Probing the structural and dynamical properties of liquid water with models including non-local electron correlation

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.

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.

Partial Molar Solvation Volume of the Hydrated Electron Simulated Via DFT

Different simulation models of the hydrated electron produce different solvation structures, but it has been challenging to determine which simulated solvation structure, if any, is the most comparable to experiment. In a recent work, Neupane et al. [J. Phys. Chem. B 2023, 127, 5941-5947] showed using Kirkwood-Buff theory that the partial molar volume of the hydrated electron, which is known experimentally, can be readily computed from an integral over the simulated electron-water radial distribution function. This provides a sensitive way to directly compare the hydration structure of different simulation models of the hydrated electron with experiment. Here, we compute the partial molar volume of an ab-initio-simulated hydrated electron model based on density-functional theory (DFT) with a hybrid functional at different simulated system sizes. We find that the partial molar volume of the DFT-simulated hydrated electron is not converged with respect to the system size for simulations with up to 128 waters. We show that even at the largest simulation sizes, the partial molar volume of DFT-simulated hydrated electrons is underestimated by a factor of 2 with respect to experiment, and at the standard 64-water size commonly used in the literature, DFT-based simulations underestimate the experimental solvation volume by a factor of ∼3.5. An extrapolation to larger box sizes does predict the experimental partial molar volume correctly; however, larger system sizes than those explored here are currently intractable without the use of machine-learned potentials. These results bring into question what aspects of the predicted hydrated electron radial distribution function, as calculated by DFT-based simulations with the PBEh-D3 functional, deviate from the true solvation structure.

Massively parallel implementation of gradients within the random phase approximation: Application to the polymorphs of benzene

The Random-Phase approximation (RPA) provides an appealing framework for semi-local density functional theory. In its Resolution-of-the-Identity (RI) approach, it is a very accurate and more cost-effective method than most other wavefunction-based correlation methods. For widespread applications, efficient implementations of nuclear gradients for structure optimizations and data sampling of machine learning approaches are required. We report a well scaling implementation of RI-RPA nuclear gradients on massively parallel computers. The approach is applied to two polymorphs of the benzene crystal obtaining very good cohesive and relative energies. Different correction and extrapolation schemes are investigated for further improvement of the results and estimations of error bars.

Machine Learning Density Functionals from the Random-Phase Approximation

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

Quantum Effects of Hydrogen Nuclei on the Nuclear Magnetic Shielding Tensor of Ice Ih

Ice is the most fundamental hydrogen-bonded system in which the hydrogen nuclear quantum effect significantly impacts the structure and relevant thermochemical and spectroscopic properties. While ice was experimentally investigated using proton nuclear magnetic resonance spectroscopy more than 40 years ago, the corresponding theoretical investigations have been rarely reported due to the difficulty in evaluating how the proton nuclear quantum effect influences the spectral characteristics of such a condensed material. In this study, we applied a combination of the ONIOM and multicomponent molecular orbital (MC_MO) methods for calculating the anisotropic and isotropic components of the nuclear magnetic shielding tensor of the hexagonal ice crystal to quantify the effects of nuclear quantum fluctuations on the spectroscopic properties of ice. The nuclear magnetic shielding values computed by incorporating the hydrogen nuclear quantum effect reasonably agree with the experimental values. The nuclear quantum effects were found to increase the anisotropic component of the magnetic shielding tensor while decreasing the isotropic component. Such a difference can be explained by their distinct dependence on the electrostatic field and hydrogen-bonding structural parameters.

Electrokinetic, electrochemical, and electrostatic surface potentials of the pristine water liquid-vapor interface

