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

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.

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.

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.

Trap-Seeking or Trap-Digging? Photoinjection of Hydrated Electrons into Aqueous NaCl Solutions

It is well-known that when excess electrons are injected into an aqueous solution, they localize and solvate in ∼1 ps. Still debated is whether localization occurs via "trap-digging", in which the electron carves out a suitable localization site, or by "trap-seeking", where the electron prefers to localize at pre-existing low-energy trap sites in solution. To distinguish between these two possible mechanisms, we study the localization dynamics of excess electrons in aqueous NaCl solutions using both ultrafast spectroscopy and mixed quantum-classical molecular dynamics simulations. By introducing pre-existing traps in the form of Na⁺ ions, we can use the cation-induced blue-shift of the hydrated electron's absorption spectrum to directly monitor the site of electron localization. Our experimental and computational results show that the electron prefers to localize directly at the sites of Na⁺ traps; the presence of concentrated electrolytes otherwise has little impact on the way trap-seeking hydrated electrons relax following injection.

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.

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.

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.

Mechanism of Aqueous Carbon Dioxide Reduction by the Solvated Electron

Aqueous solvated electron (e_aq^-), a key species in radiation and plasma chemistry, can efficiently reduce CO₂ in a potential green chemistry application. Here, the mechanism of this reaction is unravelled by condensed-phase molecular dynamics based on the correlated wave function and an accurate density functional theory (DFT) approximation. Here, we design and apply the holistic protocol for solvated electron's reactions encompassing all relevant reaction stages starting from diffusion. The carbon dioxide reduction proceeds via a cavity intermediate, which is separated from the product (CO₂^-) by an energy barrier due to the bending of CO₂ and the corresponding solvent reorganization energy. The formation of the intermediate is caused by solvated electron's diffusion, whereas the intermediate transformation to CO₂^- is triggered by hydrogen bond breaking in the second solvation shell of the solvated electron. This picture of an activation-controlled e_aq^- reaction is very different from both rapid barrierless electron transfer and proton-coupled electron transfer, where key transformations are caused by proton migration.