of aqueous solutions: the current situation in the context of experiment and theory

The advancement of experimental methods has provided new information about the structure and structural fluctuations of water. Despite the appearance of numerous models, which aim to describe a wide range of thermodynamic and electrical characteristics of water, there is a deficit in systemic understanding of structuring in aqueous solutions. A particular challenge is the fact that even pure water is a heterogeneous, multicomponent system composed of molecular and supramolecular structures. The possibility of the existence of such structures and their nature are of fundamental importance for various fields of science. However, great difficulties arise in modeling relatively large supramolecular structures (e.g. extended hydration shells), where the bonds between molecules are characterized by low energy. Generally, such structures may be non-equilibrium but relatively long-lived. Evidently, the short times of water microstructure exchanges do not mean short lifetimes of macrostructures, just as the instability of individual parts does not mean the instability of the entire structure. To explain this paradox, we review the data from experimental and theoretical research. Today, only some of the experimental results on the lifetime of water structures have been confirmed by modeling, so there is not a complete theoretical picture of the structure of water yet. We propose a new hierarchical water macrostructure model to resolve the issue of the stability of water structures. In this model, the structure of water is presented as consisting of many hierarchically related levels (the stratification model). The stratification mechanism is associated with symmetry breaking at the formation of the next level, even with minimal changes in the properties of the previous level. Such a hierarchical relationship can determine the unique physico-chemical properties of water systems and, in the future, provide a complete description of them.

Ab Initio Simulation of Liquid Water without Artificial High Temperature

Comprehending the structure and dynamics of water is crucial in various fields, such as water desalination, ion separation, electrocatalysis, and biochemical processes. While reported works show that the ab initio molecular dynamics (AIMD) can accurately portray water's structure, the artificial high temperature (AHT) from 120 to 30 K is needed to mimic the quantum nature of hydrogen-bond network from GGA, metaGGA to hybrid functionals. The AHT proves to be an inadequate approach for systems involving aqueous multiphase mixtures, such as water-solid interfaces and aqueous solutions. This is due to the activation of additional phonons in other phases, which can lead to an overestimation of the dynamics of nearby water molecules. In this work, we find that the regularized SCAN (rSCAN) functional effectively captures both the structure and dynamics of liquid water at ambient conditions without AHT. Moreover, rSCAN closely matches experimental results for the hydration structures of alkali, alkali earth, and halide ions. We anticipate that the versatile and accurate rSCAN functional will emerge as a key tool based on ab initio simulation for investigating chemical processes in aqueous environments.

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

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

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

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

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.

Tensorial Properties via the Neuroevolution Potential Framework: Fast Simulation of Infrared and Raman Spectra

Infrared and Raman spectroscopy are widely used for the characterization of gases, liquids, and solids, as the spectra contain a wealth of information concerning, in particular, the dynamics of these systems. Atomic scale simulations can be used to predict such spectra but are often severely limited due to high computational cost or the need for strong approximations that limit the application range and reliability. Here, we introduce a machine learning (ML) accelerated approach that addresses these shortcomings and provides a significant performance boost in terms of data and computational efficiency compared with earlier ML schemes. To this end, we generalize the neuroevolution potential approach to enable the prediction of rank one and two tensors to obtain the tensorial neuroevolution potential (TNEP) scheme. We apply the resulting framework to construct models for the dipole moment, polarizability, and susceptibility of molecules, liquids, and solids and show that our approach compares favorably with several ML models from the literature with respect to accuracy and computational efficiency. Finally, we demonstrate the application of the TNEP approach to the prediction of infrared and Raman spectra of liquid water, a molecule (PTAF-), and a prototypical perovskite with strong anharmonicity (BaZrO3). The TNEP approach is implemented in the free and open source software package gpumd, which makes this methodology readily available to the scientific community.

Many-body interactions and deep neural network potentials for water

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

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.

Water-in-Salt: Fast Dynamics, Structure, Thermodynamics, and Bulk Properties

We present concentration-dependent dynamics of highly concentrated LiBr solutions and LiCl temperature-dependent dynamics for two high concentrations and compare the results to those of prior LiCl concentration-dependent data. The dynamical data are obtained using ultrafast optical heterodyne-detected optical Kerr effect (OHD-OKE). The OHD-OKE decays are composed of two pairs of biexponentials, i.e., tetra-exponentials. The fastest decay (t1) is the same as pure water's at all concentrations within error, while the second component (t2) slows slightly with concentration. The slower components (t3 and t4), not present in pure water, slow substantially, and their contributions to the decays increase significantly with increasing concentration, similar to LiCl solutions. Simulations of LiCl solutions from the literature show that the slow components arise from large ion/water clusters, while the fast components are from ion/water structures that are not part of large clusters. Temperature-dependent studies (15-95 °C) of two high LiCl concentrations show that decreasing the temperature is equivalent to increasing the room temperature concentration. The LiBr and LiCl concentration dependences and the two LiCl concentrations' temperature dependences all have bulk viscosities that are linearly dependent on τcslow, the correlation time of the slow dynamics (weighted averages of t3 and t4). Remarkably, all four viscosity vs 1/τCslow plots fall on the same line. Application of transition state theory to the temperature-dependent data yields the activation enthalpies and entropies for the dynamics of the large ion/water clusters, which underpin the bulk viscosity.

