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

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.

Temperature Dependent Properties of the Aqueous Electron

The temperature‐dependent properties of the aqueous electron have been extensively studied using mixed quantum‐classical simulations in a wide range of thermodynamic conditions based on one‐electron pseudopotentials. While the cavity model appears to explain most of the physical properties of the aqueous electron, only a non‐cavity model has so far been successful in accounting for the temperature dependence of the absorption spectrum. Here, we present an accurate and efficient description of the aqueous electron under various thermodynamic conditions by combining hybrid functional‐based molecular dynamics, machine learning techniques, and multiple time‐step methods. Our advanced simulations accurately describe the temperature dependence of the absorption maximum in the presence of cavity formation. Specifically, our work reveals that the red shift of the absorption maximum results from an increasing gyration radius with temperature, rather than from global density variations as previously suggested.

Photoelectron Spectroscopy of Large Water Cluster Anions

Photoelectron spectra of large size selected water cluster anions (H₂O)_n^- (n = 100-1100) have been measured at a low cluster temperature (80 K). An extensive peak analysis has been conducted in order to determine average and isomer-resolved vertical detachment energies (VDE) of the hydrated electron. This allows us, in combination with the reevaluated data of the previously reported results on small- and medium-sized water cluster anions ( J. Chem. Phys. 2009, 131, 144303), to draw a comprehensive picture of the size-dependent development of the VDEs of water clusters. This allows for an improved extrapolation of the cluster VDEs to the bulk, which yields a value of 3.60 ± 0.03 eV. The general size dependence of the VDEs is in very good agreement with a standard dielectric model.

Ab Initio Simulations of Poorly and Well Equilibrated (CH3CN)n- Cluster Anions: Assigning Experimental Photoelectron Peaks to Surface-Bound Electrons and Solvated Monomer and Dimer Anions

Excess electrons in liquid acetonitrile are of particular interest because they exist in two different forms in equilibrium: they can be present as traditional solvated electrons in a cavity, and they can form some type of solvated molecular anion. Studies of small acetonitrile cluster anions in the gas phase show two isomers with distinct vertical detachment energies, and it is tempting to presume that the two gas-phase cluster anion isomers are precursors of the two excess electron species present in bulk solution. In this paper, we perform DFT-based ab initio molecular dynamics simulations of acetonitrile cluster anions to understand the electronic species that are present and why they have different binding energies. Using a long-range-corrected density functional that was optimally tuned to describe acetonitrile cluster anion structures, we have theoretically explored the chemistry of (CH₃CN)_n^- cluster anions with sizes n = 5, 7, and 10. Because the temperature of the experimental cluster anions is not known, we performed two sets of simulations that investigated how the way in which the cluster anions are prepared affects the excess electron binding motif: one set of simulations simply attached excess electrons to neutral (CH₃CN)_n clusters, providing little opportunity for the clusters to relax in the presence of the excess electron, while the other set allowed the cluster anions to thermally equilibrate near room temperature. We find that both sets of simulations show three distinct electron binding motifs: electrons can attach to the surface of the cluster (dipole-bound) or be present either as solvated monomer anions, CH₃CN^-, or as solvated molecular dimer anions, (CH₃CN)₂^-. All three species have higher binding energies at larger cluster sizes. Thermal equilibration strongly favors the formation of the valence-bound molecular anions relative to surface-bound excess electrons, and the dimer anion becomes more stable than the monomer anion and surface-bound species as the cluster size increases. The calculated photoelectron spectra from our simulations in which there was poor thermal equilibration are in good agreement with experiment, suggesting assignment of the two experimental cluster anion isomers as the surface-bound electron and the solvated molecular dimer anion. The simulations also suggest that the shoulder seen experimentally on the low-energy isomer's detachment peak is not part of a vibronic progression but instead results from molecular monomer anions. Nowhere in the size range that we explore do we see evidence for a nonvalence, cavity-bound interior-solvated electron, indicating that this species is likely only accessible at larger sizes with good thermal equilibration.

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.

