To be or not to be in a cavity: the hydrated electron dilemma

Photo-excited charge transfer from adamantane to electronic bound states in water

Aqueous nanodiamonds illuminated by UV light produce free solvated electrons, which may drive high-energy reduction reactions in water. However, the influence of water conformations on the excited-state electron-transfer mechanism are still under debate. In this work, we offer a theoretical study of charge-transfer states in adamantane-water structures obtained by linear-response time-dependent density-functional theory. Small water clusters with broken hydrogen bonds are found to efficiently bind the electron from adamantane. A distinction is made with respect to the nature of the water clusters: some bind the electron in a water cavity, others along a strong permanent total dipole. These two types of bound states are more strongly binding, the higher their electron affinity and their positive electrostatic potential, the latter being dominated by the energy of the lowest unoccupied molecular orbital of the isolated water clusters. Structural sampling in a thermal equilibrium at room temperature via molecular dynamics snapshots confirms under which conditions the underlying waters clusters can occur and verifies that broken hydrogen bonds in the water network close to adamantane can create traps for the solvated electron.

Empirically Optimized One-Electron Pseudopotential for the Hydrated Electron: A Proof-of-Concept Study

Mixed quantum-classical molecular dynamics simulations have been important tools for studying the hydrated electron. They generally use a one-electron pseudopotential to describe the interactions of an electron with the water molecules. This approximation shows both the strength and weakness of the approach. On the one hand, it enables extensive statistical sampling and large system sizes that are not possible with more accurate ab initio molecular dynamics methods. On the other hand, there has (justifiably) been much debate about the ability of pseudopotentials to accurately and quantitatively describe the hydrated electron properties. These pseudopotentials have largely been derived by fitting them to ab initio calculations of an electron interacting with a single water molecule. In this paper, we present a proof-of-concept demonstration of an alternative approach in which the pseudopotential parameters are determined by optimizing them to reproduce key experimental properties. Specifically, we develop a new pseudopotential, using the existing TBOpt model as a starting point, which correctly describes the hydrated electron vertical detachment energy and radius of gyration. In addition to these properties, this empirically optimized model displays a significantly modified solvation structure, which improves, for example, the prediction of the partial molar volume.

Influence of H-bonds on the photoionization of aromatic chromophores in water: The aniline molecule

We have conducted time-resolved experiments (pump-probe and pump-repump-probe) on a model aromatic chromophore, aniline, after excitation in water at 267 nm. In the initial spectra recorded, in addition to the absorption corresponding to the bright ππ* excitation, the fingerprint of a transient state with the electron located on the solvent molecule is identified. We postulate that the latter corresponds to the πσ* state along the N-H bond, whose complete relaxation with a ∼500 ps lifetime results in the formation of the fully solvated electron and cation. This ionization process occurs in parallel with the ππ* photophysical channel that yields the characteristic ∼1 ns fluorescence lifetime. The observed branched pathway is rationalized in terms of the different H-bonds that the water establishes with the amino group. The proposed mechanism could be common for aromatics in water containing N-H or O-H bonds and would allow the formation of separated charges after excitation at the threshold of their electronic absorptions.

Evidence for Water Antibonding Orbital Mixing in the Hydrated Electron from Its Oxygen 1s X-ray Absorption Spectrum

The X-ray absorption spectrum (XAS) of the hydrated electron (e_(aq)^-) has been simulated using time-dependent density functional theory with a quantum mechanics/molecular mechanics description. A unique XAS peak at 533 eV is observed with an energy and intensity in quantitative agreement with recent time-resolved experiments, allowing its assignment as arising from water O1s transitions to the singly occupied molecular orbital (SOMO) in which the excess electron resides. The transitions acquire oscillator strength due to the SOMO comprising an admixture of a cavity-localized orbital and water 4a₁ and 2b₂ antibonding orbitals. The mixing of antibonding orbitals has implications for the strength of couplings between e_(aq)^- and intramolecular modes of water.

Investigation of the Failure of Marcus Theory for Hydrated Electron Reactions

Reactions of the hydrated electron with a wide variety of substrates have been found to exhibit unusually similar activation energies in a manner incompatible with Marcus electron transfer theory. Given the fundamental linear response assumption of Marcus theory, one possible explanation for this apparent failure is that the underlying free energy surfaces governing the reactions are not harmonic; i.e., hydrated electron structural fluctuations exhibit non-Gaussian behavior. In this work, we test this hypothesis by using simulations to calculate the hydrated electron vertical detachment energy distribution. We consider both cavity and noncavity models for the hydrated electron, between which the actual hydrated electron behavior is expected to lie. Our results identify a possible origin for non-Gaussian behavior of the hydrated electron but show that it is not of sufficient magnitude to explain the failure of Marcus theory to describe its reactions. Thus, other explanations must be sought.

