Electron localization in water clusters. II. Surface and internal states

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.

Size-Resolved Electron Solvation in Neutral Water Clusters

Cluster-size-resolved ultrafast dynamics of the solvated electron in neutral water clusters with n = 3 to ∼200 molecules are studied with pump–probe time-of-flight mass spectrometry after below band gap excitation. For the smallest clusters, no longer-lived (>100–200 fs) hydrated electrons were detected, indicating a minimum size of n ∼ 14 for being able to sustain hydrated electrons. Larger clusters show a systematic increase of the number of hydrated electrons per molecule on the femtosecond to picosecond time scale. We propose that with increasing cluster size the underlying dynamics is governed by more effective electron formation processes combined with less effective electron loss processes, such as ultrafast hydrogen ejection and recombination. It appears unlikely that any size dependence of the solvent relaxation dynamics would be reflected in the observed time-resolved ion yields.

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.

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.

SCC-DFTB-PIMD Method To Evaluate a Multidimensional Quantum Free-Energy Surface for a Proton-Transfer Reaction

The self-consistent charge density functional tight binding method was combined with the path-integral molecular dynamics method for the first time to evaluate the two-dimensional free-energy surface including nuclear quantum effects of a proton-transfer reaction in a 2,4-dichlorophenol-trimethylamine complex. A statistically converged two-dimensional quantum free-energy surface was evaluated by the multidimensional blue moon ensemble method. The accuracy was guaranteed by optimizing the repulsive potential between the sp³-hybridized nitrogen and hydrogen atoms in a SCC-DFTB3 parameter set for the system to reproduce high-level quantum chemical calculations. The present study illustrates the usefulness of this new approach to investigate nuclear quantum effects in various realistic proton-transfer reactions.

Accurate Predictions of Electron Binding Energies of Dipole-Bound Anions via Quantum Monte Carlo Methods

Neutral molecules with sufficiently large dipole moments can bind electrons in diffuse nonvalence orbitals with most of their charge density far from the nuclei, forming so-called dipole-bound anions. Because long-range correlation effects play an important role in the binding of an excess electron and overall binding energies are often only on the order of 10s-100s of wave numbers, predictively modeling dipole-bound anions remains a challenge. Here, we demonstrate that quantum Monte Carlo methods can accurately characterize molecular dipole-bound anions with near-threshold dipole moments. We also show that correlated sampling Auxiliary Field Quantum Monte Carlo is particularly well-suited for resolving the fine energy differences between the neutral and anionic species. These results shed light on the fundamental limitations of quantum Monte Carlo methods and pave the way toward using them for the study of weakly bound species that are too large to model using traditional electron structure methods.

Electronic Excited State Lifetimes of Anionic Water Clusters: Dependence on Charge Solvation Motif

An ongoing controversy about water cluster anions concerns the electron-binding motif, whether the charge center is localized at the surface or within the cluster interior. Here, mixed quantum-classical dynamics simulations have been carried out for a wide range of cluster sizes (n ≤ 1000) for (H₂O)_n^- and (D₂O)_n^-, based on a nonequilibrium first-order rate constant approach. The computed data are in good general agreement with time-resolved photoelectron imaging results (n ≤ 200). The analysis reveals that, for surface state electrons, the cluster size dependence of the excited state electronic energy gap and the magnitude of the nonadiabatic couplings have compensating influences on the excited state lifetimes: the excited state lifetime for surface states reaches a minimum for n ∼ 150 and then increases for larger clusters. It is concluded that the electron resides in a surface-localized motif in all of these measured clusters, dominating at least up to n = 200.

Short-Range Electron Correlation Stabilizes Noncavity Solvation of the Hydrated Electron

