Understanding Nonequilibrium Solute and Solvent Motions through Molecular Projections: Computer Simulations of Solvation Dynamics in Liquid Tetrahydrofuran (THF)

Explicit Projection of Stokes Shifts onto Solvent Motion in an Aqueous Liquid and Linear Response Theory

We investigate the molecular origin of the fluorescence Stokes shift in an aqueous liquid. By examining the speed of energy change, the solvation response function is explicitly projected onto the translational and rotational motions of water molecules for both nonequilibrium relaxation and equilibrium fluctuations. Molecular dynamics simulations of a tryptophan solution show that these two processes have highly consistent dynamics, not only for the total response function but also for the decomposed components in terms of specific molecular movements. We found that the rotational mode governs the relaxation of the Stokes shift, whereas the translational mode contributes non-negligibly with slower dynamics. This consistency implies the similarity of the underlying translational and rotational movements of water molecules as the system is far away from and at equilibrium, supporting the validity of the linear response theory at the molecular level. The decomposition methodology is also applicable to a rigid solvent.

Understanding the Liquid States of Cyclic Hydrocarbons Containing N, O, and S Atoms via the 3D-RISM-KH Molecular Solvation Theory

The 3D-reference interaction site model (3D-RISM) molecular solvation theory in combination with the Kovalenko-Hirata (KH) closure is extended to seven heterocyclic liquids to understand their liquid states and to test the performance of the theory in solvation free energy (SFE) calculations of solutes in select solvents. The computed solvent site distribution profiles were compared with the all-atom molecular dynamics (MD) simulations, showing comparable performances. The computational results were compared against the structural parameters for liquids, whenever available, as well as against the experimental SFEs. The liquids are found to have local ordered structures held together via weak interactions in both the RISM and MD simulations. The 3D-RISM-KH computed SFEs are in good agreement with the benchmark values for the tetrahydrothiophene-S,S-dioxide, and showed comparatively larger deviations in the case of the SFEs in the tetrahydrofuran continuum.

Effect of solvent motions on the dynamics of the Diels-Alder reaction

How solvent motions affect the dynamics of chemical reactions in which the solute undergoes a substantial shape change is a fundamental but elusive issue. This work utilizes reactive simulation and Grote-Hynes theory to explore the effect of solvent motions on the dynamics of the Diels-Alder reaction (in the reverse direction, this reaction involves very substantial solute expansion) in aprotic solvents. The results reveal that the solvent environment is not sufficiently constraining to influence transition state passage dynamics, with the calculated transmission coefficients being close to unity. Even when solvent motions are suppressed or artificially slowed down, the solvent only affects the reaction dynamics in the transition state region to a very small extent. The only notable effect of solvent occurs far from the transition state region and corresponds to caging of the reactants within the reactant well.

Solvation Dynamics in Water. 4. On the Initial Regime of Solvation Relaxation

It is shown, by means of numerical and analytic work, that initial molecular momenta play little significant role in the initial fast solvation relaxation that follows electronic excitation of, and charge creation for, a standard model system of a solute in water. Instead, the nonequilibrium dynamics are predominantly described by noninertial "steering" by the torques directly generated by the newly created charge distribution. It is this process that largely overcomes inertia and drives the relaxation dynamics on a time scale of a few tens of femtoseconds in the key initial regime of the dynamics. These results are discussed in the context of commonly employed descriptions such as inertial, Gaussian, and underdamped dynamical behavior.

Time-Resolved Probing of the Nonequilibrium Structural Solvation Dynamics by the Time-Dependent Stokes Shift

The time-dependent fluorescence Stokes shift monitors the relaxation of the polarization of a polar solvent in the surroundings of a photoexcited solute molecule but also the structural variation of the solute following photoexcitation and the subsequent molecular charge redistribution. Here, we formulate a simple nonequilibrium quantum theory of solvation for an explicitly time-dependent continuous solvent. The time-dependent solvent induces nonequilibrium fluctuations on the solvent dynamics which are directly reflected in different time components in the time-dependent Stokes shift. We illustrate the structural dynamics in the presence of an explicitly time-dependent solvent by the example of a dynamically shrinking solute which leads to a bimodal Stokes shift. Interestingly, both contributions are mutually coupled. Furthermore, we can explain a prominent long-tail decay of the Stokes shift associated with slow structural dynamical variations.

