Structural and electronic properties of aqueous NaCl solutions from ab initio molecular dynamics simulations with hybrid density functionals

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.

Speeding-up Hybrid Functional-Based Ab Initio Molecular Dynamics Using Multiple Time-stepping and Resonance-Free Thermostat

Ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has become a workhorse for studying the structure, dynamics, and reactions in condensed matter systems. Currently, AIMD simulations are primarily carried out at the level of generalized gradient approximation (GGA), which is at the second rung of DFT functionals in terms of accuracy. Hybrid DFT functionals, which form the fourth rung in the accuracy ladder, are not commonly used in AIMD simulations as the computational cost involved is 100 times or higher. To facilitate AIMD simulations with hybrid functionals, we propose here an approach using multiple time stepping with adaptively compressed exchange operator and resonance-free thermostat, that could speed up the calculations by ∼30 times or more for systems with a few hundred of atoms. We demonstrate that by achieving this significant speed up and making the compute time of hybrid functional-based AIMD simulations at par with that of GGA functionals, we are able to study several complex condensed matter systems and model chemical reactions in solution with hybrid functionals that were earlier unthinkable to be performed.

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.

Ab Initio Molecular Dynamics Investigation of the Solvation States of Hydrated Ions in Confined Water

Ionic transport in nanoscale channels with a critical size comparable to that of ions and solutes exhibits exceptional performance in water desalination, ion separation, electrocatalysts, and supercapacitors. However, the solvation states (SSs), i.e., the hydration structures and probability distribution, of hydrated ions in nanochannels differ from those in the bulk and the perspective of continuum theory. In this work, we conduct ab initio enhanced-sampling atomistic simulations to investigate the ion-specific SSs of monovalent ions (including Li+, Na+, K+, F-, Cl-, and I-) in the graphene channel with a width of 1 nm. Our findings highlight that the SSs of those ions are primarily determined by ion-water hydration, where ion-wall interactions play a minor role. The distribution of ions in layered confined water is a result of ion-specific hydration, which arises from the synergy of entropy and enthalpy. The free energy barriers for transitions between SSs are on the order of 1kBT, allowing for modulation through applying external fields or modifying surface properties. As the ion-wall interaction strengthens, as observed in vermiculite and carbides and nitrides of transition metal channels, the probability of near-wall SSs increases. These results help to improve the performance of nanofluidic devices and provide crucial insights for developing accurate force fields of molecular simulations or advanced theoretical approaches for ion dynamics in confined channels.

First-principles redox energy estimates under the condition of satisfying the general form of Koopmans’ theorem: An atomistic study of aqueous iron

In this work, we explore the relative accuracy to which a hybrid functional, in the context of density functional theory, may predict redox properties under the constraint of satisfying the general form of Koopmans’ theorem. Taking aqueous iron as our model system within the framework of first-principles molecular dynamics, direct comparison between computed single-particle energies and experimental ionization data is assessed by both (1) tuning the degree of hybrid exchange, to satisfy the general form of Koopmans’ theorem, and (2) ensuring the application of finite-size corrections. These finite-size corrections are benchmarked through classical molecular dynamics calculations, extended to large atomic ensembles, for which good convergence is obtained in the large supercell limit. Our first-principles findings indicate that while precise quantitative agreement with experimental ionization data cannot always be attained for solvated systems, when satisfying the general form of Koopmans’ theorem via hybrid functionals, theoretically robust estimates of single-particle redox energies are most often arrived at by employing a total energy difference approach. That is, when seeking to employ a value of exact exchange that does not satisfy the general form of Koopmans’ theorem, but some other physical metric, the single-particle energy estimate that would most closely align with the general form of Koopmans’ theorem is obtained from a total energy difference approach. In this respect, these findings provide important guidance for the more general comparison of redox energies computed via hybrid functionals with experimental data.

