Redox levels in aqueous solution: Effect of van der Waals interactions and hybrid functionals

Dynamics of the charge transfer to solvent process in aqueous iodide

Charge-transfer-to-solvent states in aqueous halides are ideal systems for studying the electron-transfer dynamics to the solvent involving a complex interplay between electronic excitation and solvent polarization. Despite extensive experimental investigations, a full picture of the charge-transfer-to-solvent dynamics has remained elusive. Here, we visualise the intricate interplay between the dynamics of the electron and the solvent polarization occurring in this process. Through the combined use of ab initio molecular dynamics and machine learning methods, we investigate the structure, dynamics and free energy as the excited electron evolves through the charge-transfer-to-solvent process, which we characterize as a sequence of states denoted charge-transfer-to-solvent, contact-pair, solvent-separated, and hydrated electron states, depending on the distance between the iodine and the excited electron. Our assignment of the charge-transfer-to-solvent states is supported by the good agreement between calculated and measured vertical binding energies. Our results reveal the charge transfer process in terms of the underlying atomic processes and mechanisms.

Absolute energy levels of liquid water from many-body perturbation theory with effective vertex corrections

We demonstrate the importance of addressing the Γ vertex and thus going beyond the GW approximation for achieving the energy levels of liquid water in many-body perturbation theory. In particular, we consider an effective vertex function in both the polarizability and the self-energy, which does not produce any computational overhead compared with the GW approximation. We yield the band gap, the ionization potential, and the electron affinity in good agreement with experiment and with a hybrid functional description. The achieved electronic structure and dielectric screening further lead to a good description of the optical absorption spectrum, as obtained through the solution of the Bethe-Salpeter equation. In particular, the experimental peak position of the exciton is accurately reproduced.

Multifunctional Roles of Clathrate Hydrate Nanoreactors for CO2 Reduction

In this study, we explore a possible platform for the CO2 reduction (CO2 R) in one of water's solid phases, namely clathrate hydrates (CHs), by ab initio molecular dynamics and well-tempered metadynamics simulations with periodic boundary conditions. We found that the stacked H2 O nanocages in CHs help to initialize CO2 R by increasing the electron-binding ability of CO2 . The substantial CO2 R processes are further influenced by the hydrogen bond networks in CHs. The first intermediate CO2 - in this process can be stabilized through cage structure reorganization into the H-bonded [CO2 - ⋅⋅⋅H-OHcage ] complex. Further cooperative structural dynamics enables the complex to convert into a vital transient [CO2 2- ⋅⋅⋅H-OHcage ] intermediate in a low-barrier disproportionation-like process. Such a highly reactive intermediate spontaneously triggers subsequent double proton transfer along its tethering H-bonds, finally converting it into HCOOH. These hydrogen-bonded nanoreactors feature multiple functions in facilitating CO2 R such as confining, tethering, H-bond catalyzing and proton pumping. Our findings have a general interest and extend the knowledge of CO2 R into porous aqueous systems.

Many-body screening effects in liquid water

The screening arising from many-body excitations is a crucial quantity for describing absorption and inelastic X-ray scattering (IXS) of materials. Similarly, the electron screening plays a critical role in state-of-the-art approaches for determining the fundamental band gap. However, ab initio studies of the screening in liquid water have remained limited. Here, we use a combined analysis based on the Bethe-Salpeter equation and time-dependent density functional theory. We first show that absorption spectra at near-edge energies are insufficient to assess the accuracy by which the screening is described. Next, when the energy range under scrutiny is extended, we instead find that the IXS spectra are highly sensitive and allow for the selection of the optimal theoretical scheme. This leads to good agreement with experiment over a large range of transferred energies and momenta, and enables establishing the elusive fundamental band gap of liquid water at 9.3 eV.

