Quantum dynamical simulations of nonadiabatic processes: Solvation dynamics of the hydrated electron

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.

Dephasing and Decoherence in Vibrational and Electronic Line Shapes

Absorption and emission line shapes of vibrational and electronic transitions in liquids are broadened by interactions with the "bath" (in this case, the rotational and translational degrees of freedom of all the molecules in the liquid). If these degrees of freedom are treated classically, the broadening process is often known as dephasing. If, on the other hand, the bath degrees of freedom are instead treated quantum mechanically, there is additional broadening due to what is known in the chemical-physics literature as decoherence. The question addressed in this paper is the relative importance of decoherence (bath quantum effects) and dephasing. We present general developments of this subject for absorption and emission line shapes, discover several new relationships connecting classical and quantum treatments of the bath, and also consider the Stokes shift (difference in peak frequencies in absorption and emission). We next draw some general conclusions by considering a model system whose transition-frequency time-correlation function has only one bath time scale. We then consider a realistic system of the vibrational OH stretch transition of dilute HOD in liquid D₂O at room temperature. For this system, we conclude that bath quantum effects are not very important, except for the Stokes shift. More generally, we argue that this is the case for many vibrational and most electronic transitions in room-temperature liquids.

Nonadiabatic effects in electronic and nuclear dynamics

Due to their very nature, ultrafast phenomena are often accompanied by the occurrence of nonadiabatic effects. From a theoretical perspective, the treatment of nonadiabatic processes makes it necessary to go beyond the (quasi) static picture provided by the time-independent Schrödinger equation within the Born-Oppenheimer approximation and to find ways to tackle instead the full time-dependent electronic and nuclear quantum problem. In this review, we give an overview of different nonadiabatic processes that manifest themselves in electronic and nuclear dynamics ranging from the nonadiabatic phenomena taking place during tunnel ionization of atoms in strong laser fields to the radiationless relaxation through conical intersections and the nonadiabatic coupling of vibrational modes and discuss the computational approaches that have been developed to describe such phenomena. These methods range from the full solution of the combined nuclear-electronic quantum problem to a hierarchy of semiclassical approaches and even purely classical frameworks. The power of these simulation tools is illustrated by representative applications and the direct confrontation with experimental measurements performed in the National Centre of Competence for Molecular Ultrafast Science and Technology.

Non-Hermitian surface hopping

We present a generalized non-Hermitian equation of motion (nH-EOM) to go beyond standard trajectory surface hopping dynamics. The derivation is based on the Born-Huang expansion of the total wave function and the polar representation of the nuclear factor. The nH-EOM contains two additional terms, a skew symmetry term iΓ with dissipation operator Γ to account for decoherence, and a kinetic-energy renormalization term to account for phase shifts, without destroying the invariance to the choice of representation. Numerically, the nH-EOM can still be solved efficiently using a semiclassical approximation in the framework of Tully's fewest-switches surface hopping (FSSH) algorithm. Applications to model Hamiltonians demonstrate improved performance over the standard FSSH approach, through comparison to exact quantum results.

Interference, fluctuation, and alternation of electron tunneling in protein media. 2. Non-condon theory for the energy gap dependence of electron transfer rate

Developing the quantum transition rate theory of Prezhdo and Rossky (J. Chem. Phys. 1997, 107, 5863), we produced a new non-Condon theory of the rate of electron transfer (ET) which happens through a protein medium with conformational fluctuation. The new theory is expressed by a convolution form of the power spectrum for the autocorrelation function of the electronic tunneling matrix element T(DA)(t) with quantum correction and the ordinary Franck-Condon factor. The new theory satisfies the detailed balance condition for the forward and backward ET rates. The ET rate formula is divided into two terms of elastic and inelastic tunneling mechanisms on the mathematical basis. The present theory is applied to the ET from Bph(-) to Q(A) in the reaction center of Rhodobacter sphaeroides. Numerical calculations of T(DA)(t) were made by a combined method of molecular dynamics simulations and quantum chemistry calculations. We showed that the normalized autocorrelation function of T(DA)(t) is almost expressed by exponential forms. The calculated energy gap law of the ET rate is nearly Marcus' parabola in most of the normal region and around the maximum region, but it does not decay substantially in the inverted region, which is called the anomalous inverted region. We also showed that the energy gap law at the high uphill energy gap in the normal region is elevated considerably from the Marcus' parabola, which is called the anomalous normal region. Those anomalous energy gap laws are due to the inelastic tunneling mechanism which works actively at the energy gap far from zero. We presented an empirical formula for easily calculating the non-Condon ET rate, which is usable by many researchers. We provided experimental evidence for the anomalous inverted region which was basically reproduced by the present theory. The present theory was extensively compared with the previous non-Condon theories.