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.

Quantum simulations of neutral water clusters and singly-charged water cluster anions

We report a computational study of the structural and energetic properties of water clusters and singly-charged water cluster anions containing from 20 to 573 water molecules. We have used both a classical and a quantum description of the molecular degrees of freedom. Water intra and inter-molecular interactions have been modelled through the SPC/F model, while the water-excess electron interaction has been described via the well-known Turi-Borgis potential. We find that in general the quantum effects of the water degrees of freedom are small, but they do influence the cluster-size at which the excess electron stabilises inside the cluster, which occurs at smaller cluster sizes when quantum effects are taken into consideration.

Hydrated Electrons in High-Concentration Electrolytes Interact with Multiple Cations: A Simulation Study

Experimental studies have demonstrated that the hydrated electron's absorption spectrum undergoes a concentration-dependent blue-shift in the presence of electrolytes such as NaCl. The blue-shift increases roughly linearly at low salt concentration but saturates as the solubility limit of the salt is approached. Previous attempts to understand the origin of the concentration-dependent spectral shift using molecular simulation have only examined the interaction between the hydrated electron and a single sodium cation, and these simulations predicted a spectral blue-shift that was an order of magnitude larger than that seen experimentally. Thus, in this paper, we first explore the reasons for the exaggerated spectral blue-shift when a simulated hydrated electron interacts with a single Na⁺. We find that the issue arises from nonpairwise additivity of the Na⁺-e^- and H₂O-e^- pseudopotentials used in the simulation. This effect arises because the solvating water molecules donate charge into the empty orbitals of Na⁺, lowering the effective charge of the cation and thus reducing the excess electron-cation interaction. Careful analysis shows, however, that although this nonpairwise additivity changes the energetics of the electron-Na⁺ interaction, the forces between the electron, Na⁺, and water are unaffected, so that mixed quantum/classical (MQC) simulations produce the correct structure and dynamics. With this in hand, we then use MQC simulations to explore the behavior of the hydrated electron as an explicit function of NaCl salt concentration. We find that the simulations correctly reproduce the observed experimental spectral shifting behavior. The reason for the spectral shift is that as the electrolyte concentration increases, the average number of cations simultaneously interacting in contact pairs with the hydrated electron increases from 1.0 at low concentrations to ∼2.5 near the saturation limit. As the number of cations that interact with the electron increases, the cation/electron interactions becomes slightly weaker, so that the corresponding Na⁺-e^- distance increases with increasing salt concentration. We also find that the dielectric constant of the solution plays little role in the observed spectroscopy, so that the electrolyte-dependent spectral shifts of the hydrated electron are directly related to the concentration-dependent number of closely interacting cations.

Field-Induced Electron Generation in Water: Solvation Dynamics and Many-Body Interactions

The solvated electron represents an elementary quantum system in a liquid environment. Electrons solvated in water have raised strong interest because of their prototypical properties, their role in radiation chemistry, and their relevance for charge separation and transport. Nonequilibrium dynamics of photogenerated electrons in water occur on ultrafast time scales and include charge transfer, localization, and energy dissipation processes. We present new insight into the role of fluctuating electric fields of the liquid for generating electrons in the presence of an external terahertz field and address polaronic many-body properties of solvated electrons. This Perspective combines a review of recent results from experiment and theory with a discussion of basic electric interactions of electrons in water.

Flexible boundary layer using exchange for embedding theories. I. Theory and implementation

Embedding theory is a powerful computational chemistry approach to exploring the electronic structure and dynamics of complex systems, with Quantum Mechanical/Molecular Mechanics (QM/MM) being the prime example. A challenge arises when trying to apply embedding methodology to systems with diffusible particles, e.g., solvents, if some of them must be included in the QM region, for example, in the description of solvent-supported electronic states or reactions involving proton transfer or charge-transfer-to-solvent: without a special treatment, inter-diffusion of QM and MM particles will eventually lead to a loss of QM/MM separation. We have developed a new method called Flexible Boundary Layer using Exchange (FlexiBLE) that solves the problem by adding a biasing potential to the system that closely maintains QM/MM separation. The method rigorously preserves ensemble averages by leveraging their invariance to an exchange of identical particles. With a careful choice of the biasing potential and the use of a tree algorithm to include only important QM and MM exchanges, we find that the method has an MM-forcefield-like computational cost and thus adds negligible overhead to a QM/MM simulation. Furthermore, we show that molecular dynamics with the FlexiBLE bias conserves total energy, and remarkably, sub-diffusional dynamical quantities in the inner QM region are unaffected by the applied bias. FlexiBLE thus widens the range of chemistry that can be studied with embedding theory.

