A quantum molecular dynamics simulation of an excess electron in methanol

Coherent polaron dynamics of electrons solvated in polar liquids

An electron solvated in a polar liquid is an elementary quantum system with properties governed by electric interactions with a fluctuating molecular environment. In the prevailing single particle picture, the quantum ground and excited states are determined by a self-consistent potential, as defined by the particular local configuration of the solvation shell. This description neglects collective many-body excitations, which arise from the coupling of electronic degrees of freedom and nuclear motions of the environment. While recent experiments have demonstrated collective nonequilbrium electronic-nuclear motion, i.e. polaron excitations in liquid water, their relevance in the broader context of polar liquids has remained unexplored. Here, we study the nonequilibrium dielectric response of the, compared to water, less polar alcohols isopropanol, and ethylene glycol, that also display a different hydrogen bond pattern. We demonstrate that ultrafast relaxation of photogenerated electrons impulsively induces coherent charge oscillations, which persist for some 10 ps. They emit electric waves in a frequency range from 0.1 to 2 THz, depending on electron concentration. Oscillation frequencies and line shapes are reproduced by a unified polaron picture for alcohols and water, which is based on a Clausius-Mossotti local field approach for the THz dielectric function. The analysis suggests a longitudinal character of many-body polaron excitations and a weak coupling to transverse excitations, supported by the underdamped character of charge oscillations. Polaron dynamics are governed by the long-range Coulomb interaction between an excess electron and several thousands of polar solvent molecules, while local electron solvation geometries play a minor role.

Shallow and deep trap states of solvated electrons in methanol and their formation, electronic excitation, and relaxation dynamics

We present condensed-phase first-principles molecular dynamics simulations to elucidate the presence of different electron trapping sites in liquid methanol and their roles in the formation, electronic transitions, and relaxation of solvated electrons (e_met⁻) in methanol. Excess electrons injected into liquid methanol are most likely trapped by methyl groups, but rapidly diffuse to more stable trapping sites with dangling OH bonds. After localization at the sites with one free OH bond (1OH trapping sites), reorientation of other methanol molecules increases the OH coordination number and the trap depth, and ultimately four OH bonds become coordinated with the excess electrons under thermal conditions. The simulation identified four distinct trapping states with different OH coordination numbers. The simulation results also revealed that electronic transitions of e_met⁻ are primarily due to charge transfer between electron trapping sites (cavities) formed by OH and methyl groups, and that these transitions differ from hydrogenic electronic transitions involving aqueous solvated electrons (e_aq⁻). Such charge transfer also explains the alkyl-chain-length dependence of the photoabsorption peak wavelength and the excited-state lifetime of solvated electrons in primary alcohols.

Condensed-phase first-principles molecular dynamics simulations elucidate the presence of different electron trapping sites in liquid methanol and their roles in the formation, electronic transitions, and relaxation of solvated electrons.

Slow photoionization via higher excited states of N,N-dimethylaniline in ethanol solution probed by femtosecond transient absorption spectroscopy under two-pulse two-photon excitation

Photoionization dynamics of N,N-dimethylaniline (DMA) from highly electronically excited states in ethanol solution was investigated by means of femtosecond two-pulse two-photon excitation transient absorption (2PE-TA) spectroscopy. The first pump pulse prepares the lowest singlet excited state (S₁ state) of DMA, and the second one excites the S₁ state into higher excited states. In the case with the second pulse at 500 nm, the ionization took place via a rapid channel (<100 fs) and a slow one with the time constant of ∼10 ps. The excitation wavelength effect of the second pulse indicated that a specific electronic state produced directly from higher excited states was responsible for the slow ionization. By integrating these results with the time evolution of the transient absorption spectra of the solvated electron in neat ethanol detected by the simultaneous two-photon excitation, it was revealed that the slow ionization of DMA in ethanol was regulated by the formation of the anionic species just before the completion of the solvation of the electron, leading to the solvated electron in the relaxed state. From these results, it was strongly suggested that the capture of the electron of the Rydberg-like state by the solvent or solvent cluster regulates the appearance of the cation radical.

Ab initio molecular dynamics study of solvated electrons in methanol clusters

Stable surface excess electronic states in small methanol cluster anions were identified and characterized in ab initio molecular dynamics simulations.

