Observation of Large Water-Cluster Anions with Surface-Bound Excess Electrons

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.

An environmental impact statement for molecular anions

A molecular anion's (MA's) chemical reactivity and physical behavior can be quite different when it is surrounded by other molecules than when it exists in isolation. This sensitivity to the surrounding environment is especially high for anions because their outermost valence electrons are typically loosely bound and exist in rather spatially diffuse orbitals, allowing even weak intermolecular interactions arising from the environment to have strong effects. This Perspective offers illustrations of such sensitivity for a variety of cases including (i) the effect of solvation on electron binding energies, (ii) how some "well known" anions need to have solvent molecules around to even exist as stable species, (iii) how internal Coulomb repulsions within a multiply charged MA can provide temporary stability toward electron loss, (iv) how MAs arrange themselves spatially near liquid/vapor interfaces in manners that can produce unusual reactivity, (v) how nearby cationic sites can facilitate electron attachment to form a MA site elsewhere, (vi) how internal vibrational or rotational energy can make a MA detach an electron.

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.

Locking water molecules via ternary O-H⋯O intramolecular hydrogen bonds in perhydroxylated closo-dodecaborate

A multitude of applications related to perhydroxylated closo-dodecaborate B12(OH)122- in the condensed phase are inseparable from the fundamental mechanisms underlying the high water orientation selectivity based on the base B12(OH)122-. Herein, we directly compare the structural evolution of water clusters, ranging from monomer to hexamer, oriented by functional groups in the bases B12H122-, B12H11OH2- and B12(OH)122- using multiple theoretical methods. A significant revelation is made regarding B12(OH)122-: each additional water molecule is locked into the intramolecular hydrogen bond B-O-H ternary ring in an embedded form. This new pattern of water cluster growth suggests that B-(H-O)⋯H-O interactions prevail over the competition from water-hydrogen bonds (O⋯H-O), distinguishing it from the behavior observed in B12H122- and B12H11OH2- bases, in which competition arises from a mixed competing model involving dihydrogen bonds (B-H⋯H-O), conventional hydrogen bonds (B-(H-O)⋯H-O) and water hydrogen bonds (O⋯H-O). Through aqueous solvation and ab initio molecular dynamics analysis, we further demonstrate the largest water clusters in the first hydrated shell with exceptional thermodynamic stability around B12(OH)122-. These findings provide a solid scientific foundation for the design of boron cluster chemistry incorporating hydroxyl-group-modified borate salts with potential implications for various applications.

The Back Door to the Surface Hydrated Electron

We use a Mg+ metal to extend the size regime of aqueous clusters to extrapolate to the bulk limit of the vertical detachment energy (VDE) of the solvated electron to >3,200, a value between 1 to over 2 orders of magnitude larger than the one previously measured experimentally or computed theoretically. We relate the VDE to the energy difference between the Mg+(H2O)n and Mg2+(H2O)n systems and the metal's second ionization potential. The extrapolated bulk VDEs of the localized surface electron, which moves away from the metal as n increases, are 1.89 ± 0.01 eV for semiempirical (n ∼ 3,200; PM6-D3H4) and 1.73 ± 0.03 eV (n ∼ 150; HF) and 1.83 ± 0.02 eV (n ∼ 150; MP2) for ab initio, in excellent agreement with the 1.6-1.8 eV range of experimental results. The VDEs converge from above (larger values) to the bulk limit, in a manner that is qualitatively opposite from previous studies and experiments lacking a charged metal, a fact justifying the "back door" approach to the solvated electron.

Mass-selected ion-molecule cluster beam apparatus for ultrafast photofragmentation studies

We describe an apparatus for investigating the excited-state dissociation dynamics of mass-selected ion-molecule clusters by mass-resolving and detecting photofragment-ions and neutrals, in coincidence, using an ultrafast laser operating at high repetition rates. The apparatus comprises a source that generates ion-molecule clusters, a time-of-flight spectrometer, and a mass filter that selects the desired anions, and a linear-plus-quadratic reflectron mass spectrometer that discriminates the fragment anions after the femtosecond laser excites the clusters. The fragment neutrals and anions are then captured by two channeltron detectors. The apparatus performance is tested by measuring the photofragments: I-, CF3I-, and neutrals from photoexcitation of the ion-molecule cluster CF3I·I- using femtosecond UV laser pulses with a wavelength of 266 nm. The experimental results are compared with our ground state and excited state electronic structure calculations as well as the existing results and calculations, with particular attention to the generation mechanism of the anion fragments and dissociation channels of the ion-molecule cluster CF3I·I- in the charge-transfer excited state.