The hydrated electron, e^-_(aq), has often served as a model system to understand the influence of condensed-phase environments on electronic structure and dynamics. Despite over 50 years of study, however, the basic structure of e^-_(aq) is still the subject of controversy. In particular, the structure of e^-_(aq) was long assumed to be an electron localized within a solvent cavity, in a manner similar to halide solvation. Recently, however, we suggested that e^-_(aq) occupies a region of enhanced water density with little or no discernible cavity. The potential we developed was only subtly different from those that give rise to a cavity solvation motif, which suggests that the driving forces for noncavity solvation involve subtle electron-water attractive interactions at close distances. This leads to the question of how dispersion interactions are treated in simulations of the hydrated electron. Most dispersion potentials are ad hoc or are not designed to account for the type of close-contact electron-water overlap that might occur in the condensed phase, and where short-range dynamic electron correlation is important. To address this, in this paper we develop a procedure to calculate the potential energy surface between a single water molecule and an excess electron with high-level CCSD(T) electronic structure theory. By decomposing the electron-water potential into its constituent energetic contributions, we find that short-range electron correlation provides an attraction of comparable magnitude to the mean-field interactions between the electron and water. Furthermore, we find that by reoptimizing a popular cavity-forming one-electron model potential to better capture these attractive short-range interactions, the enhanced description of correlation predicts a noncavity e^-_(aq) with calculated properties in better agreement with experiment. Although much attention has been placed on the importance of long-range dispersion interactions in water cluster anions, our study reveals that largely unexplored short-range correlation effects are crucial in dictating the solvation structure of the condensed-phase hydrated electron.

Hydrated Electrons in Water Clusters: Inside or Outside, Cavity or Noncavity?

In this work, we compare the applicability of three electron–water molecule pseudopotentials in modeling the physical properties of hydrated electrons. Quantum model calculations illustrate that the recently suggested Larsen–Glover–Schwartz (LGS) model and its modified m-LGS version have a too-attractive potential in the vicinity of the oxygen. As a result, LGS models predict a noncavity hydrated electron structure in clusters at room temperature, as seen from mixed one-electron quantum–classical molecular dynamics simulations of water cluster anions, with the electron localizing exclusively in the interior of the clusters. Comparative calculations using the cavity-preferring Turi–Borgis (TB) model predict interior-state and surface-state cluster isomers. The computed associated physical properties are also analyzed and compared to available experimental data. We find that the LGS and m-LGS potentials provide results that appear to be inconsistent with the size dependence of the experimental data. The simulated TB tendencies are qualitatively correct. Furthermore, ab initio calculations on static LGS noncavity structures indicate weak stabilization of the excess electron in regions where the LGS potential preferably and strongly binds the electron. TB calculations give stabilization energies that are in line with the ab initio results. In conclusion, we observe that the cavity-preferring pseudopotential model predicts cluster physical properties in better agreement with experimental data and ab initio calculations than the models predicting noncavity structures for the hydrated electron.

Infrared spectra of small anionic water clusters from density functional theory and wavefunction theory calculations

We performed systematic theoretical studies on small anionic water/deuterated water clusters W/D(-)(N=2-6) at both density functional theory (B3LYP) and wavefunction theory (MP2) levels. The focus of the study is to examine the convergence of calculated infrared (IR) spectra with respect to the increasing number of diffuse functions. It is found that at the MP2 level for larger clusters (n = 4-6), only one extra diffuse function is needed to obtain the converged relative IR intensities, while two or three more sets of extra diffuse functions are needed for smaller clusters. Such behaviour is strongly associated with the convergence of the electronic structure of corresponding clusters at the MP2 level. It is striking to observe that at the B3LYP level, the calculated relative IR intensities for all the clusters under investigations are diverse and show no trend of convergence upon increasing the number of diffuse functions. Moreover, the increasing contribution from the extra diffuse functions to the dynamic IR dipole moment indicates that the B3LYP electronic structure also fails to converge. These results manifest that MP2 is a preferential theoretical method, as compared to the widely used B3LYP, for the IR intensity of dipole bounded electron systems.

Quantifying solvated electrons' delocalization

The electron delocalization range EDR(r;u_av) (left) captures the spin density (right) of an electron delocalized over u_av = 5.77 Å on the surface of an (H₂O)₂₀⁻ cluster.

Glucose-Promoted Localization Dynamics of Excess Electrons in Aqueous Glucose Solution Revealed by Ab Initio Molecular Dynamics Simulation

Ab initio molecular dynamics simulations reveal that an excess electron (EE) can be more efficiently localized as a cavity-shaped state in aqueous glucose solution (AGS) than in water. Compared with that (∼1.5 ps) in water, the localization time is shortened by ∼0.7-1.2 ps in three AGSs (0.56, 1.12, and 2.87 M). Although the radii of gyration of the solvated EEs are all close to 2.6 Å in the four solutions, the solvated EE cavities in the AGSs become more compact and can localize ∼80% of an EE, which is considerably larger than that (∼40-60% and occasionally ∼80%) in water. These observations are attributed to a modification of the hydrogen-bonded network by the introduction of glucose molecules into water. The water acts as a promoter and stabilizer, by forming voids around glucose molecules and, in this fashion, favoring the localization of an EE with high efficiency. This study provides important information about EEs in physiological AGSs and suggests a new strategy to efficiently localize an EE in a stable cavity for further exploration of biological function.

