Molecular simulation of a hydrated electron at different thermodynamic state points

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.

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.

First-Principles Simulations of Biological Molecules Subjected to Ionizing Radiation

Ionizing rays cause damage to genomes, proteins, and signaling pathways that normally regulate cell activity, with harmful consequences such as accelerated aging, tumors, and cancers but also with beneficial effects in the context of radiotherapies. While the great pace of research in the twentieth century led to the identification of the molecular mechanisms for chemical lesions on the building blocks of biomacromolecules, the last two decades have brought renewed questions, for example, regarding the formation of clustered damage or the rich chemistry involving the secondary electrons produced by radiolysis. Radiation chemistry is now meeting attosecond science, providing extraordinary opportunities to unravel the very first stages of biological matter radiolysis. This review provides an overview of the recent progress made in this direction, focusing mainly on the atto- to femto- to picosecond timescales. We review promising applications of time-dependent density functional theory in this context.

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.

Structure of the aqueous electron

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

Effect of the solvation state of electron in dissociative electron attachment reaction in aqueous solutions

It is generally considered that the pre-solvated electron and the solvated electron reacting with a solute yield the same product. Silver cyanide complex, Ag(CN)₂^-, is used as a simple probe to demonstrate unambiguously the existence of a different reduction mechanism for pre-hydrated electrons. Using systematic multichannel transient absorption measurements at different solute concentrations from millimolar to decimolar, global data analysis and theoretical calculations, we present the dissociative electron attachment on Ag(CN)₂^-. The short-lived silver complex, Ag⁰(CN)₂^2-, formed by hydrated electron with nanosecond pulse radiolysis, can be observed at room temperature. However, at higher temperatures only the free silver atom, Ag⁰, is detected, suggesting that Ag⁰(CN)₂^2- dissociation is fast. Surprisingly, pulse radiolysis measurements on Ag(CN)₂^- reduction, performed by a 7 ps electron pulse at room temperature, show clearly that a new reduced form of silver complex, AgCN^-, is produced within the pulse. This species, absorbing at 560 nm, is not formed by the hydrated electron but exclusively by its precursor. DFT calculations show that the different reactivity of the hydrated and pre-hydrated electrons can be due to the formation of different electronic states of Ag⁰(CN)₂^2-: the prehydrated electron can form an excited state of this complex, which mainly dissociates into Ag⁰CN^- + CN^-.

Resonance Raman and temperature-dependent electronic absorption spectra of cavity and noncavity models of the hydrated electron

Most of what is known about the structure of the hydrated electron comes from mixed quantum/classical simulations, which depend on the pseudopotential that couples the quantum electron to the classical water molecules. These potentials usually are highly repulsive, producing cavity-bound hydrated electrons that break the local water H-bonding structure. However, we recently developed a more attractive potential, which produces a hydrated electron that encompasses a region of enhanced water density. Both our noncavity and the various cavity models predict similar experimental observables. In this paper, we work to distinguish between these models by studying both the temperature dependence of the optical absorption spectrum, which provides insight into the balance of the attractive and repulsive terms in the potential, and the resonance Raman spectrum, which provides a direct measure of the local H-bonding environment near the electron. We find that only our noncavity model can capture the experimental red shift of the hydrated electron's absorption spectrum with increasing temperature at constant density. Cavity models of the hydrated electron predict a solvation structure similar to that of the larger aqueous halides, leading to a Raman O-H stretching band that is blue-shifted and narrower than that of bulk water. In contrast, experiments show the hydrated electron has a broader and red-shifted O-H stretching band compared with bulk water, a feature recovered by our noncavity model. We conclude that although our noncavity model does not provide perfect quantitative agreement with experiment, the hydrated electron must have a significant degree of noncavity character.

