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.

How Ions Break Local Symmetry: Simulations of Polarized Transient Hole Burning for Different Models of the Hydrated Electron in Contact Pairs with Na.

The hydrated electron (eaq-) is known via polarized transient hole-burning (pTHB) experiments to have a homogeneously broadened absorption spectrum. Here, we explore via quantum simulation how the pTHB spectroscopy of different eaq- models changes in the presence of electrolytes. The idea is that cation-eaq- pairing can break the local symmetry and, thus, induce persistent inhomogeneity. We find that a "hard" cavity model shows a modest increase in the pTHB recovery time in the presence of salt, while a "soft" cavity model remains homogeneously broadened independent of the salt concentration. We also explore the orientational anisotropy of a fully ab initio density functional theory-based model of the eaq-, which is strongly inhomogeneously broadened without salt and which becomes significantly more inhomogeneously broadened in the presence of salt. The results provide a direct prediction for experiments that can distinguish between different models and, thus, help pin down the hydration structure and dynamics of the eaq-.

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 (eaq-) in the presence of Na+, a system chosen because ion-pairing behavior in water depends sensitively on the local hydration structure. Experiments show that eaq-'s interact weakly with Na+; the eaq-'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 eaq- 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 eaq- is too ordered or kosmotropic. Conversely, simulations that produce eaq-'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 (eaq-) 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 eaq- 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 eaq--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 eaq- 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 eaq- 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.

Driving Force and Optical Signatures of Bipolaron Formation in Chemically Doped Conjugated Polymers.

Molecular dopants are often added to semiconducting polymers to improve electrical conductivity. However, the use of such dopants does not always produce mobile charge carriers. In this work, ultrafast spectroscopy is used to explore the nature of the carriers created following doping of conjugated push-pull polymers with both F4 TCNQ (2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane) and FeCl3 . It is shown that for one particular push-pull material, the charge carriers created by doping are entirely non-conductive bipolarons and not single polarons, and that transient absorption spectroscopy following excitation in the infrared can readily distinguish the two types of charge carriers. Based on density functional theory calculations and experiments on multiple push-pull conjugated polymers, it is argued that the size of the donor push units determines the relative stabilities of polarons and bipolarons, with larger donor units stabilizing the bipolarons by providing more area for two charges to co-reside.

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.