Excess electrons in ice: a density functional theory study

We present a density functional theory study of the localization of excess electrons in the bulk and on the surface of crystalline and amorphous water ice. We analyze the initial stages of electron solvation in crystalline and amorphous ice. In the case of crystalline ice we find that excess electrons favor surface states over bulk states, even when the latter are localized at defect sites. In contrast, in amorphous ice excess electrons find it equally favorable to localize in bulk and in surface states which we attribute to the preexisting precursor states in the disordered structure. In all cases excess electrons are found to occupy the vacuum regions of the molecular network. The electron localization in the bulk of amorphous ice is assisted by its distorted hydrogen bonding network as opposed to the crystalline phase. Although qualitative, our results provide a simple interpretation of the large differences observed in the dynamics and localization of excess electrons in crystalline and amorphous ice films on metals.

To be or not to be in a cavity: the hydrated electron dilemma

The hydrated electron-the species that results from the addition of a single excess electron to liquid water-has been the focus of much interest both because of its role in radiation chemistry and other chemical reactions, and because it provides for a deceptively simple system that can serve as a means to confront the predictions of quantum molecular dynamics simulations with experiment. Despite all this interest, there is still considerable debate over the molecular structure of the hydrated electron: does it occupy a cavity, have a significant number of interior water molecules, or have a structure somewhere in between? The reason for all this debate is that different computer simulations have produced each of these different structures, yet the predicted properties for these different structures are still in reasonable agreement with experiment. In this Feature Article, we explore the reasons underlying why different structures are produced when different pseudopotentials are used in quantum simulations of the hydrated electron. We also show that essentially all the different models for the hydrated electron, including those from fully ab initio calculations, have relatively little direct overlap of the electron's wave function with the nearby water molecules. Thus, a non-cavity hydrated electron is better thought of as an "inverse plum pudding" model, with interior waters that locally expel the surrounding electron's charge density. Finally, we also explore the agreement between different hydrated electron models and certain key experiments, such as resonance Raman spectroscopy and the temperature dependence and degree of homogeneous broadening of the optical absorption spectrum, in order to distinguish between the different simulated structures. Taken together, we conclude that the hydrated electron likely has a significant number of interior water molecules.

Dynamics and reactivity of trapped electrons on supported ice crystallites

The solvation dynamics and reactivity of localized excess electrons in aqueous environments have attracted great attention in many areas of physics, chemistry, and biology. This manifold attraction results from the importance of water as a solvent in nature as well as from the key role of low-energy electrons in many chemical reactions. One prominent example is the electron-induced dissociation of chlorofluorocarbons (CFCs). Low-energy electrons are also critical in the radiation chemistry that occurs in nuclear reactors. Excess electrons in an aqueous environment are localized and stabilized by the local rearrangement of the surrounding water dipoles. Such solvated or hydrated electrons are known to play an important role in systems such as biochemical reactions and atmospheric chemistry. Despite numerous studies over many years, little is known about the microscopic details of these electron-induced chemical processes, and interest in the fundamental processes involved in the reactivity of trapped electrons continues. In this Account, we present a surface science study of the dynamics and reactivity of such localized low-energy electrons at D(2)O crystallites that are supported by a Ru(001) single crystal metal surface. This approach enables us to investigate the generation and relaxation dynamics as well as dissociative electron attachment (DEA) reaction of excess electrons under well-defined conditions. They are generated by photoexcitation in the metal template and transferred to trapping sites at the vacuum interface of crystalline D(2)O islands. In these traps, the electrons are effectively decoupled from the electronic states of the metal template, leading to extraordinarily long excited state lifetimes on the order of minutes. Using these long-lived, low-energy electrons, we study the DEA to CFCl(3) that is coadsorbed at very low concentrations (∼10(12) cm(-2)). Using rate equations and direct measurement of the change of surface dipole moment, we estimated the electron surface density for DEA, yielding cross sections that are orders of magnitude higher than the electron density measured in the gas phase.