Although conceptually simple, the air-water interface displays rich behavior and is subject to intense experimental and theoretical investigations. Different definitions of the electrostatic surface potential as well as different calculation methods, each relevant for distinct experimental scenarios, lead to widely varying potential magnitudes and sometimes even different signs. Based on quantum-chemical density-functional-theory molecular dynamics (DFT-MD) simulations, different surface potentials are evaluated and compared to force-field (FF) MD simulations. As well explained in the literature, the laterally averaged electrostatic surface potential, accessible to electron holography, is dominated by the trace of the water molecular quadrupole moment, and using DFT-MD amounts to +4.35 V inside the water phase, very different from results obtained with FF water models which yield negative values of the order of -0.4 to -0.6 V. Thus, when predicting potentials within water molecules, as relevant for photoelectron spectroscopy and non-linear interface-specific spectroscopy, DFT simulations should be used. The electrochemical surface potential, relevant for ion transfer reactions and ion surface adsorption, is much smaller, less than 200 mV in magnitude, and depends specifically on the ion radius. Charge transfer between interfacial water molecules leads to a sizable surface potential as well. However, when probing electrokinetics by explicitly applying a lateral electric field in DFT-MD simulations, the electrokinetic ζ-potential turns out to be negligible, in agreement with predictions using continuous hydrodynamic models. Thus, interfacial polarization charges from intermolecular charge transfer do not lead to significant electrokinetic mobility at the pristine vapor-liquid water interface, even assuming these transfer charges are mobile in an external electric field.

Probing the molecular structure of aqueous triiodide via X-ray photoelectron spectroscopy and correlated electron phenomena

Liquid-microjet-based X-ray photoelectron spectroscopy was applied to aqueous triiodide solutions, I₃^-_(aq.), to investigate the anion's valence- and core-level electronic structure, ionization dynamics, associated electron-correlation effects, and nuclear geometric structure. The roles of multi-active-electron (shake-up) ionization processes - with noted sensitivity to the solute geometric structure - were investigated through I₃^-_(aq.) solution valence, I 4d, and I 3d core-level measurements. The experimental spectra were interpreted with the aid of simulated photoelectron spectra, built upon multi-reference ab initio electronic structure calculations associated with different I₃^-_(aq.) molecular geometries. A comparison of the single-to-multi-active-electron ionization signal ratios extracted from the experimental and theoretical core-level photoemission spectra suggests that the ground state of the solute adopts a near-linear average geometry in aqueous solutions. This contrasts with the interpretation of time-resolved X-ray solution scattering studies, but is found to be fully consistent with the rest of the solution-phase I₃^-_(aq.) literature. Comparing the results of low- and high-photon-energy photoemission measurements, we further suggest that the aqueous anion adopts a more asymmetric geometry at the aqueous-solution-gas interface than in the aqueous bulk.

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.

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

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

Hidden Hemibonding in the Aqueous Hydroxyl Radical

The existence of a two-center, three-electron hemibond in the first solvation shell of ^•OH(aq) has long been a matter of debate. The hemibond manifests in ab initio molecular dynamics simulations as a small-r feature in the oxygen radial distribution function (RDF) for H₂O···^•OH, but that feature disappears when semilocal density functionals are replaced with hybrids, suggesting a self-interaction artifact. Using periodic simulations at the PBE0+D3 level, we demonstrate that the hemibond is actually still present (as evidenced by delocalization of the spin density) but is obscured by the hydrogen-bonded feature in the RDF due to a slight elongation of the hemibond. Computed electronic spectra for ^•OH(aq) are in excellent agreement with experiment and confirm that hemibond-like configurations play an outsized role in the spectroscopy due to an intense charge-transfer transition that is strongly attenuated in hydrogen-bonded configurations. Apparently, 25% exact exchange (as in PBE0) is insufficient to eliminate delocalization of unpaired spins.

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.

Ab initio nanofluidics: disentangling the role of the energy landscape and of density correlations on liquid/solid friction

Despite relevance to water purification and renewable energy conversion membranes, the molecular mechanisms underlying water slip are poorly understood. We disentangle the static and dynamical origin of water slippage on graphene, hBN and MoS2 by means of large-scale ab initio molecular dynamics. Accounting for the role of the electronic structure of the interface is essential to determine that water slips five and eleven times faster on graphene compared to hBN and to MoS2, respectively. Intricate changes in the water energy landscape as well as in the density correlations of the fluid provide, respectively, the main static and dynamical origin of water slippage. Surprisingly, the timescales of the density correlations are the same on graphene and hBN, whereas they are longer on MoS2 and yield a 100% slowdown in the flow of water on this material. Our results pave the way for an in silico first principles design of materials with enhanced water slip, through the modification of properties connected not only to the structure, but also to the dynamics of the interface.