Role of Polarization Interactions in the Formation of Dipole-Bound States

Even though there is a critical dipole moment required to support a dipole-bound state (DBS), how molecular polarizability may influence the formation of DBSs is not well understood. Pyrrolide, indolide, and carbazolide provide an ideal set of anions to systematically examine the role of polarization interactions in the formation of DBSs. Here, we report an investigation of carbazolide using cryogenic photodetachment spectroscopy and high-resolution photoelectron spectroscopy (PES). A polarization-assisted DBS is observed at 20 cm^-1 below the detachment threshold for carbazolide, even though the carbazolyl neutral core has a dipole moment (2.2 D) smaller than the empirical critical value (2.5 D) to support a dipole-bound state. Photodetachment spectroscopy reveals nine vibrational Feshbach resonances of the DBS, as well as three intense and broad shape resonances. The electron affinity of carbazolyl is measured accurately to be 2.5653 ± 0.0004 eV (20,691 ± 3 cm^-1). The combination of photodetachment spectroscopy and resonant PES allows fundamental frequencies for 14 vibrational modes of carbazolyl to be measured. The three shape resonances are due to above-threshold excitation to the three low-lying electronic states (S₁-S₃) of carbazolide. Resonant PES of the shape resonances is dominated by autodetachment processes. Ultrafast relaxation from the S₂ and S₃ states to S₁ is observed, resulting in constant kinetic energy features in the resonant PES. The current study provides decisive information about the role that polarization plays in the formation of DBSs, as well as rich spectroscopic information about the carbazolide anion and the carbazolyl radical.

Distortion Correction of Low-Energy Photoelectron Spectra of Liquids Using Spectroscopic Data for Solvated Electrons

Time-resolved photoelectron spectroscopy (TRPES) enables real-time observation of ultrafast electronic dynamics in solutions. When extreme ultraviolet (EUV) probe pulses are employed, they can ionize solutes from all electronic states involved in the dynamics. However, EUV pulses also produce a strong ionization signal from a solvent that is typically 6 orders of magnitude greater than the pump-probe photoelectron signal of solutes. Alternatively, UV probe pulses enable highly sensitive and selective observation of photoexcited solutes because typical solvents such as water are transparent to UV radiation. An obstacle in such UV-TRPES measurements is spectral distortion caused by electron scattering and a yet to be identified mechanism in liquids. We have previously proposed the spectral retrieval (SR) method as an a posteriori approach to removing the distortion and overcoming this difficulty in UV-TRPES; however, its accuracy has not yet been verified by comparison with EUV-TRPES results. In the present study, we perform EUV-TRPES for charge transfer reactions in water, methanol, and ethanol, and verify SR analysis of UV-TRPES. We also estimate a previously undetermined energy-dependent intensity factor and expand the basis sets for SR analysis. The refined SR method is employed for reanalyzing the UV-TRPES data for the formation and relaxation dynamics of solvated electrons in various systems. The electron binding energy distributions for solvated electrons in liquid water, methanol, and ethanol are confirmed to be Gaussian centered at 3.78, 3.39, and 3.25 eV, respectively, in agreement with Nishitani et al. [ Sci. Adv. 2019, 5(8), eaaw6896]. An effective energy gap between the conduction band and the vacuum level at the gas-liquid interface is estimated to be 0.2 eV for liquid water and 0.1 eV for methanol and ethanol.

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.

Surface or Internal Hydration - Does It Really Matter?

The precise location of an ion or electron, whether it is internally solvated or residing on the surface of a water cluster, remains an intriguing question. Subtle differences in the hydrogen bonding network may lead to a preference for one or the other. Here we discuss spectroscopic probes of the structure of gas-phase hydrated ions in combination with quantum chemistry, as well as H/D exchange as a means of structure elucidation. With the help of nanocalorimetry, we look for thermochemical signatures of surface vs internal solvation. Examples of strongly size-dependent reactivity are reviewed which illustrate the influence of surface vs internal solvation on unimolecular rearrangements of the cluster, as well as on the rate and product distribution of ion-molecule reactions.

Evolution of Solute-Water Interactions in the Benzaldehyde-(H2O)1-6 Clusters by Rotational Spectroscopy

The investigation on the preferred arrangement and intermolecular interactions of gas phase solute-water clusters gives insights into the intermolecular potentials that govern the structure and dynamics of the aqueous solutions. Here, we report the investigation of hydrated coordination networks of benzaldehyde-(water)n (n = 1-6) clusters in a pulsed supersonic expansion using broadband rotational spectroscopy. Benzaldehyde (PhCHO) is the simplest aromatic aldehyde that involves both hydrophilic (CHO) and hydrophobic (phenyl ring) functional groups, which can mimic molecules of biological significance. For the n = 1-3 clusters, the water molecules are connected around the hydrophilic CHO moiety of benzaldehyde through a strong CO···HO hydrogen bond and weak CH···OH hydrogen bond(s). For the larger clusters, the spectra are consistent with the structures in which the water clusters are coordinated on the surface of PhCHO with both the hydrophilic CHO and hydrophobic phenyl ring groups being involved in the bonding interactions. The presence of benzaldehyde does not strongly interfere with the cyclic water tetramer and pentamer, which retain the same structure as in the pure water cluster. The book isomer instead of cage or prism isomers of the water hexamer is incorporated into the microsolvated cluster. The PhCHO molecule deviates from the planar structure upon sequential addition of water molecules. The PhCHO-(H2O)1-6 clusters may serve as a simple model system in understanding the solute-water interactions of biologically relevant molecules in an aqueous environment.