Excess electrons in methanol clusters: Beyond the one-electron picture

We performed a series of comparative quantum chemical calculations on various size negatively charged methanol clusters, CH₃OH_n^-. The clusters are examined in their optimized geometries (n = 2-4), and in geometries taken from mixed quantum-classical molecular dynamics simulations at finite temperature (n = 2-128). These latter structures model potential electron binding sites in methanol clusters and in bulk methanol. In particular, we compute the vertical detachment energy (VDE) of an excess electron from increasing size methanol cluster anions using quantum chemical computations at various levels of theory including a one-electron pseudopotential model, several density functional theory (DFT) based methods, MP2 and coupled-cluster CCSD(T) calculations. The results suggest that at least four methanol molecules are needed to bind an excess electron on a hydrogen bonded methanol chain in a dipole bound state. Larger methanol clusters are able to form stronger interactions with an excess electron. The two simulated excess electron binding motifs in methanol clusters, interior and surface states, correlate well with distinct, experimentally found VDE tendencies with size. Interior states in a solvent cavity are stabilized significantly stronger than electron states on cluster surfaces. Although we find that all the examined quantum chemistry methods more or less overestimate the strength of the experimental excess electron stabilization, MP2, LC-BLYP, and BHandHLYP methods with diffuse basis sets provide a significantly better estimate of the VDE than traditional DFT methods (BLYP, B3LYP, X3LYP, PBE0). A comparison to the better performing many electron methods indicates that the examined one-electron pseudopotential can be reasonably used in simulations for systems of larger size.

A Simple ab Initio Model for the Solvated Electron in Methanol

The solvation structure of a solvated electron in methanol is investigated with ab initio calculations of small anion methanol clusters in a polarized dielectric continuum. We find that the lowest-energy structure in best agreement with experiment, calculated with CCSD, MP2, and B3LYP methods with aug-cc-pvdz basis set, is a tetrahedral arrangement of four methanol molecules with OH bonds oriented toward the center. The optimum distance from the tetrahedron center to the hydroxyl protons is ∼1.8 Å, significantly smaller than previous estimates. We are able to reproduce experimental radius of gyration Rg (deduced from optical absorption), vertical detachment energy, and resonance Raman frequencies. The electron paramagnetic resonance g-factor shift is qualitatively reproduced using density functional theory.

Nonadiabatic dynamics of photoinduced proton-coupled electron transfer: comparison of explicit and implicit solvent simulations

Theoretical approaches for simulating the ultrafast dynamics of photoinduced proton-coupled electron transfer (PCET) reactions in solution are developed and applied to a series of model systems. These processes are simulated by propagating nonadiabatic surface hopping trajectories on electron-proton vibronic surfaces that depend on the solute and solvent nuclear coordinates. The PCET system is represented by a four-state empirical valence bond model, and the solvent is treated either as explicit solvent molecules or as a dielectric continuum, in which case the solvent dynamics is described in terms of two collective solvent coordinates corresponding to the energy gaps associated with electron and proton transfer. The explicit solvent simulations reveal two distinct solvent relaxation time scales, where the faster time scale relaxation corresponds to librational motions of solvent molecules in the first solvation shell, and the slower time scale relaxation corresponds to the bulk solvent dielectric response. The charge transfer dynamics is strongly coupled to both the fast and slow time scale solvent dynamics. The dynamical multistate continuum theory is extended to include the effects of two solvent relaxation time scales, and the resulting coupled generalized Langevin equations depend on parameters that can be extracted from equilibrium molecular dynamics simulations. The implicit and explicit solvent approaches lead to qualitatively similar charge transfer and solvent dynamics for model PCET systems, suggesting that the implicit solvent treatment captures the essential elements of the nonequilibrium solvent dynamics for many systems. A combination of implicit and explicit solvent approaches will enable the investigation of photoinduced PCET processes in a variety of condensed phase systems.

Temperature and density effects on the absorption maximum of solvated electrons in sub- and super-critical methanol

The optical absorption spectra of the solvated electron ([Formula: see text]) in sub- and super-critical methanol are measured by both electron pulse radiolysis and laser photolysis techniques, at temperatures in the range 220–270 °C. Over the density range studied (~0.45–0.59 g/cm3), the position of the absorption maximum ([Formula: see text]) of [Formula: see text] is found to shift only slightly to the red with decreasing density. In agreement with our previous work in water, at a fixed pressure, [Formula: see text] decreases monotonically with increasing temperature in passing through the phase transition at Tc (239.5 °C). By contrast, at a fixed density, [Formula: see text] exhibits a minimum as the solvent passes above the critical point into the supercritical state. These behaviors are discussed in terms of microscopic arguments based on the changes that occur in the methanol properties and methanol structure in the sub- and super-critical regimes. The effect of the addition of a small amount of water to the alcohol on the optical absorption energy of [Formula: see text] is also investigated.