Polarizability in ionic liquid simulations causes hidden breakdown of linear response theory

The validity of linear response theory (LRT) in computer simulations of solvation dynamics, i.e. the time-dependent Stokes shift, has been debated widely during the last decades. Since the use of LRT is computationally less expensive than the calculation of the true nonequilibrium response, it is often invoked for large systems exhibiting a particularly slow solvation response, e.g. ionic liquids. In the case of ionic liquids, LRT does not only need to capture the correct overall dynamics of the system, but also the contributions and timescales of the respective cation and anion movement. We show by large scale computer simulations that the contribution of the permanent dipoles to the solvation response obeys LRT to some extent, whereas the induced contributions in polarizable simulations lead to a failure of LRT for the respective ion contributions.

Solvents can control solute molecular identity

For solution-phase chemical reactions, the solvent is often considered simply as a medium to allow the reactants to encounter each other by diffusion. Although examples of direct solvent effects on molecular solutes exist, such as the compression of solute bonding electrons due to Pauli repulsion interactions, the solvent is not usually considered a part of the chemical species of interest. We show, using quantum simulations of Na₂, that when there are local specific interactions between a solute and solvent that are energetically on the same order as a hydrogen bond, the solvent controls not only the bond dynamics but also the chemical identity of the solute. In tetrahydrofuran, dative bonding interactions between the solvent and Na atoms lead to unique coordination states that must cross a free energy barrier of ~8 k_BT-undergoing a chemical reaction-to interconvert. Each coordination state has its own dynamics and spectroscopic signatures, highlighting the importance of considering the solvent in the identity of condensed-phase chemical systems.

Solvation dynamics in polar solvents and imidazolium ionic liquids: failure of linear response approximations

This study presents the large scale computer simulations of two common fluorophores, N-methyl-6-oxyquinolinium betaine and coumarin 153, in five polar or ionic solvents. The validity of linear response approximations to calculate the time-dependent Stokes shift is evaluated in each system. In most studied systems linear response theory fails. In ionic liquids the magnitude of the overall response is largely overestimated, and linear response theory is not able to capture the individual contributions of cations and anions. In polar liquids, the timescales of solvation dynamics are often not correctly reproduced. These observations are complemented by a detailed analysis of Gaussian statistics including higher order correlation functions, variance of the energy gap distribution and its time evolution. The analysis of higher order correlation functions was found to be not suitable to predict a failure of linear response theory. Further analysis of radial distribution functions and hydrogen bonds in the ground and excited state, as well as the time evolution of the number of hydrogen bonds after solute excitation reveal an influence of solvent structure in some of the studied systems.

Solvation Dynamics in Liquid Water. III. Energy Fluxes and Structural Changes

In previous installments it has been shown how a detailed analysis of energy fluxes induced by electronic excitation of a solute can provide a quantitative understanding of the dominant molecular energy flow channels characterizing solvation-and in particular, hydration- relaxation dynamics. Here this work and power approach is complemented with a detailed characterization of the changes induced by such energy fluxes. We first examine the water solvent's spatial and orientational distributions and the assorted energy fluxes in the various hydration shells of the solute to provide a molecular picture of the relaxation. The latter analysis is also used to address the issue of a possible "inverse snowball" effect, an ansatz concerning the time scales of the different hydration shells to reach equilibrium. We then establish a link between the instantaneous torque, exerted on the water solvent neighbors' principal rotational axes immediately after excitation and the final energy transferred into those librational motions, which are the dominant short-time energy receptor.