Structure, dynamics, and reactivity of hydrated electrons by ab initio molecular dynamics

Understanding the properties of hydrated electrons, which were first observed using pulse radiolysis of water in 1962, is crucial because they are key species in many radiation chemistry processes. Although time-resolved spectroscopic studies and molecular simulations have shown that an electron in water (prepared, for example, by water photoionization) relaxes quickly to a localized, cavity-like structure ∼2.5 Å in radius, this picture has recently been questioned. In another experimental approach, negatively charged water clusters of increasing size were studied with photoelectron and IR spectroscopies. Although small water clusters can bind an excess electron, their character is very different from bulk hydrated species. As data on electron binding in liquid water have become directly accessible experimentally, the cluster-to-bulk extrapolations have become a topic of lively debate. Quantum electronic structure calculations addressing experimental measurables have, until recently, been largely limited to small clusters; extended systems were approached mainly with pseudopotential calculations combining a classical description of water with a quantum mechanical treatment of the excess electron. In this Account, we discuss our investigations of electrons solvated in water by means of ab initio molecular dynamics simulations. This approach, applied to a model system of a negatively charged cluster of 32 water molecules, allows us to characterize structural, dynamical, and reactive aspects of the hydrated electron using all of the system's valence electrons. We show that under ambient conditions, the electron localizes into a cavity close to the surface of the liquid cluster. This cavity is, however, more flexible and accessible to water molecules than an analogous area around negatively charged ions. The dynamical process of electron attachment to a neutral water cluster is strongly temperature dependent. Under ambient conditions, the electron relaxes in the liquid cluster and becomes indistinguishable from an equilibrated, solvated electron on a picosecond time scale. In contrast, for solid, cryogenic systems, the electron only partially localizes outside of the cluster, being trapped in a metastable, weakly bound "cushion-like" state. Strongly bound states under cryogenic conditions could only be prepared by cooling equilibrated, liquid, negatively charged clusters. These calculations allow us to rationalize how different isomers of electrons in cryogenic clusters can be observed experimentally. Our results also bring into question the direct extrapolation of properties of cryogenic, negatively charged water clusters to those of electrons in the bulk liquid. Ab initio molecular dynamics represents a unique computational tool for investigating the reactivity of the solvated electron in water. As a prototype, the electron-proton reaction was followed in the 32-water cluster. In accord with experiment, the molecular mechanism is a proton transfer process that is not diffusion limited, but rather controlled by a proton-induced deformation of the excess electron's solvent shell. We demonstrate the necessary ingredients of a successful density functional methodology for the hydrated electron that avoids potential pitfalls, such as self-interaction error, insufficient basis set, or lack of dispersion interactions. We also benchmark the density functional theory methods and outline the path to faithful ab initio simulations of dynamics and reactivity of electrons solvated in extended aqueous systems.

Interior- and surface-bound excess electron states in large water cluster anions

We present the results of mixed quantum/classical simulations on relaxed thermal nanoscale water cluster anions, (H(2)O)(n)(-), with n=200, 500, 1000, and 8000. By using initial equilibration with constraints, we investigate stable/metastable negatively charged water clusters with both surface-bound and interior-bound excess electron states. Characterization of these states is performed in terms of geometrical parameters, energetics, and optical absorption spectroscopy of the clusters. The calculations provide data characterizing these states in the gap between previously published calculations and experiments on smaller clusters and the limiting cases of either an excess electron in bulk water or an excess electron at an infinite water/air interface. The present results are in general agreement with previous simulations and provide a consistent picture of the evolution of the physical properties of water cluster anions with size over the entire size range, including results for vertical detachment energies and absorption spectra that would signify their presence. In particular, the difference in size dependence between surface-bound and interior-bound state absorption spectra is dramatic, while for detachment energies the dependence is qualitatively the same.

Femtosecond relaxation dynamics of solvated electrons in liquid ammonia

The ultrafast relaxation dynamics of the well-known solvated electron in liquid ammonia solutions are investigated with femtosecond near-infrared pump-probe absorption spectroscopy. Immediately after photoexcitation, the dynamic absorption spectrum of the electron is substantially red-shifted with respect to its stationary spectrum. A subsequent dynamic blue shift of the pump-probe spectrum occurs on a timescale of 150 fs. The data are understood in terms of ground-state "cooling" and can be quantitatively simulated by an intuitive temperature-jump model employing a dynamically evolving Kubo line shape for the electronic resonance. A simple estimate implies that, on average, the electron in the liquid is coordinated to six nearest-neighbor ammonia molecules. An equivalent analysis of the data based on a bubble-formation/cavity-contraction mechanism is briefly outlined.