Highly Structured Water Networks in Microhydrated Dodecaborate Clusters

We report a combined photoelectron spectroscopy and theoretical investigation of a series of size-selected hydrated closo-dodecaborate clusters B₁₂X₁₂^2-·nH₂O (X = H, F, or I; n = 1-6). Distinct structural arrangements of water clusters from monomer to hexamer can be achieved by using different B₁₂X₁₂^2- bases, illustrating the evident solute specificity. Because B-H···H-O dihydrogen bonds are stronger than O···H-O hydrogen bonds in water, the added water molecules are arranged in a unified binding mode by forming highly structured water networks manipulated by B₁₂H₁₂^2-. As a comparison, the hydrated B₁₂F₁₂^2- clusters display similar water evolution for n values of 1 and 2 but different binding modes for larger clusters, while water networks in B₁₂I₁₂^2- share similarities with the free water clusters. This finding provides a consistent picture of the structural diversity of hydrogen bonding networks in microhydrated dodecaborates and a molecular-level understanding of microsolvation dynamics in aqueous borate chemistry.

Perturbative vibration of the coupled hydrogen-bond (O:H-O) in water

Perturbation Raman spectroscopy has underscored the hydrogen bond (O:H-O or HB) cooperativity and polarizability (HBCP) for water, which offers a proper parameter space for the performance of the HB and electrons in the energy-space-time domains. The OO repulsive coupling drives the O:H-O segmental length and energy to relax cooperatively upon perturbation. Mechanical compression shortens and stiffens the O:H nonbond while lengthens and softens the HO bond associated with polarization. However, electrification by an electric field or charge injection, or molecular undercoordination at a surface, relaxes the O:H-O in a contrasting way to the compression with derivation of the supersolid phase that is viscoelastic, less dense, thermally diffusive, and mechanically and thermally more stable. The HO bond exhibits negative thermal expansivity in the liquid and the ice-I phase while its length responds in proportional to temperature in the quasisolid phase. The O:H-O relaxation modifies the mass densities, phase boundaries, critical temperatures and the polarization endows the slipperiness of ice and superfluidity of water at the nanometer scale. Protons injection by acid solvation creates the H↔H anti-HB and introduction of electron lone pairs derives the O:⇔:O super-HB into the solutions of base or H₂O₂ hydrogen-peroxide. The repulsive H↔H and O:⇔:O interactions lengthen the solvent HO bond while the solute HO bond contracts because its bond order loss. Differential phonon spectroscopy quantifies the abundance, structure order, and stiffness of the bonds transiting from the mode of pristine water to the perturbed states. The HBCP and the perturbative spectroscopy have enabled the dynamic potentials for the relaxing O:H-O bond. Findings not only amplified the power of the Raman spectroscopy but also substantiated the understanding of anomalies of water subjecting to perturbation.

Observation of a transient intermediate in the ultrafast relaxation dynamics of the excess electron in strong-field-ionized liquid water

A unified picture of the electronic relaxation dynamics of ionized liquid water has remained elusive despite decades of study. Here, we employ sub-two-cycle visible to short-wave infrared pump-probe spectroscopy and ab initio nonadiabatic molecular dynamics simulations to reveal that the excess electron injected into the conduction band (CB) of ionized liquid water undergoes sequential relaxation to the hydrated electron s ground state via an intermediate state, identified as the elusive p excited state. The measured CB and p-electron lifetimes are 0.26 ± 0.02 ps and 62 ± 10 fs, respectively. Ab initio quantum dynamics yield similar lifetimes and furthermore reveal vibrational modes that participate in the different stages of electronic relaxation, with initial relaxation within the dense CB manifold coupled to hindered translational motions whereas subsequent p-to-s relaxation facilitated by librational and even intramolecular bending modes of water. Finally, energetic considerations suggest that a hitherto unobserved trap state resides ~0.3-eV below the CB edge of liquid water. Our results provide a detailed atomistic picture of the electronic relaxation dynamics of ionized liquid water with unprecedented time resolution.

Quantum simulations of neutral water clusters and singly-charged water cluster anions

We report a computational study of the structural and energetic properties of water clusters and singly-charged water cluster anions containing from 20 to 573 water molecules. We have used both a classical and a quantum description of the molecular degrees of freedom. Water intra and inter-molecular interactions have been modelled through the SPC/F model, while the water-excess electron interaction has been described via the well-known Turi-Borgis potential. We find that in general the quantum effects of the water degrees of freedom are small, but they do influence the cluster-size at which the excess electron stabilises inside the cluster, which occurs at smaller cluster sizes when quantum effects are taken into consideration.

Study of He*/Ne*+Ar, Kr, N2, H2, D2 Chemi-Ionization Reactions by Electron Velocity-Map Imaging

The chemi-ionization of Ar, Kr, N₂, H₂, and D₂ by Ne(³P₂) and of Ar, Kr, and N₂ by He(³S₁) was studied by electron velocity map imaging (e-VMI) in a crossed molecular beam experiment. A curved magnetic hexapole was used to state-select the metastable species. Collision energies of 60 meV were obtained by individually controlling the beam velocities of both reactants. The chemi-ionization of atoms and molecules can proceed along different channels, among them Penning ionization and associative ionization. The evolution of the reaction is influenced by the internal redistribution of energy, which happens at the first reaction step that involves the emission of an electron. We designed and built an e-VMI spectrometer in order to investigate the electron kinetic energy distribution, which is related to the internal state distribution of the ionic reaction products. The analysis of the electron kinetic energy distributions allows an estimation of the ratio between the two-reaction channel Penning and associative ionization. In the molecular cases the vibrational or electronic excitation enhanced the conversion of internal energy into the translational energy of the forming ions, thus influencing the reaction outcome.