How Water-Ion Interactions Control the Formation of Hydrated Electron:Sodium Cation Contact Pairs

Although solvated electrons are a perennial subject of interest, relatively little attention has been paid to the way they behave in aqueous electrolytes. Experimentally, it is known that the hydrated electron's (e_aq^-) absorption spectrum shifts to the blue in the presence of salts, and the magnitude of the shift depends on the ion concentration and the identities of both the cation and anion. Does the blue-shift result from some type of dielectric effect from the bulk electrolyte, or are there specific interactions between the hydrated electron and ions in solution? Previous work has suggested that e_aq^- forms contact pairs with aqueous ions such as Na⁺, leading to the question of what controls the stability of such contact pairs and their possible connection to the observed spectroscopy. In this work, we use mixed quantum/classical simulations to examine the nature of Na⁺:e^- contact pairs in water, using a novel method for quantum umbrella sampling to construct e_aq^--ion potentials of mean force (PMF). We find that the nature of the contact pair PMF depends sensitively on the choice of the classical interactions used to describe the Na⁺-water interactions. When the ion-water interactions are slightly stronger, the corresponding cation:e^- contact pairs form at longer distances and become free energetically less stable. We show that this is because there is a delicate balance between solvation of the cation, solvation of e_aq^- and the direct electronic interaction between the cation and the electron, so that small changes in this balance lead to large changes in the formation and stability of e^--ion contact pairs. In particular, strengthening the ion-water interactions helps to maintain a favorable local solvation environment around Na⁺, which in turn forces water molecules in the first solvation shell of the cation to be unfavorably oriented toward the electron in a contact pair; stronger solvation of the cation also reduces the electronic overlap of e_aq^- with Na⁺. We also find that the calculated spectra of different models of Na⁺:e^- contact pairs do not shift monotonically with cation-electron distance, and that the calculated spectral shifts are about an order of magnitude larger than experiment, suggesting that isolated contact pairs are not the sole explanation for the blue-shift of the hydrated electron's spectrum in the presence of electrolytes.

Evaluating Simple Ab Initio Models of the Hydrated Electron: The Role of Dynamical Fluctuations

Despite its importance in electron transfer reactions and radiation chemistry, there has been disagreement over the fundamental nature of the hydrated electron, such as whether or not it resides in a cavity. Mixed quantum/classical simulations of the hydrated electron give different structures depending on the pseudopotential employed, and ab initio models of computational necessity use small numbers of water molecules and/or provide insufficient statistics to compare to experimental observables. A few years ago, Kumar et al. (J. Phys. Chem. A 2015, 119, 9148) proposed a minimalist ab initio model of the hydrated electron with only a small number of explicitly treated water molecules plus a polarizable continuum model (PCM). They found that the optimized geometry had four waters arranged tetrahedrally around a central cavity, and that the calculated vertical detachment energy and radius of gyration agreed well with experiment, results that were largely independent of the level of theory employed. The model, however, is based on a fixed structure at 0 K and does not explicitly incorporate entropic contributions or the thermal fluctuations that should be associated with the room-temperature hydrated electron. Thus, in this paper, we extend the model of Kumar et al. by running Born-Oppenheimer molecular dynamics (BOMD) of a small number of water molecules with an excess electron plus PCM at room temperature. We find that when thermal fluctuations are introduced, the level of theory chosen becomes critical enough when only four waters are used that one of the waters dissociates from the cluster with certain density functionals. Moreover, even with an optimally tuned range-separated hybrid functional, at room temperature the tetrahedral orientation of the 0 K first-shell waters is entirely lost and the central cavity collapses, a process driven by the fact that the explicit water molecules prefer to make H-bonds with each other more than with the excess electron. The resulting average structure is quite similar to that produced by a noncavity mixed quantum/classical model, so that the minimalist 4-water BOMD models suffer from problems similar to those of noncavity models, such as predicting the wrong sign of the hydrated electron's molar solvation volume. We also performed BOMD with 16 explicit water molecules plus an extra electron and PCM. We find that the inclusion of an entire second solvation shell of explicit water leads to little change in the outcome from when only four waters were used. In fact, the 16-water simulations behave much like those of water cluster anions, in which the electron localizes at the cluster surface, showing that PCM is not acceptable for use in minimalist models to describe the behavior of the bulk hydrated electron. For both the 4- and 16-water models, we investigate how the introduction of thermal motions alters the predicted absorption spectrum, vertical detachment energy, and resonance Raman spectrum of the simulated hydrated electron. We also present a set of structural criteria that can be used to numerically determine how cavity-like (or not) a particular hydrated electron model is. All of the results emphasize that the hydrated electron is a statistical object whose properties are inadequately captured using only a small number of explicit waters, and that a proper treatment of thermal fluctuations is critical to understanding the hydrated electron's chemical and physical behavior.