Solvent dynamics effect in condensed-phase electron-transfer reactions

Channel-based reaction-diffusion equations are solved analytically for two electron transfer (ET) models, where the fast inner-sphere coordinate leads to an ET reaction treated by Fermi's golden rule, and the slow solvent coordinate moves via diffusion. The analytic solution has let us derive an ET rate constant that modifies the Marcus-Jortner formula by adding a constant alpha which we call a dynamic correction factor. The dynamic correction factor measures the effect of solvent friction. When the relaxation of solvent dynamics is fast, the dynamic correction can be neglected and the ET rate constant reduces to the traditional Marcus-Jortner formula. If the solvent dynamic relaxation is slow, the dynamic correction can be very large and the ET rate can be reduced by orders of magnitude. Using a generalized Zusman-Sumi-Marcus model as a starting point, we introduce two variants, GZSM-A and GZSM-B, where in model A, only one quantum mode is considered for inner-sphere motion and in model B, a classical mode for inner-sphere motion is added. By comparing the two models with experimental data, it is shown that model B is better than model A. For the solvents that have a relaxation time ranging between 0 and 5 ps, our result agrees fairly well with experimental data; for the solvents that have a relaxation time ranging between 5 and 40 ps, our result deviates from the experimental values. After introducing an adjustable scaling index in the effective time correlation function of the reaction coordinate, good agreement is achieved between the experiment and the theory for model B for all of the solvents studied in this paper.

Time-resolved photoelectron imaging of large anionic methanol clusters: (Methanol)n−(n∼145–535)

The dynamics of an excess electron in size-selected methanol clusters is studied via pump-probe spectroscopy with resolution of approximately 120 fs. Following excitation, the excess electron undergoes internal conversion back to the ground state with lifetimes of 260-175 fs in (CH3OH)n- (n=145-535) and 280-230 fs in (CD3OD)n- (n=210-390), decreasing with increasing cluster size. The clusters then undergo vibrational relaxation on the ground state on a time scale of 760+/-250 fs. The excited state lifetimes for (CH3OH)n- clusters extrapolate to a value of 157+/-25 fs in the limit of infinite cluster size.

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.

Quantized time correlation function approach to nonadiabatic decay rates in condensed phase: Application to solvated electrons in water and methanol

A new, alternative form of the golden rule formula defining the nonadiabatic transition rate between two quantum states in condensed phase is presented. The formula involves the quantum time correlation function of the energy gap, of the nonadiabatic coupling, and their cross terms. Those quantities can be inferred from their classical counterparts, determined via molecular dynamics simulations. The formalism is applied to the problem of the nonadiabatic p-->s relaxation of an equilibrated p-electron in water and methanol. We find that, in both solvents, the relaxation is induced by the coupling to the vibrational modes and the quantum effects modify the rate by a factor of 2-10 depending on the quantization procedure applied. The resulting p-state lifetime for a hypothetical equilibrium excited state appears extremely short, in the sub-100 fs regime. Although this result is in contrast with all previous theoretical predictions, we also illustrate that the lifetimes computed here are very sensitive to the simulated electronic quantum gap and to the strongly correlated nonadiabatic coupling.

Theory of electron solvation in polar liquids: A continuum model

The solvation of electrons in polar liquids is analyzed on the basis of an extended continuum model. In addition to the long-range electron-dipole interaction two short-range interactions are introduced. Among others one accounts for interactions with groups capable of forming hydrogen bonds and the second for quadrupolar characteristics of the liquid molecules. Both are induced by the orientation of the molecular dipole. Applying the scaling method a proper reaction coordinate is introduced and the solvation dynamics are discussed for the electron in the electronic ground state and after excitation to the p-type excited state. The observed spectral evolution of the transient absorption spectra, after two photon excitations for electrons in water and in methanol, is well described by this theory. An analytic estimate for the nonradiative deactivation from the electronically excited solvated electron is found to be consistent with an observed lifetime of 50 fs for the electron in water. The theory predicts an about three times slower internal conversion in methanol as solvent in comparison with water.

The role of solvent structure in the absorption spectrum of solvated electrons: Mixed quantum/classical simulations in tetrahydrofuran

In polar fluids such as water and methanol, the peak of the solvated electron's absorption spectrum in the red has been assigned as a sum of transitions between an s-like ground state and three nearly degenerate p-like excited states bound in a quasispherical cavity. In contrast, in weakly polar solvents such as tetrahydrofuran (THF), the solvated electron has an absorption spectrum that peaks in the mid-infrared, but no definitive assignment has been offered about the origins of the spectrum or the underlying structure. In this paper, we present the results of adiabatic mixed quantum/classical molecular dynamic simulations of the solvated electron in THF, and provide a detailed explanation of the THF-solvated electron's absorption spectrum and electronic structure. Using a classical solvent model and a fully quantum mechanical excess electron, our simulations show that although the ground and first excited states are bound in a quasispherical cavity, a multitude of other, nearby solvent cavities support numerous, nearly degenerate, bound excited states that have little Franck-Condon overlap with the ground state. We show that these solvent cavities, which are partially polarized so that they act as electron trapping sites, are an inherent property of the way THF molecules pack in the liquid. The absorption spectrum is thus assigned to a sum of bound-to-bound transitions between a localized ground state and multiple disjoint excited states scattered throughout the fluid. Furthermore, we find that the usual spherical harmonic labels (e.g., s-like, p-like) are not good descriptors of the excited-state wave functions of the solvated electron in THF. Our observation of multiple disjoint excited states is consistent with femtosecond pump-probe experiments in the literature that suggest that photoexcitation of solvated electrons in THF causes them to relocalize into solvent cavities far from where they originated.