Nanosecond solvation dynamics of the hematite/liquid water interface at hybrid DFT accuracy using committee neural network potentials

Metal oxide/water interfaces play an important role in biology, catalysis, energy storage and photocatalytic water splitting. The atomistic structure at these interfaces is often difficult to characterize by experimental techniques, whilst results from ab initio molecular dynamics simulations tend to be uncertain due to the limited length and time scales accessible. In this work, we train a committee neural network potential to simulate the hematite/water interface at the hybrid DFT level of theory to reach the nanosecond timescale and systems containing more than 3000 atoms. The NNP enables us to converge dynamical properties, not possible with brute-force ab initio molecular dynamics. Our simulations uncover a rich solvation dynamics at the hematite/water interface spanning three different time scales: picosecond H-bond dynamics between surface hydroxyls and the first water layer, in-plane/out-of-plane tilt motion of surface hydroxyls on the 10 ps time scale, and diffusion of water molecules from the oxide surface characterized by a mean residence lifetime of about 60 ps. Calculation of vibrational spectra confirm that H-bonds between surface hydroxyls and first layer water molecules are stronger than H-bonds in bulk water. Our study showcases how state of the art machine learning approaches can routinely be utilized to explore the structural dynamics at transition metal oxide interfaces with complex electronic structure. It foreshadows that c-NNPs are a promising tool to tackle the sampling problem in ab initio electrochemistry with explicit solvent molecules.

Hierarchical clustering analysis of hydrogen bond networks in aqueous solutions

To understand the relation between the macroscopic properties and microscopic structure of hydrogen bond networks in solutions, we introduced a hierarchical clustering method to analyze the typical configurations of water clusters in this type of network. Regarding hydrogen bonds as frames, the rings, fragments and clusters are defined and analyzed to provide a comprehensive perspective for the distributional and dynamic characteristics of the hydrogen-bonding network in NaCl solution at different concentrations. The properties of the radial distribution function and hydrogen bonds are first analyzed. Destruction and shorter lifetimes of hydrogen bonds are observed in solutions. In further analysis of the two-dimensional configuration, i.e., ring, and three-dimensional configuration, i.e., fragment, the average number, size and lifetime of these structures consistently decrease as the concentration increases. Ionic effects on disrupting rings and fragments are significant in the first hydration shell, especially with sodium cations, and these effects weaken beyond the first hydration shell. Regarding the clusters obtained using the Louvain algorithm, our results indicate that clusters break and become smaller as the NaCl concentration increases. The presence of ions also leads to the isolation of clusters and therefore the inhibition of changes. The lifetime of clusters increases with NaCl concentration, indicating the slowed breakage and reformation of clusters in NaCl solutions. This method can be further applied to quantitatively characterize hydrogen bond networks to elucidate more properties of aqueous solutions.

How sodium chloride extends lifetime of bulk nanobubbles in water

We present a molecular dynamics simulation study on the effects of sodium chloride addition on stability of a nitrogen bulk nanobubble in water. We find that the lifetime of the bulk nanobubble is extended in the presence of NaCl and reveal the underlying mechanisms. We do not observe spontaneous accumulation or specific arrangement of ions/charges around the nanobubble. Importantly, we quantitatively show that the N₂ molecule selectively diffuses through water molecules rather than pass by any ions after it leaves the nanobubble due to the much weaker water-water interactions than ion-water interactions. The strong ion-water interactions cause hydration effects and disrupt hydrogen bond networks in water, which leave fewer favorable paths for the diffusion of N₂ molecules, and by that reduce the degree of freedom in the dissolution of the nanobubble and prolong its lifetime. These results demonstrate that the hydration of ions plays an important role in stability of the bulk nanobubble by affecting the dynamics of hydrogen bonds and the diffusion properties of the system, which further confirm and interpret the selective diffusion path of N₂ molecules and the extension of lifetime of the nanobubble. The new atomistic insights obtained from the present research could potentially benefit the practical application of bulk nanobubbles.

