Moving solvated electrons with light: nonadiabatic mixed quantum/classical molecular dynamics simulations of the relocalization of photoexcited solvated electrons in tetrahydrofuran (THF)

Motivated by recent ultrafast spectroscopic experiments [Martini et al., Science 293, 462 (2001)], which suggest that photoexcited solvated electrons in tetrahydrofuran (THF) can relocalize (that is, return to equilibrium in solvent cavities far from where they started), we performed a series of nonequilibrium, nonadiabatic, mixed quantum/classical molecular dynamics simulations that mimic one-photon excitation of the THF-solvated electron. We find that as photoexcited THF-solvated electrons relax to their ground states either by continuous mixing from the excited state or via nonadiabatic transitions, approximately 30% of them relocalize into cavities that can be over 1 nm away from where they originated, in close agreement with the experiments. A detailed investigation shows that the ability of excited THF-solvated electrons to undergo photoinduced relocalization stems from the existence of preexisting cavity traps that are an intrinsic part of the structure of liquid THF. This explains why solvated electrons can undergo photoinduced relocalization in solvents like THF but not in solvents like water, which lack the preexisting traps necessary to stabilize the excited electron in other places in the fluid. We also find that even when they do not ultimately relocalize, photoexcited solvated electrons in THF temporarily visit other sites in the fluid, explaining why the photoexcitation of THF-solvated electrons is so efficient at promoting recombination with nearby scavengers. Overall, our study shows that the defining characteristic of a liquid that permits the photoassisted relocalization of solvated electrons is the existence of nascent cavities that are attractive to an excess electron; we propose that other such liquids can be found from classical computer simulations or neutron diffraction experiments.     

The absorption coefficient of a polar liquid with solvated electrons

An equation for the absorption coefficient of a polar liquid with excess (solvated) electrons is derived. It is taken into account that (1) each excess electron can for a certain time reside on only one liquid molecule (during this time, the molecule is in the anion-resonance state), and (2) a polar liquid is electrostatically nonuniform because it has different local potentials, which can be calculated for each molecule. The probabilities of quantum movements of excess electrons in a liquid from one molecule to another caused by the absorption of photons are considered.     

The nature of the transitions comprising the optical absorption spectra of solvated electrons

The theory of photoejection spectra of molecular anions is adapted for application to analyses of optical absorption data of solvated electrons in a number of different solvents. The results obtained generally support the identification of solvated electron optical absorption spectra entirely as bands of bound-to-continuum transitions and not as bound-to-bound transitions. Analyses of the absorbance behavior near the threshold for absorption lead to the conclusion that the solvated electron ground state deviates appreciably from spherical symmetry. Alternatively, the solvated electron ground state in ND₃ may be nearly spherically symmetric with a thermally accessible excited state of lower symmetry.     

Empirical correlations between solvent acidity and the optical characteristics of solvated electrons

Correlations between essential characteristics of the optical absorption spectrum of the solvated electron (excitation energy, band-width) and the acceptor numbers of organic solvents are established.

---

Eine empirische Korrelation zwischen der Acidität von Lösungsmitteln und spektralen Charakteristika solvatisierter Elektronen

Zusammenfassung Es wird eine Korrelation zwischen den wesentlichen Charakteristika des optischen Absorptionsspektrums von solvatisierten Elektronen (Anregungsenergie und Bandenbreite) und den Acceptornummern organischer Lösungsmittel gefunden.

     

Determination of the characteristics of solvated electrons from optical absorption data

As difficulties are encountered with model theories in describing the nature of solvated electrons, it is suggested that possible non-model relations in the theory of solvated electrons be used. In the present work the results that follow from the sum rules, virial theorem and threshold formulae of the quantum theory of scattering are examined. In this way it is possible to establish relationships that can be used for determining some of the physical characteristics of solvated electrons directly from optical data.     

Production of solvated electrons,ion-paris and alkali metal anions in tetrahydrofuran studied by pulse radiolysis

Pulse radiolysis of tetrahydrofuran (THF) and solutions of NaAIH₄ in THF shows the formation of solvated electrons (e^?_s), their conversion to Na⁺-e^?_s) ion-pairs and ultimately the alkali metal anion (Na^?).     

Independent pairs and Monte-Carlo simulations of the geminate recombination of solvated electrons in liquid-to-supercritical water

Independent pairs (IP) and Monte Carlo (MC) simulations are employed to model experimental femtosecond time-resolved pump-probe spectroscopic data on the geminate recombination dynamics of solvated electrons in liquid-to-supercritical water. The hydrated electron was created by two-photon ionization of the neat fluid with a total ionization energy of 9.3 eV. In both numerical approaches, the ejection length, , (i.e. the distance from the ionization core, at which the electron is thermally and spatially localized) is used as the primary adjustable fitting parameter that can bring both model simulations into quantitative agreement with the ultrafast kinetic experiment. The influence of the thermodynamic conditions on the ejection length and on the recombination mechanism is discussed. Whereas in the compressed liquid associated with a high dielectric constant (ε ≥ 20), the electron recombines predominantly with the OH radical, the dissociative recombination via charge neutralization with the hydronium cation takes over at small dielectric constants (ε < 20). The importance of charge-dipole interactions for Monte-Carlo simulations of the recombination reactions of the hydrated electrons in the low-permittivity region is stressed.     