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

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

Exploring the impact of ions on oxygen K-edge X-ray absorption spectroscopy in NaCl solution using the GW-Bethe-Salpeter-equation approach

X-ray absorption spectroscopy (XAS) is a powerful experimental tool to probe the local structure in materials with the core hole excitations. Here, the oxygen K-edge XAS spectra of the NaCl solution and pure water are computed by using a recently developed GW-Bethe-Salpeter equation approach, based on configurations modeled by path-integral molecular dynamics with the deep-learning technique. The neural network is trained on ab initio data obtained with strongly constrained and appropriately normed density functional theory. The observed changes in the XAS features of the NaCl solution, compared to those of pure water, are in good agreement between experimental and theoretical results. We provided detailed explanations for these spectral changes that occur when NaCl is solvated in pure water. Specifically, the presence of solvating ion pairs leads to localization of electron-hole excitons. Our theoretical XAS results support the theory that the effects of the solvating ions on the H-bond network are mainly confined within the first hydration shell of ions, however beyond the shell the arrangement of water molecules remains to be comparable to that observed in pure water.

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.

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.

Implementation of the meta-GGA exchange-correlation functional in numerical atomic orbital basis: With systematic testing on SCAN, rSCAN, and r2SCAN functionals

Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By including the kinetic energy density τ, the meta-generalized-gradient approximation (meta-GGA) family of functionals achieves better accuracy and flexibility while retaining the efficiency of semi-local functionals. For example, the strongly constrained and appropriately normed (SCAN) meta-GGA functional has been proven to yield accurate results for solid and molecular systems. We implement meta-GGA functionals with both numerical atomic orbitals and plane wave bases in the ABACUS package. Apart from the exchange-correlation potential, we also discuss the evaluation of force and stress. To validate our implementation, we perform finite-difference tests and convergence tests with the SCAN, rSCAN, and r2SCAN meta-GGA functionals. We further test water hexamers, weakly interacting molecules from the S22 dataset, as well as 13 semiconductors using the three functionals. The results show satisfactory agreement with previous calculations and available experimental values.

Why Dissolving Salt in Water Decreases Its Dielectric Permittivity

The dielectric permittivity of salt water decreases on dissolving more salt. For nearly a century, this phenomenon has been explained by invoking saturation in the dielectric response of the solvent water molecules. Herein, we employ an advanced deep neural network (DNN), built using data from density functional theory, to study the dielectric permittivity of sodium chloride solutions. Notably, the decrease in the dielectric permittivity as a function of concentration, computed using the DNN approach, agrees well with experiments. Detailed analysis of the computations reveals that the dominant effect, caused by the intrusion of ionic hydration shells into the solvent hydrogen-bond network, is the disruption of dipolar correlations among water molecules. Accordingly, the observed decrease in the dielectric permittivity is mostly due to increasing suppression of the collective response of solvent waters.

Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy

Obtaining the atomistic structure and dynamics of disordered condensed-phase systems from first-principles remains one of the forefront challenges of chemical theory. Here we exploit recent advances in periodic electronic structure and provide a data-efficient approach to obtain machine-learned condensed-phase potential energy surfaces using AFQMC, CCSD, and CCSD(T) from a very small number (≤200) of energies by leveraging a transfer learning scheme starting from lower-tier electronic structure methods. We demonstrate the effectiveness of this approach for liquid water by performing both classical and path integral molecular dynamics simulations on these machine-learned potential energy surfaces. By doing this, we uncover the interplay of dynamical electron correlation and nuclear quantum effects across the entire liquid range of water while providing a general strategy for efficiently utilizing periodic correlated electronic structure methods to explore disordered condensed-phase systems.

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

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

Recent advances in density functional theory approach for optoelectronics properties of graphene

Graphene has received tremendous attention among diverse 2D materials because of its remarkable properties. Its emergence over the last two decades gave a new and distinct dynamic to the study of materials, with several research projects focusing on exploiting its intrinsic properties for optoelectronic devices. This review provides a comprehensive overview of several published articles based on density functional theory and recently introduced machine learning approaches applied to study the electronic and optical properties of graphene. A comprehensive catalogue of the bond lengths, band gaps, and formation energies of various doped graphene systems that determine thermodynamic stability was reported in the literature. In these studies, the peculiarity of the obtained results reported is consequent on the nature and type of the dopants, the choice of the XC functionals, the basis set, and the wrong input parameters. The different density functional theory models, as well as the strengths and uncertainties of the ML potentials employed in the machine learning approach to enhance the prediction models for graphene, were elucidated. Lastly, the thermal properties, modelling of graphene heterostructures, the superconducting behaviour of graphene, and optimization of the DFT models are grey areas that future studies should explore in enhancing its unique potential. Therefore, the identified future trends and knowledge gaps have a prospect in both academia and industry to design future and reliable optoelectronic devices.