Probing the Birth and Ultrafast Dynamics of Hydrated Electrons at the Gold/Liquid Water Interface via an Optoelectronic Approach

The hydrated electron has fundamental and practical significance in radiation and radical chemistry, catalysis, and radiobiology. While its bulk properties have been extensively studied, its behavior at solid/liquid interfaces is still unclear due to the lack of effective tools to characterize this short-lived species in between two condensed matter layers. In this study, we develop a novel optoelectronic technique for the characterization of the birth and structural evolution of solvated electrons at the metal/liquid interface with a femtosecond time resolution. Using this tool, we record for the first time the transient spectra (in a photon energy range from 0.31 to 1.85 eV) in situ with a time resolution of 50 fs revealing several novel aspects of their properties at the interface. Especially the transient species show state-dependent optical transition behaviors from being isotropic in the hot state to perpendicular to the surface in the trapped and solvated states. The technique will enable a better understanding of hot electron driven reactions at electrochemical interfaces.

Destruction of Per- and Polyfluoroalkyl Substances (PFAS) with Advanced Reduction Processes (ARPs): A Critical Review

Advanced reduction processes (ARPs) have emerged as a promising method for destruction of persistent per- and polyfluoroalkyl substances (PFAS) in water due to the generation of short-lived and highly reductive hydrated electrons (e_aq^-). This study provides a critical review on the mechanisms and performance of reductive destruction of PFAS with e_aq^-. Unique properties of e_aq^- and its generation in different ARP systems, particularly UV/sulfite and UV/iodide, are overviewed. Different degradation mechanisms of PFAS chemicals, such as perfluorooctanoic acid (PFOA), perfluorooctanesulfonate (PFOS), and others (e.g., short chain perfluorocarboxylic acids (PFCAs) and perfluorosulfonic acids (PFSAs), per- and polyfluoro dicarboxylic acids, and fluorotelomer carboxylic acids), are reviewed, discussed, and compared. The degradation pathways of these PFAS chemicals rely heavily upon their head groups. For specific PFAS types, fluoroalkyl chain lengths may also affect their reductive degradation patterns. Degradation and defluorination efficiencies of PFAS are considerably influenced by solution chemistry parameters and operating factors, such as pH, dose of chemical solute (i.e., sulfite or iodide) for e_aq^- photoproduction, dissolved oxygen, humic acid, nitrate, and temperature. Furthermore, implications of the state-of-the-art knowledge on practical PFAS control actions in water industries are discussed and the priority research needs are identified.

The Fluxional Nature of the Hydrated Electron: Energy and Entropy Contributions to Aqueous Electron Free Energies