Raman spectrum modification in the presence of solvated electrons. Observation by polarization CARS

The multiple-scattering series for depolarized light scattering from simple liquids is investigated. It is found that the leading term in the series, due to double—double scattering, is probably not large compared to double—triple (DT) scattering contributions. Existing theories, which neglect DT scattering, have concluded that the experimental data cannot be explained using the dipole—induced dipole (DID) model for the pair polarizability. It is suggested that a theory which includes DT scattering will not lead to rejection of the DID model.     

Near-IR absorption spectrum of the solvated electron in alcohols and deuterated water

The absorption band profiles of the solvated electron in aqueous and alcohol glasses at 77, 115 and 300 K were calculated in terms of the theory presented in our previous paper [J. Phys. Chem.95, 6149 (1991)]. We have concentrated our attention on the problem of the IR-absorbing electrons (e^-_IR) trying to explain their appearance in alcohols, deuterated water and their lack in H₂O at low temperatures. The comparison between the experiment and the theoretical model provides new arguments to the discussion on the initial spectra of trapped electrons.     

Infrared and vibrational CD spectra of partially solvated alpha-helices: DFT-based simulations with explicit solvent

Theoretical simulations are used to investigate the effects of aqueous solvent on the vibrational spectra of model alpha-helices, which are only partly exposed to solvent to mimic alpha-helices in proteins. Infrared absorption (IR) and vibrational circular dichroism (VCD) amide I' spectra for 15-amide alanine alpha-helices are simulated using density functional theory (DFT) calculations combined with the property transfer method. The solvent is modeled by explicit water molecules hydrogen bonded to the solvated amide groups. Simulated spectra for two partially solvated model alpha-helices, one corresponding to a more exposed and the other to a more buried structure, are compared to the fully solvated and unsolvated (gas phase) simulations. The dependence of the amide I spectra on the orientation of the partially solvated helix with respect to the solvent and effects of solvation on the amide I' of 13C isotopically substituted alpha-helices are also investigated. The partial exposure to solvent causes significant broadening of the amide I' bands due to differences in the vibrational frequencies of the explicitly solvated and unsolvated amide groups. The different degree of partial solvation is reflected primarily in the frequency shifts of the unsolvated (buried) amide group vibrations. Depending on which side of the alpha-helix is exposed to solvent, the simulated IR band-shapes exhibit significant changes, from broad and relatively featureless to distinctly split into two maxima. The simulated amide I' VCD band-shapes for the partially solvated alpha-helices parallel the broadening of the IR and exhibit more sign variation, but generally preserve the sign pattern characteristic of the alpha-helical structures and are much less dependent on the alpha-helix orientation with respect to the solvent. The simulated amide I' IR spectra for the model peptides with explicitly hydrogen-bonded water are consistent with the experimental data for small alpha-helical proteins at very low temperatures, but overestimate the effects of solvent on the protein spectra at ambient temperatures, where the peptide-water hydrogen bonds are weakened by thermal motion.     

Mixed quantum classical simulations of excitons in peptide helices

We use mixed classical/quantum simulations to study the time dependence of an excitation of a C=O vibration on a 3-10 helix of α-aminoisobutyric acid, a system which represents a test case for the formation of self-trapped vibrational excitation states on protein helices. Due to the inherent disorder in the system caused by the finite temperature and fluctuations in hydrogen bonding, the excitation tunnels randomly among C=O sites along the helix. Quantum forces are insufficient to establish a coherent relationship between the location of the excitation and the contraction of hydrogen bonds around this site. Our simulations indicate that the excitation frequently becomes localized on the end of the helix due to the defect in helical structure caused by unwinding. Our results generally do not support the existence of Davydov type solitons in biological helix systems under physiological conditions.     