Improving the scaling and performance of multiple time stepping-based molecular dynamics with hybrid density functionals

Density functionals at the level of the generalized gradient approximation (GGA) and a plane-wave basis set are widely used today to perform ab initio molecular dynamics (AIMD) simulations. Going up in the ladder of accuracy of density functionals from GGA (second rung) to hybrid density functionals (fourth rung) is much desired pertaining to the accuracy of the latter in describing structure, dynamics, and energetics of molecular and condensed matter systems. On the other hand, hybrid density functional based AIMD simulations are about two orders of magnitude slower than GGA based AIMD for systems containing ~100 atoms using ~100 compute cores. Two methods, namely MTACE and s-MTACE, based on a multiple time step integrator and adaptively compressed exchange operator formalism are able to provide a speed-up of about 7-9 in performing hybrid density functional based AIMD. In this work, we report an implementation of these methods using a task-group based parallelization within the CPMD program package, with the intention to take advantage of the large number of compute cores available on modern high-performance computing platforms. We present here the boost in performance achieved through this algorithm. This work also identifies the computational bottleneck in the s-MTACE method and proposes a way to overcome it.

Modeling Electrified Pt(111)-Had/Water Interfaces from Ab Initio Molecular Dynamics

Unraveling the atomistic structures of electric double layers (EDL) at electrified interfaces is of paramount importance for understanding the mechanisms of electrocatalytic reactions and rationally designing electrode materials with better performance. Despite numerous efforts dedicated in the past, a molecular level understanding of the EDL is still lacking. Combining the state-of-the-art ab initio molecular dynamics (AIMD) and recently developed computational standard hydrogen electrode (cSHE) method, it is possible to realistically simulate the EDL under well-defined electrochemical conditions. In this work, we report extensive AIMD calculation of the electrified Pt(111)-Had/water interfaces at the saturation coverage of adsorbed hydrogen (Had) corresponding to the typical hydrogen evolution reaction conditions. We calculate the electrode potentials of a series of EDL models with various surface charge densities using the cSHE method and further obtain the Helmholtz capacitance that agrees with experiment. Furthermore, the AIMD simulations allow for detailed structural analyses of the electrified interfaces, such as the distribution of adsorbate Had and the structures of interface water and counterions, which can in turn explain the computed dielectric property of interface water. Our calculation provides valuable molecular insight into the electrified interfaces and a solid basis for understanding a variety of electrochemical processes occurring inside the EDL.

Achieving an Order of Magnitude Speedup in Hybrid-Functional- and Plane-Wave-Based Ab Initio Molecular Dynamics: Applications to Proton-Transfer Reactions in Enzymes and in Solution

Ab initio molecular dynamics (MD) with hybrid density functionals and a plane wave basis is computationally expensive due to the high computational cost of exact exchange energy evaluation. Recently, we proposed a strategy to combine adaptively compressed exchange (ACE) operator formulation and a multiple time step integration scheme to reduce the computational cost significantly [J. Chem. Phys. 2019, 151, 151102 ]. However, it was found that the construction of the ACE operator, which has to be done at least once in every MD time step, is computationally expensive. In the present work, systematic improvements are introduced to further speed up by employing localized orbitals for the construction of the ACE operator. By this, we could achieve a computational speedup of an order of magnitude for a periodic system containing 32 water molecules. Benchmark calculations were carried out to show the accuracy and efficiency of the method in predicting the structural and dynamical properties of bulk water. To demonstrate the applicability, computationally intensive free-energy computations at the level of hybrid density functional theory were performed to investigate (a) methyl formate hydrolysis reaction in neutral aqueous media and (b) proton-transfer reaction within the active-site residues of the class C β-lactamase enzyme.

Resolving the Equal Number Density Puzzle: Molecular Picture from Simulations of LiCl(aq) and NaCl(aq)

The change in number densities of aqueous solutions of alkali chlorides should be qualitatively predictable. Typically, as cations get larger, the number density of the solution decreases. However, aqueous solutions of lithium and sodium chloride exhibit at ambient conditions practically identical number densities at equal molalities despite different ionic sizes. Here, we provide an atomistic interpretation of this experimentally observed anomalous behavior using molecular dynamics simulations. The obtained results show that the rigidity of the Li⁺ first and second solvation shells and the associated compromised hydrogen bonding result in practically equal average water densities in the local hydration regions for Li⁺ and Na⁺ despite different sizes of the cations. In addition, in more distant regions from the cations, the water densities of these two solutions also coincide. These findings thus provide an atomistic interpretation for matching number densities of LiCl and NaCl solutions. In contrast, the number density differences between NaCl and KCl solutions as well as between LiCl and KCl solutions behave in a regular fashion with lower number densities of solutions observed for larger cations.