Nonstatistical Photoinduced Processes in Gaseous Organic Molecules

Processes that proceed in femtoseconds are usually referred to as being ultrafast, and they are investigated in experiments that involve laser pulses with femtosecond duration in so-called pump probe schemes, where a light pulse triggers a molecular process and a second light pulse interrogates the temporal evolution of the molecular population. The focus of this review is on the reactivity patterns that arise when energy is not equally distributed on all the available degrees of freedom as a consequence of the very short time scale in play and on how the localization of internal energy in a specific mode can be thought of as directing a process toward (or away from) a certain outcome. The nonstatistical aspects are illustrated with examples from photophysics and photochemistry for a range of organic molecules. The processes are initiated by a variety of nuclear motions that are all governed by the energy gradients in the Franck-Condon region. Essentially, the molecules will start to adapt to the new electronic environment on the excited state to eventually reach the equilibrium structure. It is this structural change that is enabling an ultrafast electronic transition in cases where the nuclear motion leads to a transition point with significant coupling between to electronic states and to ultrafast reaction if there is a coupling to a reactive mode at the transition point between the involved states. With the knowledge of the relation between electronic excitation and equilibrium structure, it is possible to predict how the nuclei move after excitation and often whether an ultrafast (and inherently nonstatistical) electronic transition or even a bond breakage will take place. In addition to the understanding of how nonstatistical photoinduced processes proceed from a given excited state, it has been found that randomization of the energy does not even always take place when the molecule takes part in processes that are normally considered statistical, such as for example nonradiative transitions between excited states. This means that energy can be localized in a specific degree of freedom on a state other than the one that is initially prepared. This is a finding that could kickoff the ultimate dream in applied photochemistry; namely light excitation that leads to the rupture of a specific bond.

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.

Simulation of Negative Ion Photoelectron Spectroscopy Using a Nuclear Ensemble Approach: Implications from a Nuclear Vibration Effect

The negative ion photoelectron spectroscopy (NIPES) has been proven to be a powerful technique to reveal the electronic structures and spectroscopic properties of various cluster anions/radicals with very high precision. However, direct comparisons of the theoretical NIPES with experimental measurements remain challenging. Particularly the nuclear vibration effect and the ionization probability are typically ignored in reproducing NIPES. In this work, the NIPES of three representative anions (NaS₅^-, P₂N₃^-, and HCPN₃^-) with significantly different spectral features were simulated by combining the nuclear ensemble approach (NEA) and Dyson orbitals (DOs). Overall, the simulated NIPES are in good agreement with the experimentally determined ones, confirming the robustness of such a strategy. The analysis of frontier molecular orbitals (MOs) and DOs further suggests the similar mixed characters for the first ionized doublet (D₀) and adjacent D₁ states of NaS₅^- with distributions on the side sulfur atoms. And the D₀ of P₂N₃* is confirmed as the lowest energy σ radical state; however, the D₀ of HCPN₃* should possess a mixture of π and σ electrons by taking into account the nuclear vibration effect. Next, the broader vibrational distribution and stronger main vibration modes of P₂N₃^- and HCPN₃^- explain why the nuclear vibration possesses a more pronounced influence in reproducing their NIPES while it has little effect on NaS₅^-. Last, the limitations based on the double-harmonic approximation model and density of state method were also discussed, highlighting that the ionization probability and orbital relaxation effect during the ionization process should be reasonably considered.

Abnormal Properties of Low-Dimensional Confined Water

Water molecules confined to low-dimensional spaces exhibit unusual properties compared to bulk water. For example, the alternating hydrophilic and hydrophobic nanodomains on flat silicon wafer can induce the abnormal spreading of water (contact angles near 0°) which is caused by the 2D capillary effect. Hence, exploring the physicochemical properties of confined water from the nanoscale is of great value for understanding the challenges in material science and promoting the applications of nanomaterials in the fields of mass transport, nanofluidic designing, and fuel cell. The knowledge framework of confined water can also help to better understand the complex functions of the hydration layer of biomolecules, and even trace the origin of life. In this review, the physical properties, abnormal behaviors, and functions of the confined water are mainly summarized through several common low-dimensional water formats in the fields of solid/air-water interface, nanochannel confinement, and biological hydration layer. These researches indicate that the unusual behaviors of the confined water depend strongly on the confinement size and the interaction between the molecules and confining surface. These diverse properties of confined water open a new door to materials science and may play an important role in the future development of biology.