Exploring the role of decoherence in condensed-phase nonadiabatic dynamics: a comparison of different mixed quantum/classical simulation algorithms for the excited hydrated electron

Mixed quantum/classical (MQC) molecular dynamics simulation has become the method of choice for simulating the dynamics of quantum mechanical objects that interact with condensed-phase systems. There are many MQC algorithms available, however, and in cases where nonadiabatic coupling is important, different algorithms may lead to different results. Thus, it has been difficult to reach definitive conclusions about relaxation dynamics using nonadiabatic MQC methods because one is never certain whether any given algorithm includes enough of the necessary physics. In this paper, we explore the physics underlying different nonadiabatic MQC algorithms by comparing and contrasting the excited-state relaxation dynamics of the prototypical condensed-phase MQC system, the hydrated electron, calculated using different algorithms, including: fewest-switches surface hopping, stationary-phase surface hopping, and mean-field dynamics with surface hopping. We also describe in detail how a new nonadiabatic algorithm, mean-field dynamics with stochastic decoherence (MF-SD), is to be implemented for condensed-phase problems, and we apply MF-SD to the excited-state relaxation of the hydrated electron. Our discussion emphasizes the different ways quantum decoherence is treated in each algorithm and the resulting implications for hydrated-electron relaxation dynamics. We find that for three MQC methods that use Tully's fewest-switches criterion to determine surface hopping probabilities, the excited-state lifetime of the electron is the same. Moreover, the nonequilibrium solvent response function of the excited hydrated electron is the same with all of the nonadiabatic MQC algorithms discussed here, so that all of the algorithms would produce similar agreement with experiment. Despite the identical solvent response predicted by each MQC algorithm, we find that MF-SD allows much more mixing of multiple basis states into the quantum wave function than do other methods. This leads to an excited-state lifetime that is longer with MF-SD than with any method that incorporates nonadiabatic effects with the fewest-switches surface hopping criterion.     

The structures of ozone and HOx radicals in aqueous solution from combined quantum/classical molecular dynamics simulations

Ozone in aqueous solution decomposes through a complex mechanism that involves initial reaction with a hydroxide ion followed by formation of a variety of oxidizing species such as HO, HO(2), and HO(3) radicals. Though a number of hydrogen-bonded complexes have been described in the gas phase, both theoretically and experimentally, the structures of ozone and HO(x) in liquid water remain uncertain. In this work, combined quantum/classical computer simulations of aqueous solutions of these species have been reported. The results show that ozone undergoes noticeable electron polarization but it does not participate in hydrogen bonds with liquid water. The main contribution of the solvation energy comes from dispersion forces. In contrast, HO(x) radicals form strong hydrogen bonds. They are better proton donors but weaker proton acceptors than water. Their electronic and geometrical structures are significantly modified by the solvent, especially in the case of HO(3). In all cases, fluctuations in amplitudes of electronic properties are considerable, suggesting that solvent effects might play a crucial role on oxidation mechanisms initiated by ozone in liquid water. These mechanisms are important in a broad range of domains, such as atmospheric processes, plant response to ambient ozone, and medical and industrial applications.     

Comparisons of classical chemical dynamics simulations of the unimolecular decomposition of classical and quantum microcanonical ensembles

Previous studies have shown that classical trajectory simulations often give accurate results for short-time intramolecular and unimolecular dynamics, particularly for initial non-random energy distributions. To obtain such agreement between experiment and simulation, the appropriate distributions must be sampled to choose initial coordinates and momenta for the ensemble of trajectories. If a molecule's classical phase space is sampled randomly, its initial decomposition will give the classical anharmonic microcanonical (RRKM) unimolecular rate constant for its decomposition. For the work presented here, classical trajectory simulations of the unimolecular decomposition of quantum and classical microcanonical ensembles, at the same fixed total energy, are compared. In contrast to the classical microcanonical ensemble, the quantum microcanonical ensemble does not sample the phase space randomly. The simulations were performed for CH(4), C(2)H(5), and Cl(-)---CH(3)Br using both analytic potential energy surfaces and direct dynamics methods. Previous studies identified intrinsic RRKM dynamics for CH(4) and C(2)H(5), but intrinsic non-RRKM dynamics for Cl(-)---CH(3)Br. Rate constants calculated from trajectories obtained by the time propagation of the classical and quantum microcanonical ensembles are compared with the corresponding harmonic RRKM estimates to obtain anharmonic corrections to the RRKM rate constants. The relevance and accuracy of the classical trajectory simulation of the quantum microcanonical ensemble, for obtaining the quantum anharmonic RRKM rate constant, is discussed.     