A "short blanket" dilemma for a state-of-the-art neural network potential for water: Reproducing experimental properties or the physics of the underlying many-body interactions?

Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. In this study, we explore the possibility of combining the computational efficiency of the DeePMD framework and the demonstrated accuracy of the MB-pol data-driven, many-body potential to train a DNN potential for large-scale simulations of water across its phase diagram. We find that the DNN potential is able to reliably reproduce the MB-pol results for liquid water, but provides a less accurate description of the vapor-liquid equilibrium properties. This shortcoming is traced back to the inability of the DNN potential to correctly represent many-body interactions. An attempt to explicitly include information about many-body effects results in a new DNN potential that exhibits the opposite performance, being able to correctly reproduce the MB-pol vapor-liquid equilibrium properties, but losing accuracy in the description of the liquid properties. These results suggest that DeePMD-based DNN potentials are not able to correctly "learn" and, consequently, represent many-body interactions, which implies that DNN potentials may have limited ability to predict the properties for state points that are not explicitly included in the training process. The computational efficiency of the DeePMD framework can still be exploited to train DNN potentials on data-driven many-body potentials, which can thus enable large-scale, "chemically accurate" simulations of various molecular systems, with the caveat that the target state points must have been adequately sampled by the reference data-driven many-body potential in order to guarantee a faithful representation of the associated properties.

Extending density functional theory with near chemical accuracy beyond pure water

Density functional simulations of condensed phase water are typically inaccurate, due to the inaccuracies of approximate functionals. A recent breakthrough showed that the SCAN approximation can yield chemical accuracy for pure water in all its phases, but only when its density is corrected. This is a crucial step toward first-principles biosimulations. However, weak dispersion forces are ubiquitous and play a key role in noncovalent interactions among biomolecules, but are not included in the new approach. Moreover, naïve inclusion of dispersion in HF-SCAN ruins its high accuracy for pure water. Here we show that systematic application of the principles of density-corrected DFT yields a functional (HF-r²SCAN-DC4) which recovers and not only improves over HF-SCAN for pure water, but also captures vital noncovalent interactions in biomolecules, making it suitable for simulations of solutions.

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.

Ab Initio Studies of Hydrated Electron/Cation Contact Pairs: Hydrated Electrons Simulated with Density Functional Theory Are Too Kosmotropic

We have performed the first DFT-based ab initio MD simulations of a hydrated electron (e_aq^-) in the presence of Na⁺, a system chosen because ion-pairing behavior in water depends sensitively on the local hydration structure. Experiments show that e_aq^-'s interact weakly with Na⁺; the e_aq^-'s spectrum blue shifts by only a few tens of meV upon ion pairing without changing shape. We find that the spectrum of the DFT-simulated e_aq^- red shifts and changes shape upon interaction with Na⁺, in contrast with experiment. We show that this is because the hydration structure of the DFT-simulated e_aq^- is too ordered or kosmotropic. Conversely, simulations that produce e_aq^-'s with a less ordered or chaotropic hydration structure form weaker ion pairs with Na⁺, yielding predicted spectral blue shifts in better agreement with experiment. Thus, ab initio simulations based on hybrid GGA DFT functionals fail to produce the correct solvation structure for the hydrated electron.

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.

Many-body effects in the X-ray absorption spectra of liquid water

SignificanceIn X-ray absorption spectroscopy, an electron-hole excitation probes the local atomic environment. The interpretation of the spectra requires challenging theoretical calculations, particularly in a system like liquid water, where quantum many-body effects and molecular disorder play an important role. Recent advances in theory and simulation make possible new calculations that are in good agreement with experiment, without recourse to commonly adopted approximations. Based on these calculations, the three features observed in the experimental spectra are unambiguously attributed to excitonic effects with different characteristic correlation lengths, which are distinctively affected by perturbations of the underlying H-bond structure induced by temperature changes and/or by isotopic substitution. The emerging picture of the water structure is fully consistent with the conventional tetrahedral model.

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

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

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.

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.

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.

Molecular Simulations of Aqueous Electrolytes: Role of Explicit Inclusion of Charge Transfer into Force Fields

We describe here simulations of aqueous salt solutions that are performed using an explicit charge transfer force field. The emphasis of the discussion is on the calculation of a dynamical property of the solutions: self-diffusion of water. While force fields that are based on pairwise additive potentials or on potentials with explicit inclusion of polarization or with scaled charges can provide at best a qualitative agreement with experiments, force fields with explicit inclusion of charge transfer can produce quantitative agreement with experiment for NaCl and KCl solutions. We argue that a force field with explicit charge transfer contains new physics absent in the previously used force fields described in recent reviews of molecular simulations of aqueous electrolytes.

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.