Reaction of Electrons with DNA: Radiation Damage to Radiosensitization

This review article provides a concise overview of electron involvement in DNA radiation damage. The review begins with the various states of radiation-produced electrons: Secondary electrons (SE), low energy electrons (LEE), electrons at near zero kinetic energy in water (quasi-free electrons, (e-qf)) electrons in the process of solvation in water (presolvated electrons, e-pre), and fully solvated electrons (e-aq). A current summary of the structure of e-aq, and its reactions with DNA-model systems is presented. Theoretical works on reduction potentials of DNA-bases were found to be in agreement with experiments. This review points out the proposed role of LEE-induced frank DNA-strand breaks in ion-beam irradiated DNA. The final section presents radiation-produced electron-mediated site-specific formation of oxidative neutral aminyl radicals from azidonucleosides and the evidence of radiosensitization provided by these aminyl radicals in azidonucleoside-incorporated breast cancer cells.

Picture of the wet electron: a localized transient state in liquid water

A transient state of the excess electron in liquid water preceding the development of the solvation shell, the so-called wet electron, has been invoked to explain spectroscopic observations, but its binding energy and atomic structure have remained highly elusive. Here, we carry out hybrid functional molecular dynamics to unveil the ultrafast solvation mechanism leading to the hydrated electron. In the pre-hydrated regime, the electron is found to repeatedly switch between a quasi-free electron state in the conduction band and a localized state with a binding energy of 0.26 eV, which we assign to the wet electron. This transient state self-traps in a region of the liquid which extends up to ∼4.5 Å and involves a severe disruption of the hydrogen-bond network. Our picture provides an unprecedented view on the nature of the wet electron, which is instrumental to understanding the properties of this fundamental species in liquid water.

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.

Thermal Equilibration Controls H-Bonding and the Vertical Detachment Energy of Water Cluster Anions

One of the outstanding puzzles in the photoelectron spectroscopy of water anion clusters, which serve as precursors to the hydrated electron, is that the excess electron has multiple vertical detachment energies (VDEs), with different groups seeing different distributions of VDEs. We have studied the photoelectron spectroscopy of water cluster anions using simulation techniques designed to mimic the different ways that water cluster anions are produced experimentally. Our simulations take advantage of density functional theory-based Born-Oppenheimer molecular dynamics with an optimally tuned range-separated hybrid functional that is shown to give outstanding accuracy for calculating electron binding energies for this system. We find that our simulations are able to accurately reproduce the experimentally observed VDEs for cluster anions of different sizes, with different VDE distributions observed depending on how the water cluster anions are prepared. For cluster anion sizes up to 20 water molecules, we see that the excess electron always resides on the surface of the cluster and that the different discrete VDEs result from the discrete number of hydrogen bonds made to the electron by water molecules on the surface. Clusters that are less thermally equilibrated have surface waters that tend to make single H-bonds to the electron, resulting in lower VDEs, while clusters that are more thermally equilibrated have surface waters that prefer to make two H-bonds to the electron, resulting in higher VDEs.

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.

Excess electrons in methanol clusters: Beyond the one-electron picture

We performed a series of comparative quantum chemical calculations on various size negatively charged methanol clusters, CH₃OH_n^-. The clusters are examined in their optimized geometries (n = 2-4), and in geometries taken from mixed quantum-classical molecular dynamics simulations at finite temperature (n = 2-128). These latter structures model potential electron binding sites in methanol clusters and in bulk methanol. In particular, we compute the vertical detachment energy (VDE) of an excess electron from increasing size methanol cluster anions using quantum chemical computations at various levels of theory including a one-electron pseudopotential model, several density functional theory (DFT) based methods, MP2 and coupled-cluster CCSD(T) calculations. The results suggest that at least four methanol molecules are needed to bind an excess electron on a hydrogen bonded methanol chain in a dipole bound state. Larger methanol clusters are able to form stronger interactions with an excess electron. The two simulated excess electron binding motifs in methanol clusters, interior and surface states, correlate well with distinct, experimentally found VDE tendencies with size. Interior states in a solvent cavity are stabilized significantly stronger than electron states on cluster surfaces. Although we find that all the examined quantum chemistry methods more or less overestimate the strength of the experimental excess electron stabilization, MP2, LC-BLYP, and BHandHLYP methods with diffuse basis sets provide a significantly better estimate of the VDE than traditional DFT methods (BLYP, B3LYP, X3LYP, PBE0). A comparison to the better performing many electron methods indicates that the examined one-electron pseudopotential can be reasonably used in simulations for systems of larger size.

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.

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.