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

Impact of electronic polarizability on protein-functional group interactions

Interactions of proteins with functional groups are key to their biological functions, making it essential that they be accurately modeled. To investigate the impact of the inclusion of explicit treatment of electronic polarizability in force fields on protein-functional group interactions, the additive CHARMM and Drude polarizable force field are compared in the context of the Site-Identification by Ligand Competitive Saturation (SILCS) simulation methodology from which functional group interaction patterns with five proteins for which experimental binding affinities of multiple ligands are available, were obtained. The explicit treatment of polarizability produces significant differences in the functional group interactions in the ligand binding sites including overall enhanced binding of functional groups to the proteins. This is associated with variations of the dipole moments of solutes representative of functional groups in the binding sites relative to aqueous solution with higher dipole moments systematically occurring in the latter, though exceptions occur with positively charged methylammonium. Such variation indicates the complex, heterogeneous nature of the electronic environments of ligand binding sites and emphasizes the inherent limitation of fixed charged, additive force fields for modeling ligand-protein interactions. These effects yield more defined orientation of the functional groups in the binding pockets and a small, but systematic improvement in the ability of the SILCS method to predict the binding orientation and relative affinities of ligands to their target proteins. Overall, these results indicate that the physical model associated with the explicit treatment of polarizability along with the presence of lone pairs in a force field leads to changes in the nature of the interactions of functional groups with proteins versus that occurring with additive force fields, suggesting the utility of polarizable force fields in obtaining a more realistic understanding of protein-ligand interactions.

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.

Accessing the Accuracy of Density Functional Theory through Structure and Dynamics of the Water-Air Interface

Density functional theory-based molecular dynamics simulations are increasingly being used for simulating aqueous interfaces. Nonetheless, the choice of the appropriate density functional, critically affecting the outcome of the simulation, has remained arbitrary. Here, we assess the performance of various exchange-correlation (XC) functionals, based on the metrics relevant to sum-frequency generation spectroscopy. The structure and dynamics of water at the water-air interface are governed by heterogeneous intermolecular interactions, thereby providing a critical benchmark for XC functionals. We find that the XC functionals constrained by exact functional conditions (revPBE and revPBE0) with the dispersion correction show excellent performance. The poor performance of the empirically optimized density functional (M06-L) indicates the importance of satisfying the exact functional condition. Understanding the performance of different XC functionals can aid in resolving the controversial interpretation of the interfacial water structure and direct the design of novel, improved XC functionals better suited to describing the heterogeneous interactions in condensed phases.

Structure and Dynamics of Water at the Water-Air Interface Using First-Principles Molecular Dynamics Simulations. II. NonLocal vs Empirical van der Waals Corrections

van der Waals (vdW) correction schemes have been recognized to be essential for an accurate description of liquid water in first-principles molecular dynamics simulation. The description of the structure and dynamics of water is governed by the type of the vdW corrections. So far, two vdW correction schemes have been often used: empirical vdW corrections and nonlocal vdW corrections. In this paper, we assess the influence of the empirical vs nonlocal vdW correction schemes on the structure and dynamics of water at the water–air interface. Since the structure of water at the water–air interface is established by a delicate balance of hydrogen bond formation and breaking, the simulation at the water–air interface provides a unique platform to testify as to the heterogeneous interaction of water. We used the metrics [Ohto et al. J. Chem. Theory Comput., 2019, 15, 595−60230468702] which are directly connected with the sum-frequency generation spectroscopic measurement. We find that the overall performance of nonlocal vdW methods is either similar or worse compared to the empirical vdW methods. We also investigated the performance of the optB88-DRSLL functional, which showed slightly less accuracy than the revPBE-D3 method. We conclude that the revPBE-D3 method shows the best performance for describing the interfacial water.

Assessment of Density Functional Theory in Predicting Interaction Energies between Water and Polycyclic Aromatic Hydrocarbons: from Water on Benzene to Water on Graphene