There has been a great deal of recent controversy over the structure of the hydrated electron and whether it occupies a cavity or contains a significant number of interior waters (noncavity). The questions we address in this work are, from a free energy perspective, how different are these proposed structures? Do the different structures all lie along a single continuum, or are there significant differences (i.e., free energy barriers) between them? To address these questions, we have performed a series of one-electron calculations using umbrella sampling with quantum biased molecular dynamics along a coordinate that directly reflects the number of water molecules in the hydrated electron's interior. We verify that a standard cavity model of the hydrated electron behaves essentially as a hard sphere: the model is dominated by repulsion at short range such that water is expelled from a local volume around the electron, leading to a water solvation shell like that of a pseudohalide ion. The repulsion is much larger than thermal energies near room temperature, explaining why such models exhibit properties with little temperature dependence. On the other hand, our calculations reveal that a noncavity model is highly fluxional, meaning that thermal motions cause the number of interior waters to fluctuate from effectively zero (i.e., a cavity-type electron) to potentially above the bulk water density. The energetic contributions in the noncavity model are still repulsive in the sense that they favor cavity formation, so the fluctuations in structure are driven largely by entropy: the entropic cost for expelling water from a region of space is large enough that some water is still driven into the electron's interior. As the temperature is lowered and entropy becomes less important, the noncavity electron's structure is predicted to become more cavity-like, consistent with the observed temperature dependence of the hydrated electron's properties. Thus, we argue that although the specific noncavity model we study overestimates the preponderance of fluctuations involving interior water molecules, with appropriate refinements to correctly capture the true average number of interior waters and molar solvation volume, a fluxional model likely makes the most sense for understanding the various experimental properties of the hydrated electron.

Ab Initio Investigation of the Resonance Raman Spectrum of the Hydrated Electron

According to the conventional picture, the aqueous or "hydrated" electron, e^-(aq), occupies an excluded volume (cavity) in the structure of liquid water. However, simulations with certain one-electron models predict a more delocalized spin density for the unpaired electron, with no distinct cavity structure. It has been suggested that only the latter (non-cavity) structure can explain the hydrated electron's resonance Raman spectrum, although this suggestion is based on calculations using empirical frequency maps developed for neat liquid water, not for e^-(aq). All-electron ab initio calculations presented here demonstrate that both cavity and non-cavity models of e^-(aq) afford significant red-shifts in the O-H stretching region. This effect is nonspecific and arises due to electron penetration into frontier orbitals of the water molecules. Only the conventional cavity model, however, reproduces the splitting of the H-O-D bend (in isotopically mixed water) that is observed experimentally and arises due to the asymmetric environments of the hydroxyl moieties in the electron's first solvation shell. We conclude that the cavity model of e^-(aq) is more consistent with the measured resonance Raman spectrum than is the delocalized, non-cavity model, despite previous suggestions to the contrary. Furthermore, calculations with hybrid density functionals and with Hartree-Fock theory predict that non-cavity liquid geometries afford only unbound (continuum) states for an extra electron, whereas in reality this energy level should lie more than 3 eV below vacuum level. As such, the non-cavity model of e^-(aq) appears to be inconsistent with available vibrational spectroscopy, photoelectron spectroscopy, and quantum chemistry.

Hydrated Electron Generation by Excitation of Copper Localized Surface Plasmon Resonance

Hydrated electrons are important in radiation chemistry and charge-transfer reactions, with applications that include chemical damage of DNA, catalysis, and signaling. Conventionally, hydrated electrons are produced by pulsed radiolysis, sonolysis, two-ultraviolet-photon laser excitation of liquid water, or photodetachment of suitable electron donors. Here we report a method for the generation of hydrated electrons via single-visible-photon excitation of localized surface plasmon resonances (LSPRs) of supported sub-3 nm copper nanoparticles in contact with water. Only excitations at the LSPR maximum resulted in the formation of hydrated electrons, suggesting that plasmon excitation plays a crucial role in promoting electron transfer from the nanoparticle into the solution. The reactivity of the hydrated electrons was confirmed via proton reduction and concomitant H₂ evolution in the presence of a Ru/TiO₂ catalyst.

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.

Structure of the aqueous electron

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

Short-Range Electron Correlation Stabilizes Noncavity Solvation of the Hydrated Electron

The hydrated electron, e^-_(aq), has often served as a model system to understand the influence of condensed-phase environments on electronic structure and dynamics. Despite over 50 years of study, however, the basic structure of e^-_(aq) is still the subject of controversy. In particular, the structure of e^-_(aq) was long assumed to be an electron localized within a solvent cavity, in a manner similar to halide solvation. Recently, however, we suggested that e^-_(aq) occupies a region of enhanced water density with little or no discernible cavity. The potential we developed was only subtly different from those that give rise to a cavity solvation motif, which suggests that the driving forces for noncavity solvation involve subtle electron-water attractive interactions at close distances. This leads to the question of how dispersion interactions are treated in simulations of the hydrated electron. Most dispersion potentials are ad hoc or are not designed to account for the type of close-contact electron-water overlap that might occur in the condensed phase, and where short-range dynamic electron correlation is important. To address this, in this paper we develop a procedure to calculate the potential energy surface between a single water molecule and an excess electron with high-level CCSD(T) electronic structure theory. By decomposing the electron-water potential into its constituent energetic contributions, we find that short-range electron correlation provides an attraction of comparable magnitude to the mean-field interactions between the electron and water. Furthermore, we find that by reoptimizing a popular cavity-forming one-electron model potential to better capture these attractive short-range interactions, the enhanced description of correlation predicts a noncavity e^-_(aq) with calculated properties in better agreement with experiment. Although much attention has been placed on the importance of long-range dispersion interactions in water cluster anions, our study reveals that largely unexplored short-range correlation effects are crucial in dictating the solvation structure of the condensed-phase hydrated electron.