Quantum molecular dynamics simulation of proton transfer in cytochrome c oxidase

Proton transfer/translocation is studied in cytochrome c oxidase (CcO) by a combination of quantum mechanics (QM) for the transferring protons and classical molecular dynamics (MD) for the protein and solvent. The possibility of a glutamate, Glu286 in the Rhodobacter sphaeroides numbering scheme, acting as a rely point for proton translocation is investigated. The MD finds a hydrogen-bonded cycle of two waters and the carboxylate oxygens of Glu286. The possibility of protonating Glu286 to form neutral GluH is studied and we find that, as experimentally inferred, this glutamate can spend most of its time as GluH. Since translocation relies on the presence of water chains within CcO channels, MD is used to assess their formation. Glu286 and Mg(2+) can be connected by continuous hydrogen-bonded chains that are robust, though transient, and the protein appears spongy above (toward the outer membrane) the Mg(2+). In contrast, the D-channel spanning Asp132, close to the inner membrane surface, to Glu286, forms water chains that are much sparser and do not continuously connect these residues. Rather, there are chains spanning Glu286 to the vicinity of Asn140, and other more robust and ramified water structures that connect Asp132 with waters close to Asn140.

Theory and simulation of proton-coupled electron transfer, hydrogen-atom transfer, and proton translocation in proteins

A theory of proton coupled electron transfer (PCET) is reviewed with application to charge transfer steps in the photosystem II oxygen-evolving complex (PSII/OEC). The relation between PCET when it is a concerted electron proton transfer (ETPT) process and hydrogen-atom transfer (HAT) reactions is discussed. Signatures expected for HAT reactions in terms of the size of the kinetic isotope effect and overall magnitude of the rate constant are discussed in the context of PSII/OEC. The formal similarity of ETPT to proton transfer and translocation is used to introduce a combined quantum mechanical (for the transferring protons) and molecular dynamics for the heavy-atom degrees of freedom approach. The method is used to examine double proton transfer in cytochrome c oxidase where two waters and a glutamate (Glu286) that is implicated in the proton translocation mechanism form a cyclic hydrogen bonded structure. Protonation of the glutamate is found to occur in agreement with experimental results.

Critical evaluation of approximate quantum decoherence rates for an electronic transition in methanol solution

We present a quantum molecular dynamics calculation of a semiclassical decoherence function to evaluate the accuracy of alternative short-time approximations for coherence loss in the dynamics of condensed phase electronically nonadiabatic processes. The semiclassical function from mixed quantum-classical molecular dynamics simulations and frozen Gaussian wave packets is computed for the electronic transition of an excited state excess electron to the ground state in liquid methanol. The decoherence function decays on a 10 fs time scale that is qualitatively similar to the aqueous case. We demonstrate that it is the motion of the hydrogen atom, and, in particular, the hydrogen rotation around the oxygen-methyl bond which is predominantly responsible for destroying the quantum correlations between alternative states. Multiple time scales due to the slower diffusive nuclear modes, which dominate the solvation response of methanol, do not contribute to the coherence loss. The choice of the coordinate representation is investigated in detail and concluded to be irrelevant to the decay. Changes in both nuclear momenta and positions on the two alternative potential surfaces are found to contribute to decoherence, the former dominating at short times (t < 5 fs), the latter controlling the decay at longer times. Various short-time approximations to the full dynamics for the decoherence function are tested for the first time. The present treatment rigorously develops the short-time description and establishes its range of validity. Whereas the lowest-order short-time approximation proves to be a very good approximation up to about 5 fs, we also find that it bounds the decay of the decoherence function. After 5 fs, the coherence decay in fact becomes faster than the single Gaussian predicted in the lowest-order short-time limit. This decay is well reflected by an enhanced low-order approximation, which is also easily computed from equilibrium classical forces.

Dynamics of chemical processes in polar solvents

Understanding solution-phase chemistry requires a microscopic description of the electronic structure of the reacting molecules, and of the complex influence of the solvent medium on the reaction energetics and dynamics. Processes involving reactant charge-transfer are of particular importance in chemistry and biochemistry, and are strongly influenced by polar media. Recent advances in experimental ultrafast laser spectroscopy and in computer simulation are working together to provide insight into the underlying molecular principles governing this class of processes in solution.