Excess electron relaxation dynamics at water/air interfaces

We have performed mixed quantum-classical molecular dynamics simulations of the relaxation of a ground state excess electron at interfaces of different phases of water with air. The investigated systems included ambient water/air, supercooled water/air, Ih ice/air, and amorphous solid water/air interfaces. The present work explores the possible connections of the examined interfacial systems to finite size cluster anions and the three-dimensional infinite, fully hydrated electron. Localization site analyses indicate that in the absence of nuclear relaxation the electron localizes in a shallow potential trap on the interface in all examined systems in a diffuse, surface-bound (SB) state. With relaxation, the weakly bound electron undergoes an ultrafast localization and stabilization on the surface with the concomitant collapse of its radius. In the case of the ambient liquid interface the electron slowly (on the 10 ps time scale) diffuses into the bulk to form an interior-bound state. In each other case, the excess electron persists on the interface in SB states. The relaxation dynamics occur through distinct SB structures which are easily distinguishable by their energetics, geometries, and interactions with the surrounding water bath. The systems exhibiting the most stable SB excess electron states (supercooled water/air and Ih ice/air interfaces) are identified by their characteristic hydrogen-bonding motifs which are found to contain double acceptor-type water molecules in the close vicinity of the electron. These surface states correlate reasonably with those extrapolated to infinite size from simulated water cluster anions.

Temperature effect on the absorption spectrum of the hydrated electron paired with a lithium cation in deuterated water

The absorption spectra of the hydrated electron in 1.0 to 4.0 M LiCl or LiClO4 deuterated water solutions were measured by pulse radiolysis techniques from room temperature to 300 degrees C at a constant pressure of 25 MPa. The results show that when the temperature is increased and the density is decreased, the absorption spectrum of the electron in the presence of a lithium cation is shifted to lower energies. Quantum classical molecular dynamics (QCMD) simulations of an excess electron in bulk water and in the presence of a lithium cation have been performed to compare with the experimental results. According to the QCMD simulations, the change in the shape of the spectrum is due to one of the three p-like excited states of the solvated electron destabilized by core repulsion. The study of s --> p transition energies for the three p-excited states reveals that for temperatures higher than room temperature, there is a broadening of each individual s --> p absorption band due to a less structured water solvation shell.

Laser-muon spin spectroscopy in liquids—A technique to study the excited state chemistry of transients

This study introduces laser-muon spin spectroscopy in the liquid phase, which extends muonium chemistry in liquids to the realm of excited states and enables the detection of muoniated molecules by their spin evolution after laser excitation. This leads to new opportunities to study the Kinetic Isotope Effects (KIEs) of muonium/atomic hydrogen reactions and to probe transient chemistry in radiolysis processes involved in muonium formation, as well as muoniated intermediates in excited states.

Moving solvated electrons with light: Nonadiabatic mixed quantum/classical molecular dynamics simulations of the relocalization of photoexcited solvated electrons in tetrahydrofuran (THF)

Motivated by recent ultrafast spectroscopic experiments [Martini et al., Science 293, 462 (2001)], which suggest that photoexcited solvated electrons in tetrahydrofuran (THF) can relocalize (that is, return to equilibrium in solvent cavities far from where they started), we performed a series of nonequilibrium, nonadiabatic, mixed quantum/classical molecular dynamics simulations that mimic one-photon excitation of the THF-solvated electron. We find that as photoexcited THF-solvated electrons relax to their ground states either by continuous mixing from the excited state or via nonadiabatic transitions, approximately 30% of them relocalize into cavities that can be over 1 nm away from where they originated, in close agreement with the experiments. A detailed investigation shows that the ability of excited THF-solvated electrons to undergo photoinduced relocalization stems from the existence of preexisting cavity traps that are an intrinsic part of the structure of liquid THF. This explains why solvated electrons can undergo photoinduced relocalization in solvents like THF but not in solvents like water, which lack the preexisting traps necessary to stabilize the excited electron in other places in the fluid. We also find that even when they do not ultimately relocalize, photoexcited solvated electrons in THF temporarily visit other sites in the fluid, explaining why the photoexcitation of THF-solvated electrons is so efficient at promoting recombination with nearby scavengers. Overall, our study shows that the defining characteristic of a liquid that permits the photoassisted relocalization of solvated electrons is the existence of nascent cavities that are attractive to an excess electron; we propose that other such liquids can be found from classical computer simulations or neutron diffraction experiments.