Hydrated electrons as nodes in porous clathrate hydrates

We investigate the structures of hydrated electrons (e^- _aq) in one of water's solid phases, namely, clathrate hydrates (CHs). Using density functional theory (DFT) calculations, DFT-based ab initio molecular dynamics (AIMD), and path-integral AIMD simulations with periodic boundary conditions, we find that the structure of the e^- _aq@node model is in good agreement with the experiment, suggesting that an e^- _aq could form a node in CHs. The node is a H₂O defect in CHs that is supposed to be composed of four unsaturated hydrogen bonds. Since CHs are porous crystals that possess cavities that can accommodate small guest molecules, we expect that these guest molecules can be used to tailor the electronic structure of the e^- _aq@node, and it leads to experimentally observed optical absorption spectra of CHs. Our findings have a general interest and extend the knowledge of e^- _aq into porous aqueous systems.

pH- and Facet-Dependent Surface Chemistry of TiO2 in Aqueous Environment from First Principles

TiO₂ is a relevant catalytic material, and its chemistry in aqueous environment is a challenging aspect to address. Also, the morphology of TiO₂ particles at the nanoscale is often complex, spanning from faceted to spherical. In this work, we study the pH- and facet-dependent surface chemistry of TiO₂/water interfaces by performing ab initio molecular dynamics simulations with the grand canonical formulation of species in solution. We first determined the acid-base equilibrium constants at the interface, which allows us to estimate the pH at the point of zero charge, an important experimental observable. Then, based on simulated equilibrium constants, we predict the amount of H⁺, OH^-, and adsorbed H₂O species present on the surfaces as a function of the pH, a relevant aspect for water splitting semi-reactions. We approximated the complex morphology of TiO₂ particles by considering the rutile (110) and (011), and anatase (101), (001), and (100) surfaces.

Birth of the Hydrated Electron via Charge-Transfer-to-Solvent Excitation of Aqueous Iodide

A primary means to generate hydrated electrons in laboratory experiments is excitation to the charge-transfer-to-solvent (CTTS) state of a solute such as I^-(aq), but this initial step in the genesis of e^-(aq) has never been simulated directly using ab initio molecular dynamics. We report the first such simulations, combining ground- and excited-state simulations of I^-(aq) with a detailed analysis of fluctuations in the Coulomb potential experienced by the nascent solvated electron. What emerges is a two-step picture of the evolution of e^-(aq) starting from the CTTS state: I^-(aq) + hν → I^-*(aq) → I^•(aq) + e^-(aq). Notably, the equilibrated ground state of e^-(aq) evolves from I^-*(aq) without any nonadiabatic transitions, simply as a result of solvent reorganization. The methodology used here should be applicable to other photochemical electron transfer processes in solution, an important class of problems directly relevant to photocatalysis and energy transfer.

Is a thin mechanism appropriate for aromatic nitration?

The mechanism of toluene nitration by NO₂BF₄ in dichloromethane solution is investigated by performing advanced ab initio MD simulations of the reaction trajectories, including at full quantum mechanical level the effects of both the solvent and of the counterion. The time evolution of the encounter complex, as well as that of the associated electronic structure, for different trajectories reveals that a single electron transfer step fastly occurs after reactants are accommodated in a common solvation shell, always preceding the formation of the σ-complex. The present results strongly suggest that the regioselectivity of the reaction is spin-density driven and that a thin mechanism, one based on reaction intermediates and transition states, can be appropriate to describe aromatic nitration.

Preparation of Heterojunctions Based on Cs3Bi2Br9 Nanocrystals and g-C3N4 Nanosheets for Photocatalytic Hydrogen Evolution

Heterojunctions based on metal halide perovskites (MHPs) are promising systems for the photocatalytic hydrogen evolution reaction (HER). In this work, we coupled Cs₃Bi₂Br₉ nanocrystals (NCs), obtained by wet ball milling synthesis, with g-C₃N₄ nanosheets (NSs), produced by thermal oxidation of bulk g-C₃N_4, in air. These methods are reproducible, inexpensive and easy to scale up. Heterojunctions with different loadings of Cs₃Bi₂Br₉ NCs were fully characterised and tested for the HER. A relevant improvement of H₂ production with respect to pristine carbon nitride was achieved at low NCs levels reaching values up to about 4600 µmol g^-1 h^-1. This work aims to provide insights into the synthesis of inexpensive and high-performing heterojunctions using MHP for photocatalytic applications.