The interactions of water with polycyclic aromatic hydrocarbons, from benzene to graphene, are investigated using various exchange-correlation functionals selected across the hierarchy of density functional theory (DFT) approximations. The accuracy of the different functionals is assessed through comparisons with random phase approximation (RPA) and coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] calculations. Diffusion Monte Carlo (DMC) data reported in the literature are also used for comparison. Relatively large variations are found in interaction energies predicted by different DFT models, with GGA functionals underestimating the interaction strength for configurations with the water oxygen pointing toward the aromatic molecules. The meta-GGA B97M-rV and range-separated hybrid, meta-GGA ωB97M-V functionals provide nearly quantitative agreement with CCSD(T) values for the water-benzene, water-coronene, and water-circumcoronene dimers, while RPA and DMC predict interaction energies that differ by up to ∼1 kcal/mol and ∼0.4 kcal/mol from the corresponding CCSD(T) values, respectively. Similar trends among GGA, meta-GGA, and hybrid functionals are observed for larger polycyclic aromatic hydrocarbons. By performing absolutely localized molecular orbital energy decomposition analyses (ALMO-EDA), it is found that, independently of the number of carbon atoms and exchange-correlation functional, the dominant contributions to the interaction energies between water and polycyclic aromatic hydrocarbon molecules are the electrostatic and dispersion terms while polarization and charge transfer effects are negligibly small. Calculations carried out with GGA and meta-GGA functionals indicate that, as the number of carbon atoms increases, the interaction energies slowly converge to the corresponding values obtained for an infinite graphene sheet.

Dynamics of the Bulk Hydrated Electron from Many-Body Wave-Function Theory

The structure of the hydrated electron is a matter of debate as it evades direct experimental observation owing to the short life time and low concentrations of the species. Herein, the first molecular dynamics simulation of the bulk hydrated electron based on correlated wave‐function theory provides conclusive evidence in favor of a persistent tetrahedral cavity made up by four water molecules, and against the existence of stable non‐cavity structures. Such a cavity is formed within less than a picosecond after the addition of an excess electron to neat liquid water, with less regular cavities appearing as intermediates. The cavities are bound together by weak H−H bonds, the number of which correlates well with the number of coordinated water molecules, each type of cavity leaving a distinct spectroscopic signature. Simulations predict regions of negative spin density and a gyration radius that are both in agreement with experimental data.

Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li+ Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations

A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy Δ_s G_M⁺,wat^◦ of the Li⁺ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy [Formula: see text] of the proton, the surface electric potential jump χ_wat^◦ upon entering bulk water, and the absolute single-electrode potential [Formula: see text] of the reference hydrogen electrode are calculated to be -1099.9 ± 4.2 kJ·mol^-1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (-1100 ± 5 kJ·mol^-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li⁺ are also compared to those for Na⁺ and K⁺ from a previous study in terms of relative hydration free energies ΔΔ_s G_M⁺,wat^◦ and relative electrode potentials [Formula: see text]. The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔ_s G_M⁺,wat^• and redox potentials [Formula: see text]. The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller-Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li⁺ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.

Machine Learning Adaptive Basis Sets for Efficient Large Scale Density Functional Theory Simulation

It is chemically intuitive that an optimal atom centered basis set must adapt to its atomic environment, for example by polarizing toward nearby atoms. Adaptive basis sets of small size can be significantly more accurate than traditional atom centered basis sets of the same size. The small size and well conditioned nature of these basis sets leads to large saving in computational cost, in particular in a linear scaling framework. Here, it is shown that machine learning can be used to predict such adaptive basis sets using local geometrical information only. As a result, various properties of standard DFT calculations can be easily obtained at much lower costs, including nuclear gradients. In our approach, a rotationally invariant parametrization of the basis is obtained by employing a potential anchored on neighboring atoms to ultimately construct a rotation matrix that turns a traditional atom centered basis set into a suitable adaptive basis set. The method is demonstrated using MD simulations of liquid water, where it is shown that minimal basis sets yield structural properties in fair agreement with basis set converged results, while reducing the computational cost in the best case by a factor of 200 and the required flops by 4 orders of magnitude. Already a very small training set yields satisfactory results as the variational nature of the method provides robustness.

Absolute Energy Levels of Liquid Water

We determine the ionization potential (IP) and the electron affinity (EA) of liquid water together with the absolute redox level of the standard hydrogen electrode (SHE) by combining advanced electronic-structure calculations, ab initio molecular dynamics simulations, thermodynamic integration, and potential alignment at the water-vacuum interface. The calculated SHE level lies at 4.56 eV below the vacuum level, close to the experimental reference of 4.44 eV inferred by Trasatti. The band edges are determined through a hybrid functional designed to reproduce the band gap achieved with highly accurate GW calculations. Our analysis yields IP = 9.7 eV and EA = 0.8 eV, consistent with both photoemission spectra of liquid water and thermodynamical data for the hydrated electron.