A Simple ab Initio Model for the Solvated Electron in Methanol

The solvation structure of a solvated electron in methanol is investigated with ab initio calculations of small anion methanol clusters in a polarized dielectric continuum. We find that the lowest-energy structure in best agreement with experiment, calculated with CCSD, MP2, and B3LYP methods with aug-cc-pvdz basis set, is a tetrahedral arrangement of four methanol molecules with OH bonds oriented toward the center. The optimum distance from the tetrahedron center to the hydroxyl protons is ∼1.8 Å, significantly smaller than previous estimates. We are able to reproduce experimental radius of gyration Rg (deduced from optical absorption), vertical detachment energy, and resonance Raman frequencies. The electron paramagnetic resonance g-factor shift is qualitatively reproduced using density functional theory.

Free Energies of Cavity and Noncavity Hydrated Electrons Near the Instantaneous Air/Water Interface

The properties of the hydrated electron at the air/water interface are computed for both a cavity and a noncavity model using mixed quantum/classical molecular dynamics simulation. We take advantage of our recently developed formalism for umbrella sampling with a restrained quantum expectation value to calculate free-energy profiles of the hydrated electron's position relative to the water surface. We show that it is critical to use an instantaneous description of the air/water interface rather than the Gibbs' dividing surface to obtain accurate potentials of mean force. We find that noncavity electrons, which prefer to encompass several water molecules, avoid the interface where water molecules are scarce. In contrast, cavity models of the hydrated electron, which prefer to expel water, have a local free-energy minimum near the interface. When the cavity electron occupies this minimum, its absorption spectrum is quite red-shifted, its binding energy is significantly lowered, and its dynamics speed up quite a bit compared with the bulk, features that have not been found by experiment. The surface activity of the electron therefore serves as a useful test of cavity versus noncavity electron solvation.

Benchmark calculations of excess electrons in water cluster cavities: balancing the addition of atom-centered diffuse functions versus floating diffuse functions

Diffuse functions have been proved to be especially crucial for the accurate characterization of excess electrons which are usually bound weakly in intermolecular zones far away from the nuclei. To examine the effects of diffuse functions on the nature of the cavity-shaped excess electrons in water cluster surroundings, both the HOMO and LUMO distributions, vertical detachment energies (VDEs) and visible absorption spectra of two selected (H2O)24(-) isomers are investigated in the present work. Two main types of diffuse functions are considered in calculations including the Pople-style atom-centered diffuse functions and the ghost-atom-based floating diffuse functions. It is found that augmentation of atom-centered diffuse functions contributes to a better description of the HOMO (corresponding to the VDE convergence), in agreement with previous studies, but also leads to unreasonable diffuse characters of the LUMO with significant red-shifts in the visible spectra, which is against the conventional point of view that the more the diffuse functions, the better the results. The issue of designing extra floating functions for excess electrons has also been systematically discussed, which indicates that the floating diffuse functions are necessary not only for reducing the computational cost but also for improving both the HOMO and LUMO accuracy. Thus, the basis sets with a combination of partial atom-centered diffuse functions and floating diffuse functions are recommended for a reliable description of the weakly bound electrons. This work presents an efficient way for characterizing the electronic properties of weakly bound electrons accurately by balancing the addition of atom-centered diffuse functions and floating diffuse functions and also by balancing the computational cost and accuracy of the calculated results, and thus is very useful in the relevant calculations of various solvated electron systems and weakly bound anionic systems.