Failure of molecular dynamics to provide appropriate structures for quantum mechanical description of the aqueous chloride ion charge-transfer-to-solvent ultraviolet spectrum

The lowest band in the charge-transfer-to-solvent ultraviolet absorption spectrum of aqueous chloride ion is studied by experiment and computation. Interestingly, the experiments indicate that at concentrations up to at least 0.25 M, where calculations indicate ion pairing to be significant, there is no notable effect of ionic strength on the spectrum. The experimental spectra are fitted to aid comparison with computations. Classical molecular dynamic simulations are carried out on dilute aqueous Cl-, Na+, and NaCl, producing radial distribution functions in reasonable agreement with experiment and, for NaCl, clear evidence of ion pairing. Clusters are extracted from the simulations for quantum mechanical excited state calculations. Accurate ab initio coupled-cluster benchmark calculations on a small number of representative clusters are carried out and used to identify and validate an efficient protocol based on time-dependent density functional theory. The latter is used to carry out quantum mechanical calculations on thousands of clusters. The resulting computed spectrum is in excellent agreement with experiment for the peak position, with little influence from ion pairing, but is in qualitative disagreement on the width, being only about half as wide. It is concluded that simulation by classical molecular dynamics fails to provide an adequate variety of structures to explain the experimental CTTS spectrum of aqueous Cl-.

Hydrogen-Bond Structure and Low-Frequency Dynamics of Electrolyte Solutions: Hydration Numbers from ab Initio Water Reorientation Dynamics and Dielectric Relaxation Spectroscopy

We present an atomistic simulation scheme for the determination of the hydration number (h) of aqueous electrolyte solutions based on the calculation of the water dipole reorientation dynamics. In this methodology, the time evolution of an aqueous electrolyte solution generated from ab initio molecular dynamics simulations is used to compute the reorientation time of different water subpopulations. The value of h is determined by considering whether the reorientation time of the water subpopulations is retarded with respect to bulk-like behavior. The application of this computational protocol to magnesium chloride (MgCl2 ) solutions at different concentrations (0.6-2.8 mol kg-1 ) gives h values in excellent agreement with experimental hydration numbers obtained using GHz-to-THz dielectric relaxation spectroscopy. This methodology is attractive because it is based on a well-defined criterion for the definition of hydration number and provides a link with the molecular-level processes responsible for affecting bulk solution behavior. Analysis of the ab initio molecular dynamics trajectories using radial distribution functions, hydrogen bonding statistics, vibrational density of states, water-water hydrogen bonding lifetimes, and water dipole reorientation reveals that MgCl2 has a considerable influence on the hydrogen bond network compared with bulk water. These effects have been assigned to the specific strong Mg-water interaction rather than the Cl-water interaction.

Efficient computation of free energy surfaces of chemical reactions using ab initio molecular dynamics with hybrid functionals and plane waves

Ab initio molecular dynamics (AIMD) simulations employing density functional theory (DFT) and plane waves are routinely carried out using density functionals at the level of generalized gradient approximation (GGA). AIMD simulations employing hybrid density functionals are of great interest as it offers a more accurate description of structural and dynamic properties than the GGA functionals. However, the computational cost for carrying out calculations using hybrid functionals and plane wave basis set is at least two orders of magnitude higher than that using GGA functionals. Recently, we proposed a strategy that combined the adaptively compressed exchange operator formulation and the multiple time step integration scheme to reduce the computational cost by an order of magnitude [J. Chem. Phys. 151, 151102 (2019)]. In this work, we demonstrate the application of this method to study chemical reactions, in particular, formamide hydrolysis in an alkaline aqueous medium. By actuating our implementation with the well-sliced metadynamics scheme, we can compute the two-dimensional free energy surface of this reaction at the level of hybrid-DFT. This work also investigates the accuracy of the PBE0 (hybrid) and the PBE (GGA) functionals in predicting the free energetics of this chemical reaction.