Critical analysis of the accuracy of models predicting or extracting liquid structure information

This work aims at a critical assessment of properties predicting or extracting information on the density and structure of liquids. State-of-the-art NVT and NpT molecular dynamics (MD) simulations have been performed on five liquids: methanol, chloroform, acetonitrile, tetrahydrofuran, and ethanol. These simulations allow the computation of properties based on first principles, including the equilibrium density and radial distribution functions (RDFs), characterizing the liquid structure. Refinements have been incorporated in the MD simulations by taking into account basis set superposition errors (BSSE). An extended BSSE model for an instantaneous evaluation of the BSSE corrections has been proposed, and their impact on the liquid properties has been assessed. If available, the theoretical RDFs have been compared with the experimentally derived RDFs. For some liquids, significant discrepancies have been observed, and a profound but critical investigation is presented to unravel the origin of these deficiencies. This discussion is focused on tetrahydrofuran where the experiment reveals some prominent peaks completely missing in any MD simulation. Experiments providing information on liquid structure consist mainly of neutron diffraction measurements offering total structure factors as the primary observables. The splitting of these factors in reciprocal space into intra- and intermolecular contributions is extensively discussed, together with their sensitivity in reproducing correct RDFs in coordinate space.

Simulating the formation of sodium:electron tight-contact pairs: watching the solvation of atoms in liquids one molecule at a time

The motions of solvent molecules during a chemical transformation often dictate both the dynamics and the outcome of solution-phase reactions. However, a microscopic picture of solvation dynamics is often obscured by the concerted motions of numerous solvent molecules that make up a condensed-phase environment. In this study, we use mixed quantum/classical molecular dynamics simulations to furnish the molecular details of the solvation dynamics that leads to the formation of a sodium cation-solvated electron contact pair, (Na(+), e(-)), in liquid tetrahydrofuran following electron photodetachment from sodide (Na(-)). Our simulations reveal that the dominant solvent response is comprised of a series of discrete solvent molecular events that work sequentially to build up a shell of coordinating THF oxygen sites around the sodium cation end of the contact pair. With the solvent response described in terms of the sequential motion of single molecules, we are then able to compare the calculated transient absorption spectroscopy of the sodium species to experiment, providing a clear microscopic interpretation of ultrafast pump-probe experiments on this system. Our findings suggest that for solute-solvent interactions similar to the ones present in our study, the solvation dynamics is best understood as a series of kinetic events consisting of reactions between chemically distinct local structures in which key solvent molecules must be considered to be part of the identity of the reacting species.

On the connection between Gaussian statistics and excited-state linear response for time-dependent fluorescence

Time-dependent fluorescence (TDF) of a chromophore in a polar or nonpolar solvent is frequently simulated using linear-response approximations. It is shown that one such linear-response-type approximation for the TDF Stokes shift derived by Carter and Hynes [J. Chem. Phys. 94, 5961 (1991)] that is based on excited-state dynamics gives the same result as that obtained by assuming Gaussian statistics for the energy gap. The derivation provides insight into the much discussed relationship between linear response and Gaussian statistics. In particular, subtle but important differences between the two approximations are illuminated that suggest that the result is likely more generally applicable than suggested by the usual linearization procedure. In addition, the assumption of Gaussian statistics directly points to straightforward checks of the validity of the approximation with essentially no additional computational effort.

Watching Na Atoms Solvate into (Na+,e-) Contact Pairs: Untangling the Ultrafast Charge-Transfer-to-Solvent Dynamics of Na- in Tetrahydrofuran (THF)

