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

Direct Observation of Anionic Yields from the Liquid-Vapor Interface by Electron Irradiation

Dissociative electron attachment (DEA) is widely believed to play a high-profile role in ionizing radiation damages of bioorganic molecules, and its fundamentals are mainly learned from the gas-phase studies. However, the DEA process in aqueous solution is still in debate. Here we provide experimental evidence about the DEA processes of liquid methanol by using electron-impact-time-delayed mass spectrometry. In contrast to the gas- and solid-phase DEAs, methoxide ion CH3O- is the predominant product from the liquid interface. Furthermore, this anion can be produced with both the primary low-energy electrons and the inelastically scattered and secondary low-energy electrons. On the contrary, the primary low-energy electrons in the liquid bulk are more likely to be solvated, rather than directly participating in the DEA process. Our study provides new insights into radiation chemistry, particularly of bioorganic relevance.

Mechanisms and Opportunities for Rational In Silico Design of Enzymes to Degrade Per- and Polyfluoroalkyl Substances (PFAS)

Per and polyfluoroalkyl substances (PFAS) present a unique challenge to remediation techniques because their strong carbon-fluorine bonds make them difficult to degrade. This review explores the use of in silico enzymatic design as a potential PFAS degradation technique. The scope of the enzymes included is based on currently known PFAS degradation techniques, including chemical redox systems that have been studied for perfluorooctanesulfonic acid (PFOS) and perfluorooctanoic acid (PFOA) defluorination, such as those that incorporate hydrated electrons, sulfate, peroxide, and metal catalysts. Bioremediation techniques are also discussed, namely the laccase and horseradish peroxidase systems. The redox potential of known reactants and enzymatic radicals/metal-complexes are then considered and compared to potential enzymes for degrading PFAS. The molecular structure and reaction cycle of prospective enzymes are explored. Current knowledge and techniques of enzyme design, particularly radical-generating enzymes, and application are also discussed. Finally, potential routes for bioengineering enzymes to enable or enhance PFAS remediation are considered as well as the future outlook for computational exploration of enzymatic in situ bioremediation routes for these highly persistent and globally distributed contaminants.

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.

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

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

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.

Competitive Ion Pairing and the Role of Anions in the Behavior of Hydrated Electrons in Electrolytes

Experiments have shown that in the presence of electrolytes, the hydrated electron's absorption spectrum experiences a blue shift whose magnitude depends on both the salt concentration and chemical identity. Previous computer simulations have suggested that the spectral blue shift results from the formation of (cation, electron) contact pairs and that the concentration dependence arises because the number of cations simultaneously paired with the electron increases with increasing concentration. In this work, we perform new simulations to build an atomistic picture that explains the effect of salt identity on the observed hydrated electron spectral shifts. We simulate hydrated electrons in the presence of both monovalent (Na⁺) and divalent (Ca²⁺) cations paired with both Cl^- and a spherical species representing ClO₄^- anions. Our simulations reproduce the experimental observations that divalent ions produce larger blue shifts of the hydrated electron's spectrum than monovalent ions with the same anion and that perchlorate salts show enhanced blue shifts compared to chloride salts with the same cation. We find that these observations can be explained by competitive ion pairing. With small kosmotropic cations such as Na⁺ and Ca²⁺, aqueous chloride salts tend to form (cation, anion) contact pairs, whereas there is little ion pairing between these cations and chaotropic perchlorate anions. Hydrated electrons also strongly interact with these cations, but if the cations are also paired with anions, this affects the free energy of the electron-cation interaction. With chloride salts, hydrated electrons end up in complexes containing multiple cations plus a few anions as well as the electron. Repulsive interactions between the electron and the nearby Cl^- anions reduce the cation-induced spectral blue shift of the hydrated electron. With perchlorate salts, hydrated electrons pair with multiple cations without any associated anions, leading to the largest possible cation-induced spectral blue shift. We also see that the reason multivalent cations produce larger spectral blue shifts than monovalent cations is because hydrated electrons are able to simultaneously pair with a larger number of multivalent cations due to a larger free energy of interaction. Overall, the interaction of hydrated electrons with electrolytes fits well with the Hofmeister series, where the electron behaves as an anion that is slightly more able to break water's H-bond structure than chloride.

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.

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.

Flexible boundary layer using exchange for embedding theories. II. QM/MM dynamics of the hydrated electron

The FlexiBLE embedding method introduced in Paper I [Z. Shen and W. J. Glover, J. Chem. Phys. 155, 224112 (2021)] is applied to explore the structure and dynamics of the aqueous solvated electron at an all-electron density functional theory Quantum Mechanics/Molecular Mechanics level. Compared to a one-electron mixed quantum/classical description, we find the dynamics of the many-electron model of the hydrated electron exhibits enhanced coupling to water OH stretch modes. Natural bond orbital analysis reveals this coupling is due to significant population of water OH σ^* orbitals, reaching 20%. Based on this, we develop a minimal frontier orbital picture of the hydrated electron involving a cavity orbital and important coupling to 4-5 coordinating OH σ^* orbitals. Implications for the interpretation of the spectroscopy of this interesting species are discussed.

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.

Simulating the ghost: quantum dynamics of the solvated electron

The nature of the bulk hydrated electron has been a challenge for both experiment and theory due to its short lifetime and high reactivity, and the need for a high-level of electronic structure theory to achieve predictive accuracy. The lack of a classical atomistic structural formula makes it exceedingly difficult to model the solvated electron using conventional empirical force fields, which describe the system in terms of interactions between point particles associated with atomic nuclei. Here we overcome this problem using a machine-learning model, that is sufficiently flexible to describe the effect of the excess electron on the structure of the surrounding water, without including the electron in the model explicitly. The resulting potential is not only able to reproduce the stable cavity structure but also recovers the correct localization dynamics that follow the injection of an electron in neat water. The machine learning model achieves the accuracy of the state-of-the-art correlated wave function method it is trained on. It is sufficiently inexpensive to afford a full quantum statistical and dynamical description and allows us to achieve accurate determination of the structure, diffusion mechanisms, and vibrational spectroscopy of the solvated electron.

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.