Predicting vapor liquid equilibria using density functional theory: A case study of argon

Predicting vapor liquid equilibria (VLE) of molecules governed by weak van der Waals (vdW) interactions using the first principles approach is a significant challenge. Due to the poor scaling of the post Hartree-Fock wave function theory with system size/basis functions, the Kohn-Sham density functional theory (DFT) is preferred for systems with a large number of molecules. However, traditional DFT cannot adequately account for medium to long range correlations which are necessary for modeling vdW interactions. Recent developments in DFT such as dispersion corrected models and nonlocal van der Waals functionals have attempted to address this weakness with a varying degree of success. In this work, we predict the VLE of argon and assess the performance of several density functionals and the second order Møller-Plesset perturbation theory (MP2) by determining critical and structural properties via first principles Monte Carlo simulations. PBE-D3, BLYP-D3, and rVV10 functionals were used to compute vapor liquid coexistence curves, while PBE0-D3, M06-2X-D3, and MP2 were used for computing liquid density at a single state point. The performance of the PBE-D3 functional for VLE is superior to other functionals (BLYP-D3 and rVV10). At T = 85 K and P = 1 bar, MP2 performs well for the density and structural features of the first solvation shell in the liquid phase.

Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis

We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O(N⁴), with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.

First-Principles Simulations of Liquid Water Using a Dielectric-Dependent Hybrid Functional

We carried out first-principles simulations of liquid water under ambient conditions using a dielectric-dependent hybrid functional, where the fraction of exact exchange is set equal to the inverse of the high-frequency dielectric constant of the liquid. We found excellent agreement with experiment for the oxygen-oxygen partial correlation function at the experimental equilibrium density and 311 ± 3 K. Other structural and dynamical properties, such as the diffusion coefficient, molecular dipole moments, and vibrational spectra, are also in good agreement with experiment. Our results, together with previous findings on electronic properties of the liquid with the same functional, show that the dielectric-dependent hybrid functional accurately describes both the structural and electronic properties of liquid water.

Hydrogen-bond structure dynamics in bulk water: insights from ab initio simulations with coupled cluster theory

An accurate and efficient ab initio molecular dynamics (AIMD) simulation of liquid water was made possible using the fragment-based approach (J. F. Liu, X. He and J. Z. H. Zhang, Phys. Chem. Chem. Phys., 2017, 19, 11931-11936). In this study, we advance the AIMD simulations using the fragment-based coupled cluster (CC) theory, more accurately revealing the structural and dynamical properties of liquid water under ambient conditions. The results show that the double-donor hydrogen-bond configurations in liquid water are nearly in balance with the single-donor configurations, with a slight bias towards the former. Our observation is in contrast to the traditional tetrahedral water structure. The hydrogen-bond switching dynamics in liquid water are very fast, with a hydrogen-bond life time of around 0.78 picoseconds, determined using AIMD simulation at the CCD/aug-cc-pVDZ level. This time scale is remarkably shorter than the ∼3.0 picoseconds that is commonly obtained from traditional nonpolarized force fields and density functional theory (DFT) based first-principles simulations. Additionally, the obtained radial distribution functions, triplet oxygen angular distribution, diffusion coefficient, and the dipole moment of the water molecule are uniformly in good agreement with the experimental observations. The current high-level AIMD simulation sheds light on the understanding of the structural and dynamical properties of liquid water.

Laplace transformed MP2 for three dimensional periodic materials using stochastic orbitals in the plane wave basis and correlated sampling

We present an implementation and analysis of a stochastic high performance algorithm to calculate the correlation energy of three-dimensional periodic systems in second-order Møller-Plesset perturbation theory (MP2). In particular we measure the scaling behavior of the sample variance and probe whether this stochastic approach is competitive if accuracies well below 1 meV per valence orbital are required, as it is necessary for calculations of adsorption, binding, or surface energies. The algorithm is based on the Laplace transformed MP2 (LTMP2) formulation in the plane wave basis. The time-dependent Hartree-Fock orbitals, appearing in the LTMP2 formulation, are stochastically rotated in the occupied and unoccupied Hilbert space. This avoids a full summation over all combinations of occupied and unoccupied orbitals, as inspired by the work of Neuhauser, Rabani, and Baer [J. Chem. Theory Comput. 9, 24 (2013)]. Additionally, correlated sampling is introduced, accelerating the statistical convergence significantly.