Enhanced alteration of poly(vinyl chloride) microplastics by hydrated electrons derived from indole-3-acetic acid assisted by a common cationic surfactant

In this study, a new photo-irradiated reductive dechlorination pathway and the underlying transformation mechanism are described for poly(vinyl chloride) microplastics (PVC-MPs). PVC-MPs underwent photo-reductive dechlorination process with the release of chloride ions. This reaction could be facilitated in the presence of indole-3-acetic acid (IAA) and hexadecyltrimethylammonium bromide (CTAB) under neutral pH and simulated sunlight irradiation conditions. Electrostatic interaction between IAA and CTAB produced neutral IAA/CTAB complex, which might account for the enhanced adsorption of IAA on PVC powders. Upon photo-irradiation, the adsorbed IAA was excited to generate hydrated electrons (e_aq^-), which could pass through a shorter distance to PVC-MP surface than that derived from homogeneous IAA molecules in aqueous solution. Transient spectra of laser flash photolysis provided direct evidence for the generation of e_aq^-, which supported the proposed dechlorination mechanism. Based on the results of attenuated total reflectance/Fourier transform infrared (ATR/FTIR) and Raman spectra, C-Cl bond cleavage and polyene formation were involved in the structural transformation of PVC-MPs. Due to the hydrophobic effects and π-π interactions between aromatic rings and polyene structures in PVC-MP surface, the PVC-MP powders irradiated in the presence of IAA/CTAB showed an enhanced sorption for both hydrophobic and hydrophilic aromatic chemicals.

Molecular Dynamics Characterization of Dielectron Hydration in Liquid Water with Unique Double Proton Transfers

Radiation chemistry of water and aqueous solutions has always been an interesting scientific issue owing to involving electronic excitations, ionization of solvated species, and formation of radiolytic species and many elementary reactions, but the underlying mechanisms are still poorly understood. Here, we for the first time molecular dynamics characterize the hydration dynamics of two correlated electrons and their triggered unique phenomena in liquid water associated with radiolysis of water using the combined hybrid functional and nonlocal dispersion functional. Hydration of two electrons may experience two distinctly different mechanisms, one forming a spin-paired closed-shell unicaged dielectron hydrate (e₂^2-_aq) and the other forming a spin-paired metastable open-shell bicaged hydrated electron pair (e^-_aq···e^-_aq) which exhibits intriguing antiferromagnetic spin coupling dynamics (in a range of -40 cm^-1 to -500 cm^-1). e^-_aq···e^-_aq can recombine to e₂^2-_aq through a unique solvent fluctuation-controlled gradual-flowing mechanism, and enlarging fluctuation can promote the conversion. Interestingly, we directly observe that e₂^2-_aq as the precursor can trigger hydrogen evolution via unique continuous spontaneous double proton transfer to the dielectron with a short-lived H^-_aq intermediate, but e^-_aq···e^-_aq does not directly. This is the first direct observation for the connection between e₂^2-_aq and spontaneous hydrogen evolution including participation of H^-_aq in aqueous solution, bridging relevant experimental phenomena. This work also evidences an unnoticed process, the double proton transfer mediated charge separation, and presents the first detailed analysis regarding the evolution dynamics of e₂^2-_aq for the understanding of the radiolysis reactions in aqueous solutions.

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.

In Vivo Molecular Insights into Syntrophic Geobacter Aggregates

Direct interspecies electron transfer (DIET) has been considered as a novel and highly efficient strategy in both natural anaerobic environments and artificial microbial fuel cells. A syntrophic model consisting of Geobacter metallireducens and Geobacter sulfurreducens was studied in this work. We conducted in vivo molecular mapping of the outer surface of the syntrophic community as the interface of nutrients and energy exchange. System for Analysis at the Liquid Vacuum Interface combined with time-of-flight secondary ion mass spectrometry was employed to capture the molecular distribution of syntrophic Geobacter communities in the living and hydrated state. Principal component analysis with selected peaks revealed that syntrophic Geobacter aggregates were well differentiated from other control samples, including syntrophic planktonic cells, pure cultured planktonic cells, and single population biofilms. Our in vivo imaging indicated that a unique molecular surface was formed. Specifically, aromatic amino acids, phosphatidylethanolamine components, and large water clusters were identified as key components that favored the DIET of syntrophic Geobacter aggregates. Moreover, the molecular changes in depths of the Geobacter aggregates were captured using dynamic depth profiling. Our findings shed new light on the interface components supporting electron transfer in syntrophic communities based on in vivo molecular imaging.

Infrared spectroscopy of neutral water clusters at finite temperature: Evidence for a noncyclic pentamer

Infrared spectroscopic study of neutral water clusters is crucial to understanding of the hydrogen-bonding networks in liquid water and ice. Here we report infrared spectra of size-selected neutral water clusters, (H₂O) _n (n = 3-6), in the OH stretching vibration region, based on threshold photoionization using a tunable vacuum ultraviolet free-electron laser. Distinct OH stretch vibrational fundamentals observed in the 3,500-3,600-cm^-1 region of (H₂O)₅ provide unique spectral signatures for the formation of a noncyclic pentamer, which coexists with the global-minimum cyclic structure previously identified in the gas phase. The main features of infrared spectra of the pentamer and hexamer, (H₂O) _n (n = 5 and 6), span the entire OH stretching band of liquid water, suggesting that they start to exhibit the richness and diversity of hydrogen-bonding networks in bulk water.