With the large dye molecules employed in typical studies of solvation dynamics, it is often difficult to separate the intramolecular relaxation of the dye from the relaxation associated with dynamic solvation. One way to avoid this difficulty is to study solvation dynamics using an atom as the solvation probe; because atoms have only electronic degrees of freedom, all of the observed spectroscopic dynamics must result from motions of the solvent. In this paper, we use ultrafast transient absorption spectroscopy to investigate the solvation dynamics of newly created sodium atoms that are formed following the charge transfer to solvent (CTTS) ejection of an electron from sodium anions (sodide) in liquid tetrahydrofuran (THF). Because the absorption spectra of the sodide reactant, the sodium atom, and the solvated electron products overlap, we first examined the dynamics of the ejected CTTS electron in the infrared to build a detailed model of the CTTS process that allowed us to subtract the spectroscopic contributions of the sodide bleach and the solvated electron and cleanly reveal the spectroscopy of the solvated atom. We find that the neutral sodium species created following CTTS excitation of sodide initially absorbs near 590 nm, the position of the gas-phase sodium D-line, suggesting that it only weakly interacts with the surrounding solvent. We then see a fast solvation process that causes a red-shift of the sodium atom's spectrum in approximately 230 fs, a time scale that matches well with the results of MD simulations of solvation dynamics in liquid THF. After the fast solvation is complete, the neutral sodium atoms undergo a chemical reaction that takes place in approximately 740 fs, as indicated by the observation of an isosbestic point and the creation of a species with a new spectrum. The spectrum of the species created after the reaction then red-shifts on a approximately 10-ps time scale to become the equilibrium spectrum of the THF-solvated sodium atom, which is known from radiation chemistry experiments to absorb near approximately 900 nm. There has been considerable debate as to whether this 900-nm absorbing species is better thought of as a solvated atom or a sodium cation:solvated electron contact pair, (Na+,e-). The fact that we observe the initially created neutral Na atom undergoing a chemical reaction to ultimately become the 900-nm absorbing species suggests that it is better assigned as (Na+,e-). The approximately 10-ps solvation time we observe for this species is an order of magnitude slower than any other solvation process previously observed in liquid THF, suggesting that this species interacts differently with the solvent than the large molecules that are typically used as solvation probes. Together, all of the results allow us to build the most detailed picture to date of the CTTS process of Na- in THF as well as to directly observe the solvation dynamics associated with single sodium atoms in solution.

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.

Projections of quantum observables onto classical degrees of freedom in mixed quantum-classical simulations: understanding linear response failure for the photoexcited hydrated electron

We present a general analytic method for understanding how specific motions of a classical bath influence the dynamics of quantum-mechanical observables in mixed quantum-classical molecular dynamics simulations. We apply our method and develop expressions for the special case of quantum solvation, allowing us to examine how specific classical solvent motions couple to the equilibrium energy fluctuations and nonequilibrium energy relaxation of a quantum-mechanical solute. As a first application of our formalism, we investigate the motions of classical water underlying the equilibrium and nonequilibrium excited-state solvent response functions of the hydrated electron; the results allow us to explain why the linear response approximation fails for this system.

The molecular origins of nonlinear response in solute energy relaxation: The example of high-energy rotational relaxation

A key step in solution-phase chemical reactions is often the removal of excess internal energy from the product. Yet, the way one typically studies this process is to follow the relaxation of a solute that has been excited into some distribution of excited states quite different from that produced by any reaction of interest. That the effects of these different excitations can frequently be ignored is a consequence of the near universality of linear-response behavior, the idea that relaxation dynamics is determined by the solvent fluctuations (which may not be all that different for different kinds of solute excitation). Nonetheless, there are some clear examples of linear-response breakdowns seen in solute relaxation, including a recent theoretical and experimental study of rapidly rotating diatomics in liquids. In this paper we use this rotational relaxation example to carry out a theoretical exploration of the conditions that lead to linear-response failure. Some features common to all of the linear-response breakdowns studied to date, including our example, are that the initial solute preparation is far from equilibrium, that the subsequent relaxation promotes a significant rearrangement of the liquid structure, and that the nonequilibrium response is nonstationary. However, we show that none of these phenomena is enough to guarantee a nonlinear response. One also needs a sufficient separation between the solute time scale and that of the solvent geometry evolution. We illustrate these points by demonstrating precisely how our relaxation rate is tied to our liquid-structural evolution, how we can quantitatively account for the initial nonstationarity of our effective rotational friction, and how one can tune our rotational relaxation into and out of linear response.

