Temperature Dependent Properties of the Aqueous Electron

2-in-1 Phase Space Sampling for Calculating the Absorption Spectrum of the Hydrated Electron

The investigation of vibrational effects on absorption spectrum calculations often employs Wigner sampling or thermal sampling. While Wigner sampling incorporates zero-point energy, it may not be suitable for flexible systems. Thermal sampling is applicable to anharmonic systems yet treats nuclei classically. The application of generalized smoothed trajectory analysis (GSTA) as a postprocessing method allows for the incorporation of nuclear quantum effects (NQEs), combining the advantages of both sampling methods. We demonstrate this approach in computing the absorption spectrum of a hydrated electron. Theoretical exploration of the hydrated electron and its embryonic forms, such as water cluster anions, poses a significant challenge due to the diffusivity of the excess electron and the continuous motion of water molecules. In many previous studies, the wave nature of atomic nuclei is often neglected, despite the substantial impact of NQEs on thermodynamic and spectroscopic properties, particularly for hydrogen atoms. In our studies, we examine these NQEs for the excess electrons in various water systems. We obtained structures from mixed classical-quantum simulations for water cluster anions and the hydrated electron by incorporating the quantum effects of atomic nuclei with the filtration of the classical trajectories. Absorption spectra were determined at different theoretical levels. Our results indicate significant NQEs, red shift, and broadening of the spectra for hydrated electron systems. This study demonstrates the applicability of GSTA to complex systems, providing insights into NQEs on energetic and structural properties.

Dynamics of the charge transfer to solvent process in aqueous iodide

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

Partial Molar Solvation Volume of the Hydrated Electron Simulated Via DFT

Different simulation models of the hydrated electron produce different solvation structures, but it has been challenging to determine which simulated solvation structure, if any, is the most comparable to experiment. In a recent work, Neupane et al. [J. Phys. Chem. B 2023, 127, 5941-5947] showed using Kirkwood-Buff theory that the partial molar volume of the hydrated electron, which is known experimentally, can be readily computed from an integral over the simulated electron-water radial distribution function. This provides a sensitive way to directly compare the hydration structure of different simulation models of the hydrated electron with experiment. Here, we compute the partial molar volume of an ab-initio-simulated hydrated electron model based on density-functional theory (DFT) with a hybrid functional at different simulated system sizes. We find that the partial molar volume of the DFT-simulated hydrated electron is not converged with respect to the system size for simulations with up to 128 waters. We show that even at the largest simulation sizes, the partial molar volume of DFT-simulated hydrated electrons is underestimated by a factor of 2 with respect to experiment, and at the standard 64-water size commonly used in the literature, DFT-based simulations underestimate the experimental solvation volume by a factor of ∼3.5. An extrapolation to larger box sizes does predict the experimental partial molar volume correctly; however, larger system sizes than those explored here are currently intractable without the use of machine-learned potentials. These results bring into question what aspects of the predicted hydrated electron radial distribution function, as calculated by DFT-based simulations with the PBEh-D3 functional, deviate from the true solvation structure.

Exploring the Unusual Reactivity of the Hydrated Electron with CO2

Many questions remain about the reactions of the hydrated electron despite decades of study. Of particular note is that they do not appear to follow the Marcus theory of electron transfer reactions, a feature that is yet to be explained. To investigate these issues, we used ab initio molecular dynamics (AIMD) simulations to investigate one of the better studied reactions, the hydrated electron reduction of CO2. The rate constant for the hydrated electron-CO2 reaction complex to react to form CO2- is for the first time estimated from AIMD simulations. Results at 298 and 373 K show the rate constant is insensitive to temperature, consistent with the low measured activation energy for the reaction, and the implications of this behavior are examined. The sampling provided by the simulations yields insight into the reaction mechanism. The reaction is found to involve both solvent reorganization and changes in the carbon dioxide structure. The latter leads to significant vibrational excitation of the bending and symmetric stretch vibrations in the CO2- product, indicating the reaction is vibrationally nonadiabatic. The former is estimated from the calculation of an approximate collective solvent coordinate and the free energy in this coordinate is determined. These results indicate that AIMD simulations can reasonably estimate hydrated electron reaction activation energies and provide new insight into the mechanism that can help illuminate the features of this unusual chemistry.

Spectroscopy and dynamics of the hydrated electron at the water/air interface

The hydrated electron, e-(aq), has attracted much attention as a central species in radiation chemistry. However, much less is known about e-(aq) at the water/air surface, despite its fundamental role in electron transfer processes at interfaces. Using time-resolved electronic sum-frequency generation spectroscopy, the electronic spectrum of e-(aq) at the water/air interface and its dynamics are measured here, following photo-oxidation of the phenoxide anion. The spectral maximum agrees with that for bulk e-(aq) and shows that the orbital density resides predominantly within the aqueous phase, in agreement with supporting calculations. In contrast, the chemistry of the interfacial hydrated electron differs from that in bulk water, with e-(aq) diffusing into the bulk and leaving the phenoxyl radical at the surface. Our work resolves long-standing questions about e-(aq) at the water/air interface and highlights its potential role in chemistry at the ubiquitous aqueous interface.

Controlled Radical Polymerization Initiated by Solvated Electrons

Solvated electron (esol - ) is highly reducing species and apt to initiate monomers via one-electron transfer reaction. Herein, utilizing the esol - solution of Na/hexamethylphosphoramide, radical and anionic initiations are observed respectively, which heavily depend on Na concentrations. Interestingly, this initiation system, in states of lower Na concentrations, higher molar conductivities and less paired esol - , give rise to a controlled radical polymerization (CRP) to yield polymers with predictable molecular weights and narrow molecular weight distributions (the lowest Ð = 1.25). This CRP presents unique behaviors, like solvent effect, electric field effect, and unusual copolymerization phenomenon. A semi-conjugated radical carrying a negative charge is proposed to be responsible for the CRP. This system gives a distinct way to regulate CRP from current CRPs, and offers new insights into the monomer initiation by esol - .

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.

Hydrated electrons as nodes in porous clathrate hydrates

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

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

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

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.