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.

Understanding the Temperature Dependence and Finite Size Effects in Ab Initio MD Simulations of the Hydrated Electron

The hydrated electron is of interest to both theorists and experimentalists as a paradigm solution-phase quantum system. Although the bulk of the theoretical work studying the hydrated electron is based on mixed quantum/classical (MQC) methods, recent advances in computer power have allowed several attempts to study this object using ab initio methods. The difficulty with employing ab initio methods for this system is that even with relatively inexpensive quantum chemistry methods such as density functional theory (DFT), such calculations are still limited to at most a few tens of water molecules and only a few picoseconds duration, leaving open the question as to whether the calculations are converged with respect to either system size or dynamical fluctuations. Moreover, the ab initio simulations of the hydrated electron that have been published to date have provided only limited analysis. Most works calculate the electron's vertical detachment energy, which can be compared to experiment, and occasionally the electronic absorption spectrum is also computed. Structural features, such as pair distribution functions, are rare in the literature, with the majority of the structural analysis being simple statements that the electron resides in a cavity, which are often based only on a small number of simulation snapshots. Importantly, there has been no ab initio work examining the temperature-dependent behavior of the hydrated electron, which has not been satisfactorily explained by MQC simulations. In this work, we attempt to remedy this situation by running DFT-based ab initio simulations of the hydrated electron as a function of both box size and temperature. We show that the calculated properties of the hydrated electron are not converged even with simulation sizes up to 128 water molecules and durations of several tens of picoseconds. The simulations show significant changes in the water coordination and solvation structure with box size. Our temperature-dependent simulations predict a red-shift of the absorption spectrum (computed using TD-DFT with an optimally tuned range-separated hybrid functional) with increasing temperature, but the magnitude of the predicted red-shift is larger than that observed experimentally, and the absolute position of the calculated spectra are off by over half an eV. The spectral red-shift at high temperatures is accompanied by both a partial loss of structure of the electron's central cavity and an increased radius of gyration that pushes electron density onto and beyond the first solvation shell. Overall, although ab initio simulations can provide some insights into the temperature-dependent behavior of the hydrated electron, the simulation sizes and level of quantum chemistry theory that are currently accessible are inadequate for correctly describing the experimental properties of this fascinating object.

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

Within the framework of Kohn-Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob's ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric-isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

Probing Interfacial Effects on Ionization Energies: The Surprising Banality of Anion-Water Hydrogen Bonding at the Air/Water Interface

Liquid microjet photoelectron spectroscopy is an increasingly common technique to measure vertical ionization energies (VIEs) of aqueous solutes, but the interpretation of these experiments is subject to questions regarding sensitivity to bulk versus interfacial solvation environments. We have computed aqueous-phase VIEs for a set of inorganic anions, using a combination of molecular dynamics simulations and electronic structure calculations, with results that are in excellent agreement with experiment regardless of whether the simulation data are restricted to ions at the air/water interface or to those in bulk aqueous solution. Although the computed VIEs are sensitive to ion-water hydrogen bonding, we find that the short-range solvation structure is sufficiently similar in both environments that it proves impossible to discriminate between the two on the basis of the VIE, a conclusion that has important implications for the interpretation of liquid-phase photoelectron spectroscopy. More generally, analysis of the simulation data suggests that the surface activity of soft anions is largely a second or third solvation shell effect, arising from disruption of water-water hydrogen bonds and not from significant changes in first-shell anion-water hydrogen bonding.