Role of Nonvalence States in the Ultrafast Dynamics of Isolated Anions

Nonvalence states of neutral molecules (Rydberg states) play important roles in nonadiabatic dynamics of excited states. In anions, such nonadiabatic transitions between nonvalence and valence states have been much less explored even though they are believed to play important roles in electron capture and excited state dynamics of anions. The aim of this Feature Article is to provide an overview of recent experimental observations, based on time-resolved photoelectron imaging, of valence to nonvalence and nonvalence to valence transitions in anions and to demonstrate that such dynamics may be commonplace in the excited state dynamics of molecular anions and cluster anions.

Vibrationally Mediated Stabilization of Electrons in Nonpolar Matter

We explore solvation of electrons in nonpolar matter, here represented by butadiene clusters. Isolated butadiene supports only the existence of transient anions (resonances). Two-dimensional electron energy loss spectroscopy shows that the resonances lead to an efficient vibrational excitation of butadiene, which can result into the almost complete loss of energy of the interacting electron. Cluster-beam experiments show that molecular clusters of butadiene form stable anions, however only at sizes of more than 9 molecular units. We have calculated the distribution of electron affinities of clusters using classical and path integral molecular dynamics simulations. There is almost a continuous transition from the resonant to the bound anions with an increase in cluster size. The comparison of the classical and quantum dynamics reveals that the electron binding is strongly supported by molecular vibrations, brought about by nuclear zero-point motion and thermal agitation. We also inspected the structure of the solvated electron, finding it well localized.

Fate of Dipole-Bound Anion States when Hydrated

Many strongly polar molecules can form an anion by attaching an electron to either an empty or half-filled valence-bound (VB) orbital or a so-called dipole-bound (DB) orbital. These two families of orbitals can be very different in their radial extent (the former are usually more compact, while the latter are quite diffuse) and in the degree to which they are affected by surrounding solvent molecules. In this study, the effects of hydration (representative of strong solvation) on the DB state of a model polar species are investigated with an eye toward determining whether this state is stabilized or even persists when a few to 100 water molecules surround the polar molecule. It is found that in the presence of up to ca. 10-12 water molecules, the excess electron can remain in a DB orbital. However, once there are enough water molecules to form a complete first hydration shell (or more), the excess electron migrates into an orbital localized on the outer surface of the water solvent cage. These findings have implications on the possible role of DB states as doorways to facilitating electron attachment and subsequent electron transfer to VB states. It is shown that even when the electron is bound to the surface of the surrounding solvent, the dipole potential of the solute molecule can influence where on the surface the electron binds. It is also illustrated that using continuum dielectric methods to describe the hydration of DB states is fraught with danger because much of the outermost electron density in such states penetrates outside the boundary of the cavity used in these methods.

Impact of Electron Solvation on Ice Structures at the Molecular Scale

Electron attachment and solvation at ice structures are well-known phenomena. The energy liberated in such events is commonly understood to cause temporary changes at such ice structures, but it may also trigger permanent modifications to a yet unknown extent. We determine the impact of electron solvation on D₂O structures adsorbed on Cu(111) with low-temperature scanning tunneling microscopy, two-photon photoemission, and ab initio theory. Solvated electrons, generated by ultraviolet photons, lead not only to transient but also to permanent structural changes through the rearrangement of individual molecules. The persistent changes occur near sites with a high density of dangling OD groups that facilitate electron solvation. We conclude that energy dissipation during solvation triggers permanent molecular rearrangement via vibrational excitation.

Real-time observation of water radiolysis and hydrated electron formation induced by extreme-ultraviolet pulses

The dominant pathway of radiation damage begins with the ionization of water. Thus far, however, the underlying primary processes could not be conclusively elucidated. Here, we directly study the earliest steps of extreme ultraviolet (XUV)-induced water radiolysis through one-photon excitation of large water clusters using time-resolved photoelectron imaging. Results are presented for H2O and D2O clusters using femtosecond pump pulses centered at 133 or 80 nm. In both excitation schemes, hydrogen or proton transfer is observed to yield a prehydrated electron within 30 to 60 fs, followed by its solvation in 0.3 to 1.0 ps and its decay through geminate recombination on a ∼10-ps time scale. These results are interpreted by comparison with detailed multiconfigurational non-adiabatic ab-initio molecular dynamics calculations. Our results provide the first comprehensive picture of the primary steps of radiation chemistry and radiation damage and demonstrate new approaches for their study with unprecedented time resolution.

Excess electrons bound to H2S trimer and tetramer clusters

We have prepared the hydrogen sulfide trimer and tetramer anions, (H2S)3− and (H2S)4−, measured their anion photoelectron spectra, and applied high-level quantum chemical calculations to interpret the results.

Importance of self-interaction-error removal in density functional calculations on water cluster anions

Removing self-interaction errors in density functional approximations results in significantly improved vertical detachment energies of water anions and is essential for obtaining orbital energies consistent with electron binding energies.