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

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

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

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

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

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

Importance of van der Waals effects on the hydration of metal ions from the Hofmeister series

The van der Waals (vdW) interaction plays a crucial role in the description of liquid water. Based on ab initio molecular dynamics simulations, including the non-local and fully self-consistent density-dependent implementation of the Tkatchenko-Scheffler dispersion correction, we systematically studied the aqueous solutions of metal ions (K⁺, Na⁺, and Ca²⁺) from the Hofmeister series. Similar to liquid water, the vdW interactions strengthen the attractions among water molecules in the long-range, leading to the hydrogen bond networks softened in all the ion solutions. However, the degree that the hydration structure is revised by the vdW interactions is distinct for different ions, depending on the strength of short-range interactions between the hydrated ion and surrounding water molecules. Such revisions by the vdW interactions are important for the understanding of biological functionalities of ion channels.

Beyond Koopmans' theorem: electron binding energies in disordered materials

The topical review focuses on calculating ionization energies (IE), or electronic polarons in quasi-particle terminology, in large disordered systems, e.g. for a solute dissolved in a molecular solvent. The simplest estimate of the ionization energy is provided by one-electron energies in the Hartree-Fock theory, but the calculated quantities are not accurate. Density functional theory as many-body theory provides a principal opportunity for calculating one-electron energies including correlation and relaxation effects, i.e. the true energies of electronic polarons. We argue that such a principal possibility materializes within the concept of optimally tuned range-separated hybrid functionals (OT-RSH). We describe various schemes for optimal tuning. Importantly, the OT-RSH scheme is investigated for systems capped with dielectric continuum, providing a consistent picture on the QM/dielectric boundary. Finally, some limitations and open issues of the OT-RSH approach are addressed.

Ionic radii of hydrated sodium cation from QTAIM

The sodium cation is ubiquitous in aqueous chemistry and biological systems. Yet, in spite of numerous studies, the (average) distance between the sodium cation and its water ligands, and the corresponding ionic radii, are still controversial. Recent experimental values in solution are notably smaller than those from previous X-ray studies and ab initio molecular dynamics. Here we adopt a "bottom-up" approach of obtaining these distances from quantum chemistry calculations [full MP2 with the 6-31++G(d,p) and cc-pVTZ basis-sets] of gas-phase Na⁺(H₂O)_n clusters, as a function of the sodium coordination number (CN = 2-6). The bulk limit is obtained by the polarizable continuum model, which acts to increase the interatomic distances at small CN, but has a diminishing effect as the CN increases. This extends the CN dependence of the sodium-water distances from crystal structures (CN = 4-12) to lower CN values, revealing a switch between two power laws, having a small exponent at small CNs and a larger one at large CNs. We utilize Bader's theory of atoms in molecules to bisect the Na⁺-O distances into Na⁺ and water radii. Contrary to common wisdom, the water radius is not constant, decreasing even more than that of Na⁺ as the CN decreases. We also find that the electron density at the bond critical point increases exponentially as the sodium radius decreases.

Solvation Properties of Silver and Copper Ions in a Room Temperature Ionic Liquid: A First-Principles Study

Understanding the behavior of metal ions in room temperature ionic liquids (ILs) is essential for predicting and optimizing performance for technologies like metal electrodeposition; however, many mechanistic details remain enigmatic, including the solvation properties of the ions in ILs and how they are governed by the intrinsic interaction between the ions and the liquid species. Here, we utilize first-principles molecular dynamics simulations to unravel and compare the key structural properties of Ag⁺ and Cu⁺ ions in a common room temperature IL, 1-ethyl-3-methylimidazolium trifluoromethanesulfonate. We find that, when compared to Cu⁺, the larger Ag⁺ shows a more disordered and flexible solvation structure with a more frequent exchange of the IL species between its solvation shells. In addition, our simulations reveal an interesting analog in the solvation behavior of the ions in the IL and aqueous environments, particularly in the effect of the ion electronic structures on their solvation properties. This work provides fundamental understanding of the intrinsic properties of the metal ions in the IL, while offering mechanistic understanding and strategy for future selection of ILs for metal electrodeposition processes.