Electronic Structure of Water from Koopmans-Compliant Functionals

Obtaining a precise theoretical description of the spectral properties of liquid water poses challenges for both molecular dynamics (MD) and electronic structure methods. The lower computational cost of the Koopmans-compliant functionals with respect to Green's function methods allows the simulations of many MD trajectories, with a description close to the state-of-art quasi-particle self-consistent GW plus vertex corrections method (QSGW + f_xc). Thus, we explore water spectral properties when different MD approaches are used, ranging from classical MD to first-principles MD, and including nuclear quantum effects. We have observed that different MD approaches lead to up to 1 eV change in the average band gap; thus, we focused on the band gap dependence with the geometrical properties of a system to explain such spread. We have evaluated the changes in the band gap due to variations in the intramolecular O-H bond distance and HOH angle, as well as the intermolecular hydrogen bond O···O distance and the OHO angles. We have observed that the dominant contribution comes from the O-H bond length; the O···O distance plays a secondary role, and the other geometrical properties do not significantly influence the gap. Furthermore, we analyze the electronic density of states (DOS), where the KIPZ functional shows good agreement with the DOS obtained with state-of-art approaches employing quasi-particle self-consistent GW plus vertex corrections. The O-H bond length also significantly influences the DOS. When nuclear quantum effects are considered, broadening of the peaks driven by the broader distribution of the O-H bond lengths is observed, leading to a closer agreement with the experimental photoemission spectra.

Molecular Dynamics Characterization of Dielectron Hydration in Liquid Water with Unique Double Proton Transfers

Radiation chemistry of water and aqueous solutions has always been an interesting scientific issue owing to involving electronic excitations, ionization of solvated species, and formation of radiolytic species and many elementary reactions, but the underlying mechanisms are still poorly understood. Here, we for the first time molecular dynamics characterize the hydration dynamics of two correlated electrons and their triggered unique phenomena in liquid water associated with radiolysis of water using the combined hybrid functional and nonlocal dispersion functional. Hydration of two electrons may experience two distinctly different mechanisms, one forming a spin-paired closed-shell unicaged dielectron hydrate (e₂^2-_aq) and the other forming a spin-paired metastable open-shell bicaged hydrated electron pair (e^-_aq···e^-_aq) which exhibits intriguing antiferromagnetic spin coupling dynamics (in a range of -40 cm^-1 to -500 cm^-1). e^-_aq···e^-_aq can recombine to e₂^2-_aq through a unique solvent fluctuation-controlled gradual-flowing mechanism, and enlarging fluctuation can promote the conversion. Interestingly, we directly observe that e₂^2-_aq as the precursor can trigger hydrogen evolution via unique continuous spontaneous double proton transfer to the dielectron with a short-lived H^-_aq intermediate, but e^-_aq···e^-_aq does not directly. This is the first direct observation for the connection between e₂^2-_aq and spontaneous hydrogen evolution including participation of H^-_aq in aqueous solution, bridging relevant experimental phenomena. This work also evidences an unnoticed process, the double proton transfer mediated charge separation, and presents the first detailed analysis regarding the evolution dynamics of e₂^2-_aq for the understanding of the radiolysis reactions in aqueous solutions.

Water-Stable DMASnBr3 Lead-Free Perovskite for Effective Solar-Driven Photocatalysis

Water-stable metal halide perovskites could foster tremendous progresses in several research fields where their superior optical properties can make differences. In this work we report clear evidence of water stability in a lead-free metal halide perovskite, namely DMASnBr₃ , obtained by means of diffraction, optical and X-ray photoelectron spectroscopy. Such unprecedented water-stability has been applied to promote photocatalysis in aqueous medium, in particular by devising a novel composite material by coupling DMASnBr₃ to g-C₃ N₄ , taking advantage from the combination of their optimal photophysical properties. The prepared composites provide an impressive hydrogen evolution rate >1700 μmol g^-1  h^-1 generated by the synergistic activity of the two composite costituents. DFT calculations provide insight into this enhancement deriving it from the favorable alignment of interfacial energy levels of DMASnBr₃ and g-C₃ N₄ . The demonstration of an efficient photocatalytic activity for a composite based on lead-free metal halide perovskite in water paves the way to a new class of light-driven catalysts working in aqueous environments.