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

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

HYDRATION FREE ENERGY AND ABSORPTION SPECTRUM OF AN EXTRA ELECTRON IN WATER BY QUANTUM-CONTINUUM MODEL

In this paper, the hydration energy of electron and absorption spectrum at room temperature have been estimated by quantum-continuum model. Taking a number of negatively charged water clusters as the quantum part, the hydration energy is calculated at high levels associated with IPCM and IEFPCM. The optical absorption spectrum is calculated by TDDFT with different basis sets. The vertical detachment energy and cluster reorganization energy in gas phase are also investigated. The results have been discussed by comparing with the experimental observations.

Instability range of microsolvated multiply charged negative ions: prediction from detachment energy of stable hydrated clusters

We have presented a first-principle theory-based derivation of an exact expression for the solvent number-dependent electron-detachment energy of a solvated species in the thermodynamic limit. We also propose a generalized equation bridging the electron detachment energies for small and infinitely large clusters, thus providing a new route to calculate the ionization potential of a negatively charged ion from the electron-detachment energies of its stable hydrated clusters. Most importantly, it has the ability to predict the instability range of microhydrated anions. The calculated results for the ionization potential for a number of ions are found to be in good agreement with the available experimental results, and the predicted instability range for the doubly charged anions SO₄²⁻ and C₂O₄²⁻ is also consistent with experimental and ab initio results.

Excess electron and lithium atom solvation in water clusters at finite temperature: an ab initio molecular dynamics study of the structural, spectral, and dynamical behavior of (H2O)6- and Li(H2O)6

The roles of hydrogen bonds in the solvation of an excess electron and a lithium atom in water hexamer cluster at 150 K have been studied by means of ab initio molecular dynamics simulations. It is found that the hydrogen bonded structures of (H(2)O)(6)(-) and Li(H(2)O)(6) clusters are very different from each other and they dynamically evolve from one conformer to other along their simulation trajectories. The populations of the single acceptor, double acceptor, and free type water molecules are found to be significantly high unlike that in pure water clusters. Free hydrogens of these type of water molecules primarily capture the unbound electron density in these clusters. It is found that the binding motifs of the free electron evolve with time and the vertical detachment energy of (H(2)O)(6)(-) and vertical ionization energy of Li(H(2)O)(6) also change with time. Assignments of the observed peaks in vibrational power spectra are done, and we found direct correlations between the time-averaged population of water molecules in different hydrogen bonding states and the spectral features. The dynamical aspects of these clusters have also been studied through calculations of time correlations of instantaneous stretch frequencies of OH modes which are obtained from the simulation trajectories through a time series analysis.

Dynamics of electron localization in warm versus cold water clusters

The process of electron localization on a cluster of 32 water molecules at 20, 50, and 300 K is unraveled using ab initio molecular dynamics simulations. In warm, liquid clusters, the excess electron relaxes from an initial diffuse and weakly bound structure to an equilibrated, strongly bound species within 1.5 ps. In contrast, in cold, glassy clusters the relaxation processes is not completed and the electron becomes trapped in a metastable surface state with an intermediate binding energy. These results question the validity of extrapolations of the properties of solvated electrons from cold clusters of increasing size to the liquid bulk.

Binding energies, lifetimes and implications of bulk and interface solvated electrons in water

Solvated electrons in liquid water are one of the seemingly simplest, but most important, transients in chemistry and biology, but they have resisted disclosing important information about their energetics, binding motifs and dynamics. Here we report the first ultrafast liquid-jet photoelectron spectroscopy measurements of solvated electrons in liquid water. The results prove unequivocally the existence of solvated electrons bound at the water surface and of solvated electrons in the bulk solution, with vertical binding energies of 1.6 eV and 3.3 eV, respectively, and with lifetimes longer than 100 ps. The unexpectedly long lifetime of solvated electrons bound at the water surface is attributed to a free-energy barrier that separates surface and interior states. Beyond constituting important energetic and kinetic benchmark and reference data, the results also help to understand the mechanisms of a number of very efficient electron-transfer processes in nature.