Probing the Structural Evolution of the Hydrated Electron in Water Cluster Anions (H2O)n-, n ≤ 200, by Electronic Absorption Spectroscopy

Electronic absorption spectra of water cluster anions (H₂O)_n^–, n ≤ 200, at T = 80 K are obtained by photodissociation spectroscopy and compared with simulations from literature and experimental data for bulk hydrated electrons. Two almost isoenergetic electron binding motifs are seen for cluster sizes 20 ≤ n ≤ 40, which are assigned to surface and partially embedded isomers. With increasing cluster size, the surface isomer becomes less populated, and for n ≥ 50, the partially embedded isomer prevails. The absorption shifts to the blue, reaching a plateau at n ≈ 100. In this size range, the absorption spectrum is similar to that of the bulk hydrated electron but is slightly red-shifted; spectral moment analysis indicates that these clusters are reasonable model systems for hydrated electrons near the liquid–vacuum interface.

Interaction between particles with inhomogeneous surface charge distributions: Revisiting the Coulomb fission of dication molecular clusters

An analytical solution describing the electrostatic interaction between particles with inhomogeneous surface charge distributions has been developed. For particles, each carrying a single charge, the solution equates to the presence of a point charge residing on the surface, which makes it particularly suitable for investigating the Coulomb fission of doubly charged clusters close to the Rayleigh instability limit. For a series of six separate molecular dication clusters, center-of-mass kinetic energy releases have been extracted from experimental measurements of their kinetic energy spectra following Coulomb fission. These data have been compared with Coulomb energy barriers calculated from the electrostatic interaction energies given by this new solution. For systems with high dielectric permittivity, results from the point charge model provide a viable alternative to kinetic energy releases calculated on the assumption of a uniform distribution of surface charge. The equivalent physical picture for the clusters would be that of a trapped proton. For interacting particles with low dielectric permittivity, a uniform distribution of charge provides better agreement with the experimental results.

Trapping a Photoelectron behind a Repulsive Coulomb Barrier in Solution

Multiply charged anions (MCAs) display unique photophysics and solvent-stabilizing effects. Well-known aqueous species such as SO₄^2- and PO₄^3- experience spontaneous electron detachment or charge-separation fragmentation in the gas phase owing to the strong Coulomb repulsion arising from the excess of negative charge. Thus, anions often present low photodetachment thresholds and the ability to quickly eject electrons into the solvent via charge-transfer-to-solvent (CTTS) states. Here, we report spectroscopic evidence for the existence of a repulsive Coulomb barrier (RCB) that blocks the ejection of "CTTS-like" electrons of the aqueous B₁₂F₁₂^2- dianion. Our spectroscopic experimental and theoretical studies indicate that despite the exerted Coulomb repulsion by the nascent radical monoanion B₁₂F₁₂^-•_aq, the photoexcited electron remains about the B₁₂F₁₂^-• core. The RCB is an established feature of the potential energy landscape of MCAs in vacuo, which seems to extend to the liquid phase highlighting recent observations about the dielectric behavior of confined water.

Relaxation Dynamics and Genuine Properties of the Solvated Electron in Neutral Water Clusters

We have investigated the solvation dynamics and the genuine binding energy and photoemission anisotropy of the solvated electron in neutral water clusters with a combination of time-resolved photoelectron velocity map imaging and electron scattering simulations. The dynamics was probed with a UV probe pulse following above-band-gap excitation by an EUV pump pulse. The solvation dynamics is completed within about 2 ps. Only a single band is observed in the spectra, with no indication for isomers with distinct binding energies. Data analysis with an electron scattering model reveals a genuine binding energy in the range of 3.55-3.85 eV and a genuine anisotropy parameter in the range of 0.51-0.66 for the ground-state hydrated electron. All of these observations coincide with those for liquid bulk, which is rather unexpected for an average cluster size of 300 molecules.

Ultrafast Internal Conversion and Solvation of Electrons in Water, Methanol, and Ethanol

Ultrafast internal conversion from the first excited state of a solvated electron in water, methanol, and ethanol is investigated using time-resolved photoelectron spectroscopy of liquid microjets and a spectral retrieval method. Photoelectron spectra corrected for inelastic scattering clearly reveal well-separated signals from the excited and ground states, and the latter enables us to analyze the solvation dynamics in the ground state after internal conversion. Measurements with 25 fs time resolution identify a rapid increase in the vertical electron binding energy of the solvated electron owing to nuclear wave packet motions in the excited state and allow us to precisely determine the internal conversion time.

Binding energy of solvated electrons and retrieval of true UV photoelectron spectra of liquids

The electronic energy and dynamics of solvated electrons, the simplest yet elusive chemical species, is of interest in chemistry, physics, and biology. Here, we present the electron binding energy distributions of solvated electrons in liquid water, methanol, and ethanol accurately measured using extreme ultraviolet (EUV) photoelectron spectroscopy of liquids with a single-order high harmonic. The distributions are Gaussian in all cases. Using the EUV and UV photoelectron spectra of solvated electrons, we succeeded in retrieving sharp electron kinetic energy distributions from the spectra broadened and energy shifted by inelastic scattering in liquids, overcoming an obstacle in ultrafast UV photoelectron spectroscopy of liquids. The method is demonstrated for the benchmark systems of charge transfer to solvent reaction and ultrafast internal conversion of hydrated electron from the first excited state.