Comparison of Penta and Tetra-pyridyl Cobalt-based Catalysts for Water Reduction: H2 Production Cycle, Solvent Response and Reduction Free Energy

Understanding water reduction towards H₂ generation is crucial to overcome today's renewable energy obstacles. Previous studies have shown the superior H₂ production performances of Cobalt based penta-pyridyl (CoaPPy) and tetra-pyridyl (CoaTPy) complexes in solution. We investigate H₂ production cycles of CoaPPy and CoaTPy complexes immersed in water solution by means of Ab-initio Molecular Dynamics and Density Functional Theory. We monitor dynamic properties of the systems, solvent response and structural changes occurring in the catalysts, by simulating all intermediate steps of the H₂ production cycle. Reduction free energies and reorganization energies are calculated. Our results show that, following the first electron injection, H₂ production proceeds with the singlet spin state. Following the first electron insertion, we observe a significant rearrangement of the hydrogen bonding network in the first solvation shell. The cobalt center turns out to be more accessible for the surrounding water molecules in the case of CoaTPy at all the intermediate steps, which explains its higher catalytic performance over CoaPPy. Following the first reduction reaction, a larger gain in reduction free energy is estimated for CoaTPy with respect to CoaPPy, with a difference of 0.14 eV, in line with the experiments. For the second reduction, instead, CoaPPy shows more negative reduction potential, by 0.41 eV.

Combined Computational and Experimental Investigation on the Nature of Hydrated Iodoplumbate Complexes: Insights into the Dual Role of Water in Perovskite Precursor Solutions

Water is generally considered an enemy of metal halide perovskites, being responsible for their rapid degradation and, consequently, undermining the long-term stability of perovskite-based solar cells. However, beneficial effects of liquid water have been surprisingly observed, and synthetic routes including water treatments have shown to improve the quality of perovskite films. This suggests that the interactions of water with perovskites and their precursors are far from being completely understood, as water appears to play a puzzling dual role in perovskite precursor solutions. In this context, studying the basic interactions between perovskite precursors in the aqueous environment can provide a deeper comprehension of this conundrum. In this context, it is fundamental to understand how water impacts the chemistry of iodoplumbate perovskite precursor species, PbI_x^2–x. Here, we investigate the chemistry of these complexes using a combined experimental and theoretical strategy to unveil their peculiar structural and optical properties and eventually to assign the species present in the solution. Our study indicates that iodide-rich iodoplumbates, which are generally key to the formation of lead halide perovskites, are not easily formed in aqueous solutions because of the competition between iodide and solvent molecules in coordinating Pb²⁺ ions, explaining the difficulty of depositing lead iodide perovskites from aqueous solutions. We postulate that the beneficial effect of water when used as an additive is then motivated by its behavior being similar to high coordinative polar aprotic solvents usually employed as additives in one-step perovskite depositions.

Strong Hole Trapping Due to Oxygen Dimers in BiVO4: Effect on the Water Oxidation Reaction

We present a study of hole bipolarons in BiVO₄. We show that in the presence of two holes O-O dimers are formed, leading to strong charge trapping. While the formation of bipolarons in bulk BiVO₄ requires overcoming a kinetic barrier, we find that these defects should be spontaneously formed at the surface of the material and its interface with water. Through molecular dynamics simulations, we study the effect of bipolarons on the water-splitting reaction and show that their presence may be especially beneficial in alkaline conditions.