Inertial solvent dynamics and the analysis of spectral line shapes: Temperature-dependent absorption spectrum of beta-carotene in nonpolar solvent

The influence of solvent dynamics on optical spectra is often described by a stochastic model which assumes exponential relaxation of the time-correlation function for solvent-induced frequency fluctuations. In contrast, theory and experiment suggest that the initial (subpicosecond) phase of solvent relaxation, resulting from inertial motion of the solvent, is a Gaussian function of time. In this work, we employ numerical and analytical calculations to compare the predicted absorption line shapes and the derived solvent reorganization energies obtained from exponential (Brownian oscillator) versus Gaussian (inertial) solvent dynamics. Both models predict motional narrowing as the ratio kappa = Lambda/Delta is increased, where Lambda and Delta are the frequency and variance, respectively, of the solvent-induced frequency fluctuations. However, the motional narrowing limit is achieved at lower values of kappa for the Brownian oscillator model compared to the inertial model. For a given line shape, the derived value of the solvent reorganization energy lambdasolv is only weakly dependent on the solvent relaxation model employed, though different solvent parameters Lambda and Delta are obtained. The two models are applied to the analysis of the temperature-dependent absorption spectrum of beta-carotene in isopentane and CS2. The derived values of lambdasolv using the Gaussian model are found to be in better agreement with the high temperature limit of Delta2/2kBT than are the values obtained using the Brownian oscillator model. In either approach, the solvent reorganization energy is found to increase slightly with temperature as a result of an increase in the variance Delta of the solvent-induced frequency fluctuations.     

Reactivity between biphenyl and precursor of solvated electrons in tetrahydrofuran measured by picosecond pulse radiolysis in near-ultraviolet, visible, and infrared

The initial decrease of solvated electrons in tetrahydrofuran (THF) upon addition of biphenyl was investigated by picosecond pulse radiolysis. Transient absorption spectra derived from the biphenyl radical anion (centered at 408 and 655 nm) and solvated electrons of THF (infrared) were successfully measured in the wavelength region from 400 to 900 nm by the extension of a femtosecond continuum probe light to near-ultraviolet using a second harmonic generation of Ti:sapphire laser and a CaF2 plate. From the analysis of kinetic traces at 1300 nm considering the overlap of primary solvated electrons and partial biphenyl radical anion, C37, which is defined by the solute concentration to reduce the initial yield of solvated electrons to 1/e, was found to be 87 +/- 3 mM. The rate constant of solvated electrons with biphenyl was determined as 5.8 +/- 0.3 x 10(10) M(-1) s(-1). We demonstrate that the kinetic traces at both 408 nm mainly due to biphenyl radical anion and 1300 nm mainly due to solvated electrons are reproduced with high accuracy and consistency by a simple kinetic analysis. Much higher concentrations of biphenyl (up to 2 M) were examined, showing further increase of the initial yield of biphenyl radical anion accompanying a fast decay component. This observation is discussed in terms of geminate ion recombination, scavenging, delayed geminate ion recombination, and direct ionization of biphenyl at high concentration.     

The structure of the hydrated electron. Part 2. A mixed quantum/classical molecular dynamics embedded cluster density functional theory: single-excitation configuration interaction study

Adiabatic mixed quantum/classical (MQC) molecular dynamics (MD) simulations were used to generate snapshots of the hydrated electron in liquid water at 300 K. Water cluster anions that include two complete solvation shells centered on the hydrated electron were extracted from the MQC MD simulations and embedded in a roughly 18 Ax18 Ax18 A matrix of fractional point charges designed to represent the rest of the solvent. Density functional theory (DFT) with the Becke-Lee-Yang-Parr functional and single-excitation configuration interaction (CIS) methods were then applied to these embedded clusters. The salient feature of these hybrid DFT(CIS)/MQC MD calculations is significant transfer (approximately 18%) of the excess electron's charge density into the 2p orbitals of oxygen atoms in OH groups forming the solvation cavity. We used the results of these calculations to examine the structure of the singly occupied and the lower unoccupied molecular orbitals, the density of states, the absorption spectra in the visible and ultraviolet, the hyperfine coupling (hfcc) tensors, and the infrared (IR) and Raman spectra of these embedded water cluster anions. The calculated hfcc tensors were used to compute electron paramagnetic resonance (EPR) and electron spin echo envelope modulation (ESEEM) spectra for the hydrated electron that compared favorably to the experimental spectra of trapped electrons in alkaline ice. The calculated vibrational spectra of the hydrated electron are consistent with the red-shifted bending and stretching frequencies observed in resonance Raman experiments. In addition to reproducing the visible/near IR absorption spectrum, the hybrid DFT model also accounts for the hydrated electron's 190-nm absorption band in the ultraviolet. Thus, our study suggests that to explain several important experimentally observed properties of the hydrated electron, many-electron effects must be accounted for: one-electron models that do not allow for mixing of the excess electron density with the frontier orbitals of the first-shell solvent molecules cannot explain the observed magnetic, vibrational, and electronic properties of this species. Despite the need for multielectron effects to explain these important properties, the ensemble-averaged radial wavefunctions and energetics of the highest occupied and three lowest unoccupied orbitals of the hydrated electrons in our hybrid model are close to the s- and p-like states obtained in one-electron models. Thus, one-electron models can provide a remarkably good approximation to the multielectron picture of the hydrated electron for many applications; indeed, the two approaches appear to be complementary.