Surface charge-dependent hydrodynamic properties of an electroosmotic slip flow

The electroosmosis effects at the interface of an aqueous NaCl solution and a charged silicon surface are studied using a molecular dynamics (MD) method. Considering a plug-like electroosmotic flow, we identified a thin interfacial layer in the immediate vicinity of the charged surface, where the flow velocity experiences almost linear spatial variations. The thickness of this interfacial layer is found to be linearly dependent on the surface charge density, with a negative slope which slightly depends on the surface hydrophobicity while being independent of the salt concentration, electric field strength, and orientation of the surface lattice. It is also found that upon increasing the surface charge density, the effective slip length first increases up to a maximum amount and then follows an almost linear reduction. We found that increasing the salt concentration drastically reduces the surface charge at which the effective slip length reaches its maximum amount. For highly concentrated solutions, therefore, the effective slip length could be assumed to change linearly in the whole range of the surface charge density, with a slope which is proportional to the square root of the electric field strength divided by the depth of the potential well assigned to the surface atoms εwall. Also, in a wide range of the surface charge density, the slip velocity is found to be a constant fraction of the electroosmotic velocity, which could be measured experimentally. Finally, by comparing the electroosmotic velocities calculated from the Stokes equation (considering both the slip and no-slip boundary conditions) with our MD results, we found that the no-slip boundary condition, which is normally used in analytical calculations, leads to a very inaccurate result for the studied system.

Understanding the apparent fractional charge of protons in the aqueous electrochemical double layer

A detailed atomic-scale description of the electrochemical interface is essential to the understanding of electrochemical energy transformations. In this work, we investigate the charge of solvated protons at the Pt(111) | H₂O and Al(111) | H₂O interfaces. Using semi-local density-functional theory as well as hybrid functionals and embedded correlated wavefunction methods as higher-level benchmarks, we show that the effective charge of a solvated proton in the electrochemical double layer or outer Helmholtz plane at all levels of theory is fractional, when the solvated proton and solvent band edges are aligned correctly with the Fermi level of the metal (E_F). The observed fractional charge in the absence of frontier band misalignment arises from a significant overlap between the proton and the electron density from the metal surface, and results in an energetic difference between protons in bulk solution and those in the outer Helmholtz plane.

A detailed atomic-scale description of the electrochemical interface is essential to the understanding of electrochemical energy transformations. Here, the authors investigate the solvated proton at the electrochemical interface and show that it unexpectedly carries a fractional charge.

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.

Unusual Influence of Fluorinated Anions on the Stretching Vibrations of Liquid Water

Infrared (IR) spectroscopy is a commonly used and invaluable tool in the studies of solvation phenomena in aqueous solutions. Concurrently, ab initio molecular dynamics (AIMD) simulations deliver the solvation shell picture at a molecular detail level and allow for a consistent decomposition of the theoretical IR spectrum into underlying spatial correlations. Here, we demonstrate how the novel spectral decomposition techniques can extract important information from the computed IR spectra of aqueous solutions of BF₄^- and PF₆^-, interesting weakly coordinating anions that have been known for a long time to alter the IR spectrum of water in an unusual manner. The distance-dependent spectra of both ions are analyzed using the spectral similarity method that provides a quantitative picture of both the spectrum of the solute-affected solvent and the number of solvent molecules thus altered. We find, in accordance with previous experiments, a considerable blue shift of the ν_OH stretching band of liquid water by 264 cm^-1 for BF₄^- and 306 cm^-1 for PF₆^-, with the affected numbers being 3.7 and 4.2, respectively. Considering also the additional information on solute-solvent dipolar couplings delivered by radially and spatially resolved IR spectra, the computational IR spectroscopy based on AIMD simulations is shown to be a viable predictive tool with strong interpretative power.

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.