Computational Design of Mixed-Valence Tin Sulfides as Solar Absorbers

Binary tin sulfides, such as SnS and SnS₂, are appealing because of their simple stoichiometry and semiconducting properties and are, therefore, being pursued as potentially cost-effective materials for optoelectronic applications. The multivalency of Sn, that is, Sn(+2) and Sn(+4) allows yet more intermediate compositions, Sn_xS_y, whose structures and properties are of interest. Sn₂S₃ is already under consideration as a mixed-valence semiconductor. Other intermediate compositions, for example, Sn₃S₄ and Sn₄S₅ have remained elusive, although their existences have been alluded to in literature. Here we report a comprehensive study of phase stability of the Sn_xS_y series compounds, utilizing swarm-intelligence crystal structure search method combined with first-principles energetic calculations. We find that the stability of mixed-valence Sn_xS_y compounds with respect to decomposition into pure-valence SnS and SnS₂ is in general weaker than the Sn_xO_y counterparts, likely due to differences in chemical bonding. Besides identifying the experimentally discovered stable phases of Sn₂S₃, our calculations indicate that the Sn₃S₄ phase is another mixed-valence composition which shows marginal stability with respect to decomposition into SnS and SnS₂. Other studied compositions may be metastable under ambient conditions, with slightly positive formation enthalpies. We find two structures of Sn₃S₄ having comparably low energies, both of which feature one-dimensional chain-like fragments obtained by breaking up the edge-connected octahedral layers of SnS₂. Both structures indicate lattice phonon stability and one shows quasi-direct band gap with a calculated value of 1.43 eV, ideal for solar absorbers. A further analysis of the composition-structure-property relationship supports the notion that low-dimensional Sn-S motifs and van der Waals interaction may lead to diverse structure types and chemical compositions, having functional properties that are yet to be identified in the Sn_xS_y series with mixed valency.

Structure of the aqueous electron

A cavity or excluded-volume structure best explains the experimental properties of the aqueous or “hydrated” electron.

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.

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.

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.

pH-Dependent Surface Chemistry from First Principles: Application to the BiVO4(010)-Water Interface

We present a theoretical formulation for studying the pH-dependent interfacial coverage of semiconductor-water interfaces through ab initio electronic structure calculations, molecular dynamics simulations, and the thermodynamic integration method. This general methodology allows one to calculate the acidity of the individual adsorption sites on the surface and consequently the pH at the point of zero charge, pH_PZC, and the preferential adsorption mode of water molecules, either molecular or dissociative, at the semiconductor-water interface. The proposed method is applied to study the BiVO₄(010)-water interface, yields a pH_PZC in excellent agreement with the experimental characterization. Furthermore, from the calculated p K_a values of the individual adsorption sites, we construct an ab initio concentration diagram of all adsorbed species at the interface as a function of the pH of the aqueous solution. The diagram clearly illustrates the pH-dependent coverage of the surface and indicates that protons are found to be significantly adsorbed (∼1% of available sites) only in highly acidic conditions. The surface is found to be mostly covered by molecularly adsorbed water molecules in a wide interval of pH values ranging from 2 to 8. Hydroxyl ions are identified as the dominant adsorbed species at pH larger than 8.2.

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.

Reactivity and energy level of a localized hole in liquid water

Reaction and redox level of hole capture in liquid water from first principles.

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.

Electronic Levels of Excess Electrons in Liquid Water

We provide a consistent description of the electronic levels associated with localized and delocalized excess electrons in liquid water by combining hybrid-functional molecular dynamics simulations with a grand canonical formulation of solutes in aqueous solution. The excess electron localizes in a cavity with an average radius of 1.8 Å and a majority coordination of five water molecules. The vertical binding energy, the optical s-p transitions, and the adiabatic redox level are found to agree closely with their experimental counterparts. The energy level associated with electron delocalization V₀ is inferred to lie at -0.97 eV with respect to the vacuum level.

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.

Ab initio Electronic Structure of Liquid Water

Self-consistent GW calculations with efficient vertex corrections are employed to determine the electronic structure of liquid water. Nuclear quantum effects are taken into account through ab initio path-integral molecular dynamics simulations. We reveal a sizable band-gap renormalization of up to 0.7 eV due to hydrogen-bond quantum fluctuations. Our calculations lead to a band gap of 8.9 eV, in accord with the experimental estimate. We further resolve the ambiguities in the band-edge positions of liquid water. The valence-band maximum and the conduction-band minimum are found at -9.4 and -0.5  eV with respect to the vacuum level, respectively.