A Simple ab Initio Model for the Hydrated Electron That Matches Experiment

Since its discovery over 50 years ago, the "structure" and properties of the hydrated electron have been a subject for wonderment and also fierce debate. In the present work we seriously explore a minimal model for the aqueous electron, consisting of a small water anion cluster embedded in a polarized continuum, using several levels of ab initio calculation and basis set. The minimum energy "zero Kelvin" structure found for any 4-water (or larger) anion cluster, at any post-Hartree–Fock theory level, is very similar to a recently reported embedded-DFT-in-classical-water-MD simulation (Uhlig, Marsalek, and Jungwirth, J. Phys. Chem. Lett. 2012, 3, 3071−3075), with four OH bonds oriented toward the maximum charge density in a small central "void". The minimum calculation with just four water molecules does a remarkably good job of reproducing the resonance Raman properties, the radius of gyration derived from the optical spectrum, the vertical detachment energy, and the hydration free energy. For the first time we also successfully calculate the EPR g-factor and (low temperature ice) hyperfine couplings. The simple tetrahedral anion cluster model conforms very well to experiment, suggesting it does in fact represent the dominant structural motif of the hydrated electron.

Hydrated Electrons in Water Clusters: Inside or Outside, Cavity or Noncavity?

In this work, we compare the applicability of three electron–water molecule pseudopotentials in modeling the physical properties of hydrated electrons. Quantum model calculations illustrate that the recently suggested Larsen–Glover–Schwartz (LGS) model and its modified m-LGS version have a too-attractive potential in the vicinity of the oxygen. As a result, LGS models predict a noncavity hydrated electron structure in clusters at room temperature, as seen from mixed one-electron quantum–classical molecular dynamics simulations of water cluster anions, with the electron localizing exclusively in the interior of the clusters. Comparative calculations using the cavity-preferring Turi–Borgis (TB) model predict interior-state and surface-state cluster isomers. The computed associated physical properties are also analyzed and compared to available experimental data. We find that the LGS and m-LGS potentials provide results that appear to be inconsistent with the size dependence of the experimental data. The simulated TB tendencies are qualitatively correct. Furthermore, ab initio calculations on static LGS noncavity structures indicate weak stabilization of the excess electron in regions where the LGS potential preferably and strongly binds the electron. TB calculations give stabilization energies that are in line with the ab initio results. In conclusion, we observe that the cavity-preferring pseudopotential model predicts cluster physical properties in better agreement with experimental data and ab initio calculations than the models predicting noncavity structures for the hydrated electron.

Electron Solvation in Liquid Ammonia: Lithium, Sodium, Magnesium, and Calcium as Electron Sources

A free electron in solution, known as a solvated electron, is the smallest possible anion. Alkali and alkaline earth atoms serve as electron donors in solvents that mediate outer-sphere electron transfer. We report herein ab initio molecular dynamics simulations of lithium, sodium, magnesium, and calcium in liquid ammonia at 250 K. By analyzing the electronic properties and the ionic and solvation structures and dynamics, we systematically characterize these metals as electron donors and ammonia molecules as electron acceptors. We show that the solvated metal strongly modifies the properties of its solvation shells and that the observed effect is metal-specific. Specifically, the radius and charge exhibit major impacts. The single solvated electron present in the alkali metal systems is distributed more uniformly among the solvent molecules of each metal's two solvation shells. In contrast, alkaline earth metals favor a less uniform distribution of the electron density. Alkali and alkaline earth atoms are coordinated by four and six NH3 molecules, respectively. The smaller atoms, Li and Mg, are stronger electron donors than Na and Ca. This result is surprising, as smaller atoms in a column of the periodic table have higher ionization potentials. However, it can be explained by stronger electron donor-acceptor interactions between the smaller atoms and the solvent molecules. The structure of the first solvation shell is sharpest for Mg, which has a large charge and a small radius. Solvation is weakest for Na, which has a small charge and a large radius. Weak solvation leads to rapid dynamics, as reflected in the diffusion coefficients of NH3 molecules of the first two solvation shells and the Na atom. The properties of the solvated electrons established in the present study are important for radiation chemistry, synthetic chemistry, condensed-matter charge transfer, and energy sources.

On the nature of the solvated electron in ice Ih

The water-solvated excess electron (EE) is a key chemical agent whose hallmark signature, its asymmetric optical absorption spectrum, continues to be a topic of debate.