Concluding remarks for advances in ion spectroscopy Faraday Discussion

Because the Introductory Lecture of this Faraday Discussion emphasized the recent history and exciting developments in the fields of experimental methods and applications of gaseous ion spectroscopy, these Concluding Remarks are, by design, directed somewhat more toward the roles played by theory. In discussing both the experimental and theoretical studies of gaseous ions, it is important to recognize and appreciate the delicate balance workers in the field are pursuing in terms of methodological/tool development and applications to current-day pressing problems in chemistry, physics, materials science, and biology. Without both components of modern research in this field, progress will not be efficient. Substantial discussion is included about the reductive approach that is commonly used to attempt to connect studies of ions in the gas phase (i.e., as isolated species) with properties of these ions as they exist in nature. Issues of how small a model system can be, to what extent surroundings/solvation can be addressed, and how our experimental or theoretical tools might limit us are all discussed in some detail. The current ability of theory to assist in the interpretation of experimental spectral data on gaseous ions is discussed, as are several of the most pressing limitations of theory on this front. Finally, the author offers his thoughts about what advances/improvements in theory are needed and the outlook for when they might be expected, and urges the experimental community to remain in close contact with theory groups developing new methods so that progress can be optimized.

Hydration of Hofmeister ions

Water dissolves salt into ions and then hydrates the ions to form an aqueous solution. Hydration of ions deforms the hydrogen bonding network and triggers the solution with what the pure water never shows such as conductivity, molecular diffusivity, thermal stability, surface stress, solubility, and viscosity, having enormous impact to many branches in biochemistry, chemistry, physics, and energy and environmental industry sectors. However, regulations for the solute-solute-solvent interactions are still open for exploration. From the perspective of the screened ionic polarization and O:H-O bond relaxation, this treatise features the recent progress and a perspective in understanding the hydration dynamics of Hofmeister ions in the typical YI, NaX, ZX₂, and NaT salt solutions (Y = Li, Na, K, Rb, Cs; X = F, Cl, Br, I; Z = Mg, Ca, Ba, Sr; T = ClO₄, NO₃, HSO₄, SCN). Phonon spectrometric analysis turned out the f(C) number fraction of bonds transition from the mode of deionized water to the hydrating. The linear f(C) ∝ C form features the invariant hydration volume of small cations that are fully-screened by their hydration H₂O dipoles. The nonlinear f(C) ∝ 1 - exp.(-C/C₀) form describes that the number insufficiency of the ordered hydrating H₂O dipoles partially screens the anions. Molecular anions show stronger yet shorter electric field of dipoles. The screened ionic polarization, inter-solute interaction, and O:H-O bond transition unify the solution conductivity, surface stress, viscosity, and critical energies for phase transition.

Real-Time Dynamics of the Formation of Hydrated Electrons upon Irradiation of Water Clusters with Extreme Ultraviolet Light

Free electrons in a polar liquid can form a bound state via interaction with the molecular environment. This so-called hydrated electron state in water is of fundamental importance, e.g., in cellular biology or radiation chemistry. Hydrated electrons are highly reactive radicals that can either directly interact with DNA or enzymes, or form highly excited hydrogen (H^{*}) after being captured by protons. Here, we investigate the formation of the hydrated electron in real-time employing extreme ultraviolet femtosecond pulses from a free electron laser, in this way observing the initial steps of the hydration process. Using time-resolved photoelectron spectroscopy we find formation timescales in the low picosecond range and resolve the prominent dynamics of forming excited hydrogen states.

Selectivity in Electron Attachment to Water Clusters

Electron attachment onto water clusters to form water cluster anions is studied by varying the point of electron attachment along a molecular beam axis and probing the produced cluster anions using photoelectron spectroscopy. The results show that the point of electron attachment has a clear effect on the final distribution of isomers for a cluster containing 78 water molecules, with isomer I formed preferentially near the start of the expansion and isomer II formed preferentially once the molecular beam has progressed for several millimeters. These changes can be accounted for by the cluster growth rate along the beam. Near the start of the expansion, cluster growth is proceeding rapidly with condensing water molecules solvating the electron, while further along the expansion, the growth has terminated and electrons are attached to large and cold preformed clusters, leading to the isomer associated with a loosely bound surface state.

Microscopic Insight into Electron-Induced Dissociation of Aromatic Molecules on Ice

We use scanning tunneling microscopy, photoelectron spectroscopy, and ab initio calculations to investigate the electron-induced dissociation of halogenated benzene molecules adsorbed on ice. Dissociation of halobenzene is triggered by delocalized excess electrons attaching to the π^{*} orbitals of the halobenzenes from where they are transferred to σ^{*} orbitals. The latter orbitals provide a dissociative potential surface. Adsorption on ice sufficiently lowers the energy barrier for the transfer between the orbitals to facilitate dissociation of bromo- and chloro- but not of flourobenzene at cryogenic temperatures. Our results shed light on the influence of environmentally important ice particles on the reactivity of halogenated aromatic molecules.

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.