Interaction between Water and Alkali Metal Ions and Its Temperature Dependence Revealed by Oxygen K-Edge X-ray Absorption Spectroscopy

Interaction between water molecules and alkali metal ions in aqueous salt solutions has been studied by the oxygen K-edge soft X-ray absorption spectroscopy (XAS) in transmission mode. In the measurement of several alkali halide aqueous solutions with different alkali chlorides (Li, Na, and K) and different sodium halides (Cl, Br, and I), the pre-edge component arising from the hydration water molecules shows a blue shift in peak energy as strongly depending on cations but not on anions. In the temperature dependent measurement, the pre-edge component arising from water molecules beyond the first hydration shell shows the same behavior as that of pure liquid water. On the other hand, the pre-edge component arising from water molecules in the first hydration shell of Li⁺ ions is not evidently dependent on the temperature, indicating that the hydration water molecules are more strongly bound with Li⁺ ions than the other water molecules. These experimental results are supported by the results of radial distribution functions of the first hydration shell and their temperature dependence, evaluated by molecular dynamics simulations.

Electronic structure of aqueous solutions: Bridging the gap between theory and experiments

Predicting the electronic properties of aqueous liquids has been a long-standing challenge for quantum mechanical methods. However, it is a crucial step in understanding and predicting the key role played by aqueous solutions and electrolytes in a wide variety of emerging energy and environmental technologies, including battery and photoelectrochemical cell design. We propose an efficient and accurate approach to predict the electronic properties of aqueous solutions, on the basis of the combination of first-principles methods and experimental validation using state-of-the-art spectroscopic measurements. We present results of the photoelectron spectra of a broad range of solvated ions, showing that first-principles molecular dynamics simulations and electronic structure calculations using dielectric hybrid functionals provide a quantitative description of the electronic properties of the solvent and solutes, including excitation energies. The proposed computational framework is general and applicable to other liquids, thereby offering great promise in understanding and engineering solutions and liquid electrolytes for a variety of important energy technologies.

Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis

The importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized with respect to both the QM electronic density and the MM induced dipoles. This QM/AMOEBA model is implemented through the Q-Chem/LibEFP code interface and then applied to the evaluation of solute-solvent interaction energies for various systems ranging from the water dimer to neutral and ionic solutes (NH₃, NH₄⁺, CN^-) surrounded by increasing numbers of water molecules (up to 100). In order to analyze the resulting interaction energies, we also utilize an energy decomposition analysis (EDA) scheme which identifies contributions from permanent electrostatics, polarization, and van der Waals (vdW) interaction for the interaction between the QM solute and the solvent molecules described by AMOEBA. This facilitates a component-wise comparison against full QM calculations where the corresponding energy components are obtained via a modified version of the absolutely localized molecular orbitals (ALMO)-EDA. The results show that the present QM/AMOEBA model can yield reasonable solute-solvent interaction energies for neutral and cationic species, while further scrutiny reveals that this accuracy highly relies on the delicate balance between insufficiently favorable permanent electrostatics and softened vdW interaction. For anionic solutes where the charge penetration effect becomes more pronounced, the QM/MM interface turns out to be unbalanced. These results are consistent with and further elucidate our findings in a previous study using a slightly different QM/AMOEBA model ( Dziedzic et al. J. Chem. Phys. 2016 , 145 , 124106 ). The implications of these results for further refinement of this model are also discussed.

Local and Global Effects of Dissolved Sodium Chloride on the Structure of Water

Determining how the structure of water is modified by the presence of salts is instrumental to understanding the solvation of biomolecules and, in general, the role played by salts in biochemical processes. However, the extent of hydrogen bonding disruption induced by salts remains controversial. We performed extensive first-principles simulations of solutions of a simple salt (NaCl) and found that, while the cation does not significantly change the structure of water beyond the first solvation shell, the anion has a further reaching effect, modifying the hydrogen-bond network even outside its second solvation shell. We found that a distinctive fingerprint of hydrogen bonding modification is the change in polarizability of water molecules. Molecular dipole moments are instead insensitive probes of long-range modifications induced by Na⁺ and Cl^- ions. Though noticeable, the long-range effect of Cl^- is expected to be too weak to affect solubility of large biomolecules.