Structure of liquid water - a dynamical mixture of tetrahedral and 'ring-and-chain' like structures

The nature of the dynamical hydrogen-bond network of liquid water under ambient conditions has challenged both experimental and theoretical researchers for decades and remains a topic of intense debate. In this work, we addressed the structural issue of the hydrogen-bond network of liquid water based on an accurate ab initio molecular dynamics simulation. The present work showed clearly that liquid water is neither accurately described by a static picture of mostly tetrahedral water molecules nor dominated by "ring-and-chain" like structures. Instead, the structure of water is a dynamical mixture of tetrahedral and 'ring-and-chain' like structures with a slight bias toward the former. On average, each water molecule forms about three hydrogen bonds with the surrounding water molecules. The present accurate ab initio molecular dynamics simulation of liquid water was made possible by using a fragment-based second-order Møller-Plesset perturbation theory (MP2) with a large basis set to treat a large body of water molecules. This level of ab initio theory is sufficiently accurate for describing water interactions, and the simulated structural and dynamical properties of liquid water, including radial distribution functions, diffusion coefficient, dipole moment, etc., are uniformly in excellent agreement with experimental observations.

Electron affinity of liquid water

Understanding redox and photochemical reactions in aqueous environments requires a precise knowledge of the ionization potential and electron affinity of liquid water. The former has been measured, but not the latter. We predict the electron affinity of liquid water and of its surface from first principles, coupling path-integral molecular dynamics with ab initio potentials, and many-body perturbation theory. Our results for the surface (0.8 eV) agree well with recent pump-probe spectroscopy measurements on amorphous ice. Those for the bulk (0.1-0.3 eV) differ from several estimates adopted in the literature, which we critically revisit. We show that the ionization potential of the bulk and surface are almost identical; instead their electron affinities differ substantially, with the conduction band edge of the surface much deeper in energy than that of the bulk. We also discuss the significant impact of nuclear quantum effects on the fundamental gap and band edges of the liquid.

Ab initio theory and modeling of water

Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice Ih at ambient conditions, as well as many important structural, electronic, and dynamic properties of liquid water. These successful predictions of the versatile SCAN functional open the gates to study complex processes in aqueous phase chemistry and the interactions of water with other materials in an efficient, accurate, and predictive, ab initio manner.

Real single ion solvation free energies with quantum mechanical simulation

Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Our research suggests that lithium's solvation free energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model.

Quantum Dynamics and Spectroscopy of Ab Initio Liquid Water: The Interplay of Nuclear and Electronic Quantum Effects

Understanding the reactivity and spectroscopy of aqueous solutions at the atomistic level is crucial for the elucidation and design of chemical processes. However, the simulation of these systems requires addressing the formidable challenges of treating the quantum nature of both the electrons and nuclei. Exploiting our recently developed methods that provide acceleration by up to 2 orders of magnitude, we combine path integral simulations with on-the-fly evaluation of the electronic structure at the hybrid density functional theory level to capture the interplay between nuclear quantum effects and the electronic surface. Here we show that this combination provides accurate structure and dynamics, including the full infrared and Raman spectra of liquid water. This allows us to demonstrate and explain the failings of lower-level density functionals for dynamics and vibrational spectroscopy when the nuclei are treated quantum mechanically. These insights thus provide a foundation for the reliable investigation of spectroscopy and reactivity in aqueous environments.

Nuclear Quantum Effects on Aqueous Electron Attachment and Redox Properties

Nuclear quantum effects (NQEs) on the reduction and oxidation properties of small aqueous species (CO₂, HO₂, and O₂) are quantified and rationalized by first-principles molecular dynamics and thermodynamic integration. Vertical electron attachment, or electron affinity, and detachment energies (VEA and VDE) are strongly affected by NQEs, decreasing in absolute value by 0.3 eV going from a classical to a quantum description of the nuclei. The effect is attributed to NQEs that lessen the solvent response upon oxidation/reduction. The reduction of solvent reorganization energy is expected to be general for small solutes in water. In the thermodynamic integral that yields the free energy of oxidation/reduction, these large changes enter with opposite sign, and only a small net effect (0.1 eV) remains. This is not obvious for CO₂, where the integrand is strongly influenced by NQEs due to the onset of interaction of the reduced orbital with the conduction band of the liquid during thermodynamic integration. We conclude that NQEs might not have to be included in the computation of redox potentials, unless high accuracy is needed, but are important for VEA and VDE calculations.