Excess electron relaxation dynamics at water/air interfaces

We have performed mixed quantum-classical molecular dynamics simulations of the relaxation of a ground state excess electron at interfaces of different phases of water with air. The investigated systems included ambient water/air, supercooled water/air, Ih ice/air, and amorphous solid water/air interfaces. The present work explores the possible connections of the examined interfacial systems to finite size cluster anions and the three-dimensional infinite, fully hydrated electron. Localization site analyses indicate that in the absence of nuclear relaxation the electron localizes in a shallow potential trap on the interface in all examined systems in a diffuse, surface-bound (SB) state. With relaxation, the weakly bound electron undergoes an ultrafast localization and stabilization on the surface with the concomitant collapse of its radius. In the case of the ambient liquid interface the electron slowly (on the 10 ps time scale) diffuses into the bulk to form an interior-bound state. In each other case, the excess electron persists on the interface in SB states. The relaxation dynamics occur through distinct SB structures which are easily distinguishable by their energetics, geometries, and interactions with the surrounding water bath. The systems exhibiting the most stable SB excess electron states (supercooled water/air and Ih ice/air interfaces) are identified by their characteristic hydrogen-bonding motifs which are found to contain double acceptor-type water molecules in the close vicinity of the electron. These surface states correlate reasonably with those extrapolated to infinite size from simulated water cluster anions.

Temperature effect on the absorption spectrum of the hydrated electron paired with a lithium cation in deuterated water

The absorption spectra of the hydrated electron in 1.0 to 4.0 M LiCl or LiClO4 deuterated water solutions were measured by pulse radiolysis techniques from room temperature to 300 degrees C at a constant pressure of 25 MPa. The results show that when the temperature is increased and the density is decreased, the absorption spectrum of the electron in the presence of a lithium cation is shifted to lower energies. Quantum classical molecular dynamics (QCMD) simulations of an excess electron in bulk water and in the presence of a lithium cation have been performed to compare with the experimental results. According to the QCMD simulations, the change in the shape of the spectrum is due to one of the three p-like excited states of the solvated electron destabilized by core repulsion. The study of s --> p transition energies for the three p-excited states reveals that for temperatures higher than room temperature, there is a broadening of each individual s --> p absorption band due to a less structured water solvation shell.

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.

Nonadiabatic Molecular Dynamics Simulations of Correlated Electrons in Solution. 1. Full Configuration Interaction (CI) Excited-State Relaxation Dynamics of Hydrated Dielectrons

The hydrated dielectron is composed of two excess electrons dissolved in liquid water that occupy a single cavity; in both its singlet and triplet spin states there is a significant exchange interaction so the two electrons cannot be considered to be independent. In this paper and the following paper,we present the results of mixed quantum/classical molecular dynamics simulations of the nonadiabatic relaxation dynamics of photoexcited hydrated dielectrons, where we use full configuration interaction (CI) to solve for the two-electron wave function at every simulation time step. To the best of our knowledge, this represents the first systematic treatment of excited-state solvation dynamics where the multiple-electron problem is solved exactly. The simulations show that the effects of exchange and correlation contribute significantly to the relaxation dynamics. For example, spin-singlet dielectrons relax to the ground state on a time scale similar to that of single electrons excited at the same energy, but spin-triplet dielectrons relax much faster. The difference in relaxation dynamics is caused by exchange and correlation: The Pauli exclusion principle imposes very different electronic structure when the electrons' spins are singlet paired than when they are triplet paired, altering the available nonadiabatic relaxation pathways. In addition, we monitor how electronic correlation changes dynamically during nonadiabatic relaxation and show that solvent dynamics cause electron correlation to evolve quite differently for singlet and triplet dielectrons. Despite such differences, our calculations show that both spin states are stable to excited-state dissociation, but that the excited-state stability has different origins for the two spin states. For singlet dielectrons, the stability depends on whether the solvent structure can rearrange to create a second cavity before the ground state is reached. For triplet dielectrons, in contrast, electronic correlation ensures that the two electrons do not dissociate, even if the dielectron is artificially kept from reaching the ground state. In addition, both singlet and triplet dielectrons change shape dramatically during relaxation, so that linear response fails to describe the solvation dynamics for either spin state. In the following paper (Larsen, R. E.; Schwartz, B. J. J. Phys. Chem. B 2006, 110, 9692), we use these simulations to calculate the pump-probe spectroscopic signal expected for photoexcited hydrated dielectrons and to predict an experiment to observe hydrated dielectrons directly.

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.