Modelling heterogeneous interfaces for solar water splitting

The generation of hydrogen from water and sunlight offers a promising approach for producing scalable and sustainable carbon-free energy. The key of a successful solar-to-fuel technology is the design of efficient, long-lasting and low-cost photoelectrochemical cells, which are responsible for absorbing sunlight and driving water splitting reactions. To this end, a detailed understanding and control of heterogeneous interfaces between photoabsorbers, electrolytes and catalysts present in photoelectrochemical cells is essential. Here we review recent progress and open challenges in predicting physicochemical properties of heterogeneous interfaces for solar water splitting applications using first-principles-based approaches, and highlights the key role of these calculations in interpreting increasingly complex experiments.

The fate of carbon dioxide in water-rich fluids under extreme conditions

Investigating the fate of dissolved carbon dioxide under extreme conditions is critical to understanding the deep carbon cycle in Earth, a process that ultimately influences global climate change. We used first-principles molecular dynamics simulations to study carbonates and carbon dioxide dissolved in water at pressures (P) and temperatures (T) approximating the conditions of Earth's upper mantle. Contrary to popular geochemical models assuming that molecular CO₂(aq) is the major carbon species present in water under deep Earth conditions, we found that at 11 GPa and 1000 K, carbon exists almost entirely in the forms of solvated carbonate ([Formula: see text]) and bicarbonate ([Formula: see text]) ions and that even carbonic acid [H₂CO₃(aq)] is more abundant than CO₂(aq). Furthermore, our simulations revealed that ion pairing between Na⁺ and [Formula: see text]/[Formula: see text] is greatly affected by P-T conditions, decreasing with increasing pressure at 800 to 1000 K. Our results suggest that in Earth's upper mantle, water-rich geofluids transport a majority of carbon in the form of rapidly interconverting [Formula: see text] and [Formula: see text] ions, not solvated CO₂(aq) molecules.

Solvation structure of the halides from x-ray absorption spectroscopy

Three-dimensional models for the aqueous solvation structures of chloride, bromide, and iodide are reported. K-edge extended X-ray absorption fine structure (EXAFS) and Minuit X-ray absorption near edge (MXAN) analyses found well-defined single shell solvation spheres for bromide and iodide. However, dissolved chloride proved structurally distinct, with two solvation shells needed to explain its strikingly different X-ray absorption near edge structure (XANES) spectrum. Final solvation models were as follows: iodide, 8 water molecules at 3.60 ± 0.13 Å and bromide, 8 water molecules at 3.40 ± 0.14 Å, while chloride solvation included 7 water molecules at 3.15 ± 0.10 Å, and a second shell of 7 water molecules at 4.14 ± 0.30 Å. Each of the three derived solvation shells is approximately uniformly disposed about the halides, with no global asymmetry. Time-dependent density functional theory calculations simulating the chloride XANES spectra following from alternative solvation spheres revealed surprising sensitivity of the electronic state to 6-, 7-, or 8-coordination, implying a strongly bounded phase space for the correct structure during an MXAN fit. MXAN analysis further showed that the asymmetric solvation predicted from molecular dynamics simulations using halide polarization can play no significant part in bulk solvation. Classical molecular dynamics used to explore chloride solvation found a 7-water solvation shell at 3.12 (-0.04/+0.3) Å, supporting the experimental result. These experiments provide the first fully three-dimensional structures presenting to atomic resolution the aqueous solvation spheres of the larger halide ions.

Pairwise-additive force fields for selected aqueous monovalent ions from adaptive force matching

Simple non-polarizable potentials were developed for Na(+), K(+), Cl(-), and Br(-) using the adaptive force matching (AFM) method with ab initio MP2 method as reference. Our MP2-AFM force field predicts the solvation free energies of the four salts formed by the ions with an error of no more than 5%. Other properties such as the ion-water radial distribution functions, first solvation shell water tilt angle distributions, ion diffusion constants, concentration dependent diffusion constant of water, and concentration dependent surface tension of the solutions were calculated with this potential. Very good agreement was achieved for these properties. In particular, the diffusion constants of the ions are within 6% of experimental measurements. The model predicts bromide to be enriched at the interface in the 1.6M KBr solution but predicts the ion to be repelled for the surface at lower concentration.