Molecular dynamics simulations of the Ag+ or Na+ cation with an excess electron in bulk water

The properties of an excess electron interacting with a monovalent cation in bulk water are studied by molecular dynamics simulations. Sodium and silver cations are chosen as prototypical cases because of their very different redox properties. In both cases, mixed quantum classical molecular dynamics simulations reproduce the experimental UV-Vis spectra. In the case of silver, we observe a highly polarized neutral atom, corresponding to a dipolar excitonic state. For sodium a contact cation/electron pair is observed. Free energy curves along the cation electron coordinate are calculated using quantum Umbrella Sampling technique. The relative stability of the different chemical species is discussed.

Excess electron localization sites in neutral water clusters

We present approximate pseudopotential quantum-mechanical calculations of the excess electron states of equilibrated neutral water clusters sampled by classical molecular dynamics simulations. The internal energy of the clusters are representative of those present at temperatures of 200 and 300 K. Correlated electronic structure calculations are used to validate the pseudopotential for this purpose. We find that the neutral clusters support localized, bound excess electron ground states in about 50% of the configurations for the smallest cluster size studied (n = 20), and in almost all configurations for larger clusters (n > 66). The state is always exterior to the molecular frame, forming typically a diffuse surface state. Both cluster size and temperature dependence of energetic and structural properties of the clusters and the electron distribution are explored. We show that the stabilization of the electron is strongly correlated with the preexisting instantaneous dipole moment of the neutral clusters, and its ground state energy is reflected in the electronic radius. The findings are consistent with electron attachment via an initial surface state. The hypothetical spectral dynamics following such attachment is also discussed.

Photoelectron spectra of hydrated electron clusters: Fitting line shapes and grouping isomers

The photoelectron spectra of (H2O)(n = 2-69) - and (D2O)(n = 2-23) - are presented, and their spectral line shapes are analyzed in detail. This analysis revealed the presence of three different groupings of species, each of which are seen over the range, n = 11-16. These three groups are designated as dipole boundlike states, seen from n = 2-16, intermediate states, found from n = 6-16, and bulk embryonts, starting at n = 11 and continuing up through the largest sizes studied. Almost two decades ago [J. V. Coe et al., J. Chem. Phys. 92, 3980 (1990)], before the present comprehensive analysis, we concluded that the latter category of species were embryonic hydrated electrons with internalizing excess electrons (thus the term embryonts). Recent experiments with colder expansion (high stagnation chamber pressures) conditions by Neumark and coworkers [J. R. R. Verlet et al., Science 307, 93 (2005)] have also found three groups of isomers including the long-sought-after surface states of large water cluster anions. This work confirms that the species here designated as embryonts are in the process of internalizing the excess electron states as the cluster size increases (for n > or = 11).

Molecular Dynamics Simulations of Electron−Alkali Cation Pairs in Bulk Water

The structural, dynamic, and thermodynamic properties of an excess electron interacting with an alkali cation (Na+, K+, Li+) in bulk water were investigated by means of a mixed quantum-classical molecular dynamics simulation technique. This study includes a reparametrization of the electron-cation pseudopotentials. The free energy calculations for all three systems show that a contact electron-cation pair can be observed, which is either as stable as the dissociated pair (Li+) or more stable by only a few kT (Na+, K+). Given that the dissociation barrier is also quite small, we suggest that the average cation-electron distance in the experiments at room temperature will not depend on this free energy profile but rather on the minimization of the Coulombic repulsive interaction between like charges in the solvent medium. This enables us to compare the present molecular dynamics simulations with the spectroscopic data obtained for different ionic strengths. The overall trend of the UV-vis hydrated absorption spectra, namely, the shift toward shorter wavelengths at high ionic strengths, is fairly well reproduced. This confirms our hypothesis of statistical distribution of the cations and solvated electrons.

Characterization of excess electrons in water-cluster anions by quantum simulations

Water-cluster anions can serve as a bridge to understand the transition from gaseous species to the bulk hydrated electron. However, debate continues regarding how the excess electron is bound in (H2O)-n, as an interior, bulklike, or surface electronic state. To address the uncertainty, the properties of (H2O)-n clusters with 20 to 200 water molecules have been evaluated by mixed quantum-classical simulations. The theory reproduces every observed energetic, spectral, and structural trend with cluster size that is seen in experimental photoelectron and optical absorption spectra. More important, surface states and interior states each manifest a characteristic signature in the simulation data. The results strongly support assignment of surface-bound electronic states to the water-cluster anions in published experimental studies thus far.