Characterization of solvated electrons in hydrogen cyanide clusters: (HCN)n− (n=3, 4)

Theoretical studies of the solvated electrons (HCN)n- (n=3, 4) reveal a variety of electron trapping possibilities in the (HCN)n (n=3, 4) clusters. Two isomers for (HCN)3- and four isomers for (HCN)4- are obtained at the MP2aug-cc-pVDZ+dBF (diffusive bond functions) level of theory. In view of vertical electron detachment energies (VDEs) at the CCSD(T) level, the excess electron always "prefers" locating in the center of the system, i.e., the isomer with higher coordination number shows larger VDE value. However, the most stable isomers of the solvated electron state (HCN)3- and (HCN)4- are found to be the linear Cinfinitynu and Dinfinityh structures, respectively, but not the fullyl symmetric structures which have the largest VDE values.

Full Configuration Interaction Computer Simulation Study of the Thermodynamic and Kinetic Stability of Hydrated Dielectrons

The hydrated electron is a unique solvent-supported state comprised of an excess electron that is confined to a cavity by the surrounding water. Theoretical studies have suggested that two-electron solvent-supported states also can be formed; in particular, simulations indicate that two excess electrons could pair up and occupy a single cavity, forming a so-called hydrated dielectron. Although hydrated dielectrons have not been observed directly by experiment, their existence has been posited to explain the lack of an ionic strength effect in hydrated electron bimolecular annihilation [Schmidt, K. H.; Bartels, D. M. Chem. Phys. 1995, 190, 145]. To determine whether dielectrons may be created in the laboratory, we use thermodynamic integration (TI), combined with mixed quantum/classical molecular dynamics simulation, to examine the thermodynamic stability of hydrated electrons and dielectrons. For the dielectron calculations, we solve the two-electron quantum problem using full configuration interaction. Our results suggest that hydrated dielectrons are thermodynamically unstable relative to separated (single) hydrated electrons, although we also show that increasing the pressure could drive the equilibrium toward the formation of dielectrons. Because the simulations suggest that hydrated dielectrons are kinetically stable, we also examine a scenario for creating metstable, nonequilibrium populations of dielectrons, which involves the capture of a newly injected electron by a preexisting, equilibrated hydrated electron. These calculations, which allow for the full nonadiabatic relaxation of the injected electron, show that hydrated electrons may indeed act as trapping sites for unequilibrated electrons, so that capture may be a viable mechanism for creating dielectrons. We suggest possible experimental procedures to create such nonequilibrium hydrated dielectrons using either pulse radiolysis or ultrafast spectroscopic techniques.

Electronic Relaxation Dynamics of Water Cluster Anions

The electronic relaxation dynamics of water cluster anions, (H(2)O)(n)(-), have been studied with time-resolved photoelectron imaging. In this investigation, the excess electron was excited through the p<--s transition with an ultrafast laser pulse, with subsequent electronic evolution monitored by photodetachment. All excited-state lifetimes exhibit a significant isotope effect (tau(D)2(O)/tau(H)2(O) approximately 2). Additionally, marked dynamical differences are found for two classes of water cluster anions, isomers I and II, previously assigned as clusters with internally solvated and surface-bound electrons, respectively. Isomer I clusters with n > or = 25 decay exclusively by internal conversion, with relaxation times that extrapolate linearly with 1/n toward an internal conversion lifetime of 50 fs in bulk water. Smaller isomer I clusters (13 < or = n < or = 25) decay through a combination of excited-state autodetachment and internal conversion. The relaxation of isomer II clusters shows no significant size dependence over the range of n = 60-100, with autodetachment an important decay channel following excitation of these clusters. Photoelectron angular distributions (PADs) were measured for isomer I and isomer II clusters. The large differences in dynamical trends, relaxation mechanisms, and PADs between large isomer I and isomer II clusters are consistent with their assignment to very different electron binding motifs.

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.

Electrons in Finite-Sized Water Cavities: Hydration Dynamics Observed in Real Time

We directly observed the hydration dynamics of an excess electron in the finite-sized water clusters of (H2O)n- with n = 15, 20, 25, 30, and 35. We initiated the solvent motion by exciting the hydrated electron in the cluster. By resolving the binding energy of the excess electron in real time with femtosecond resolution, we captured the ultrafast dynamics of the electron in the presolvated ("wet") and hydrated states and obtained, as a function of cluster size, the subsequent relaxation times. The solvation time (300 femtoseconds) after the internal conversion [140 femtoseconds for (H2O)35-] was similar to that of bulk water, indicating the dominant role of the local water structure in the dynamics of hydration. In contrast, the relaxation in other nuclear coordinates was on a much longer time scale (2 to 10 picoseconds) and depended critically on cluster size.