Solvation in supercritical water

Solvation in supercritical water under equilibrium and nonequilibrium conditions is studied via molecular dynamics simulations. The influence of solute charge distributions and solvent density on the solvation structures and dynamics is examined with a diatomic probe solute molecule. It is found that the solvation structure varies dramatically with the solute dipole moment, especially in low-density water, in accord with many previous studies on ion solvation. This electrostrictive effect has important consequences for solvation dynamics. In the case of a nonequilibrium solvent relaxation, if there are sufficiently many water molecules close to the solute at the outset of the relaxation, the solvent response measured as a dynamic Stokes shift is almost completely governed by inertial rotations of these water molecules. By contrast, in the opposite case of a low local solvent density near the solute, not only rotations but also translations of water molecules play an important role in solvent relaxation dynamics. The applicability of a linear response is found to be significantly restricted at low water densities.

Dynamics of Photoinduced Electron Transfer in a Molecular Donor−Acceptor Quartet

The electronic structures and dynamics of photoinduced charge separation and recombination in a new donor/acceptor quartet molecule with bis-oligothiophene (BOTH) and bis-perylenediimide (BPDI) blocks attached to a benzene ring were described. Detailed transient spectroscopic studies were carried out on this compound and reference compounds at isolated molecular levels in solution. Two different dynamics of charge separation and recombination associated with two types of donor/acceptor pair conformations in solution were observed. These results were discussed based on Marcus theory and ascribed to both through-bond and through-space electron-transfer processes associated with two different orientations of the acceptors relative to the donor group. This molecular system exhibits a more efficient charge separation than charge recombination processes in both polar and nonpolar organic solvents, indicating that the material is an interesting candidate for photovoltaic studies in solid state.

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.

The Structure of Liquid Tetrahydrofuran

Hydrogen/deuterium isotopic substitution neutron diffraction techniques have been used to measure the structural correlation functions of liquid tetrahydrofuran at room temperature. Empirical potential structure refinement (EPSR) has been used to build a three-dimensional model of the liquid structure that is consistent with the experimental data. Analysis to the level of the orientational correlation functions shows that the liquid displays a preference for T-like configurations between the tetrahydrofuran molecules, a local structure that results in void-like regions of approximately 1.25 angstroms radius within the bulk liquid. The surface chemistry of these voids suggests a slightly positive electrostatic character. These findings are consistent with the known propensity of the liquid to solvate free electrons.

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.

A molecular dynamics computer simulation study of room-temperature ionic liquids. II. Equilibrium and nonequilibrium solvation dynamics

The molecular dynamics (MD) simulation study of solvation structure and free energetics in 1-ethyl-3-methylimidazolium chloride and 1-ethyl-3-methylimidazolium hexafluorophosphate using a probe solute in the preceding article [Y. Shim, M. Y. Choi and H. J. Kim, J. Chem. Phys. 122, 044510 (2005)] is extended to investigate dynamic properties of these liquids. Solvent fluctuation dynamics near equilibrium are studied via MD and associated time-dependent friction is analyzed via the generalized Langevin equation. Nonequilibrium solvent relaxation following an instantaneous change in the solute charge distribution and accompanying solvent structure reorganization are also investigated. Both equilibrium and nonequilibrium solvation dynamics are characterized by at least two vastly different time scales--a subpicosecond inertial regime followed by a slow diffusive regime. Solvent regions contributing to the subpicosecond nonequilibrium relaxation are found to vary significantly with initial solvation configurations, especially near the solute. If the solvent density near the solute is sufficiently high at the outset of the relaxation, subpicosecond dynamics are mainly governed by the motions of a few ions close to the solute. By contrast, in the case of a low local density, solvent ions located not only close to but also relatively far from the solute participate in the subpicosecond relaxation. Despite this difference, linear response holds reasonably well in both ionic liquids.