The solvation of electrons by an atmospheric-pressure plasma

Solvated electrons are typically generated by radiolysis or photoionization of solutes. While plasmas containing free electrons have been brought into contact with liquids in studies dating back centuries, there has been little evidence that electrons are solvated by this approach. Here we report direct measurements of solvated electrons generated by an atmospheric-pressure plasma in contact with the surface of an aqueous solution. The electrons are measured by their optical absorbance using a total internal reflection geometry. The measured absorption spectrum is unexpectedly blue shifted, which is potentially due to the intense electric field in the interfacial Debye layer. We estimate an average penetration depth of 2.5±1.0 nm, indicating that the electrons fully solvate before reacting through second-order recombination. Reactions with various electron scavengers including H⁺, NO₂⁻, NO₃⁻ and H₂O₂ show that the kinetics are similar, but not identical, to those for solvated electrons formed in bulk water by radiolysis.

Free, or solvated, electrons in a solution are known to form at the interface between a liquid and a gas. Here, the authors use absorption spectroscopy in a total internal reflection geometry to probe solvated electrons generated at a plasma in contact with the surface of an aqueous solution

Quantifying solvated electrons' delocalization

The electron delocalization range EDR(r;u_av) (left) captures the spin density (right) of an electron delocalized over u_av = 5.77 Å on the surface of an (H₂O)₂₀⁻ cluster.

Deciphering the reaction between a hydrated electron and a hydronium ion at elevated temperatures

The formation of a H˙ atom in liquid water from the reaction of a hydrated electron with a hydronium cation is a very challenging subject in chemical processes.

Glucose-Promoted Localization Dynamics of Excess Electrons in Aqueous Glucose Solution Revealed by Ab Initio Molecular Dynamics Simulation

Ab initio molecular dynamics simulations reveal that an excess electron (EE) can be more efficiently localized as a cavity-shaped state in aqueous glucose solution (AGS) than in water. Compared with that (∼1.5 ps) in water, the localization time is shortened by ∼0.7-1.2 ps in three AGSs (0.56, 1.12, and 2.87 M). Although the radii of gyration of the solvated EEs are all close to 2.6 Å in the four solutions, the solvated EE cavities in the AGSs become more compact and can localize ∼80% of an EE, which is considerably larger than that (∼40-60% and occasionally ∼80%) in water. These observations are attributed to a modification of the hydrogen-bonded network by the introduction of glucose molecules into water. The water acts as a promoter and stabilizer, by forming voids around glucose molecules and, in this fashion, favoring the localization of an EE with high efficiency. This study provides important information about EEs in physiological AGSs and suggests a new strategy to efficiently localize an EE in a stable cavity for further exploration of biological function.

Direct observation of the collapse of the delocalized excess electron in water

It is generally assumed that the hydrated electron occupies a quasi-spherical cavity surrounded by only a few water molecules in its equilibrated state. However, in the very moment of its generation, before water has had time to respond to the extra charge, it is expected to be significantly larger in size. According to a particle-in-a-box picture, the frequency of its absorption spectrum is a sensitive measure of the initial size of the electronic wavefunction. Here, using transient terahertz spectroscopy, we show that the excess electron initially absorbs in the far-infrared at a frequency for which accompanying ab initio molecular dynamics simulations estimate an initial delocalization length of ≈ 40 Å. The electron subsequently shrinks due to solvation and thereby leaves the terahertz observation window very quickly, within ≈ 200 fs.

High pressure electrides: a predictive chemical and physical theory

Electrides, in which electrons occupy interstitial regions in the crystal and behave as anions, appear as new phases for many elements (and compounds) under high pressure. We propose a unified theory of high pressure electrides (HPEs) by treating electrons in the interstitial sites as filling the quantized orbitals of the interstitial space enclosed by the surrounding atom cores, generating what we call an interstitial quasi-atom, ISQ. With increasing pressure, the energies of the valence orbitals of atoms increase more significantly than the ISQ levels, due to repulsion, exclusion by the atom cores, effectively giving the valence electrons less room in which to move. At a high enough pressure, which depends on the element and its orbitals, the frontier atomic electron may become higher in energy than the ISQ, resulting in electron transfer to the interstitial space and the formation of an HPE. By using a He lattice model to compress (with minimal orbital interaction at moderate pressures between the surrounding He and the contained atoms or molecules) atoms and an interstitial space, we are able to semiquantitatively explain and predict the propensity of various elements to form HPEs. The slopes in energy of various orbitals with pressure (s > p > d) are essential for identifying trends across the entire Periodic Table. We predict that the elements forming HPEs under 500 GPa will be Li, Na (both already known to do so), Al, and, near the high end of this pressure range, Mg, Si, Tl, In, and Pb. Ferromagnetic electrides for the heavier alkali metals, suggested by Pickard and Needs, potentially compete with transformation to d-group metals.