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.     

Solvation dynamics of Hoechst 33258 in water: an equilibrium and nonequilibrium molecular dynamics study

Integrated within an appropriate theoretical framework, molecular dynamics (MD) simulations are a powerful tool to complement experimental studies of solvation dynamics. Together, experiment, theory, and simulation have provided substantial insight into the dynamic behavior of polar solvents. MD investigations of solvation dynamics are especially valuable when applied to the heterogeneous environments found in biological systems, where the calculated response of the environment to the electrostatic perturbation of the probe molecule can easily be decomposed by component (e.g., aqueous solvent, biomolecule, ions), greatly aiding the molecular-level interpretation of experiments. A comprehensive equilibrium and nonequilibrium MD study of the solvation dynamics of the fluorescent dye Hoechst 33258 (H33258) in aqueous solution is presented. Many fluorescent probes employed in experimental studies of solvation dynamics in biological systems, such as the DNA minor groove binder H33258, have inherently more conformational flexibility than prototypical fused-ring chromophores. The role of solute flexibility was investigated by developing a fully flexible force-field for the H33258 molecule and by simulating its solvation response. While the timescales for the total solvation response calculated using both rigid (0.16 and 1.3 ps) and flexible (0.17 and 1.4 ps) models of the probe closely matched the experimentally measured solvation response (0.2 and 1.2 ps), there were subtle differences in the response profiles, including the presence of significant oscillations for the flexible probe. A decomposition of the total response of the flexible probe revealed that the aqueous solvent was responsible for the overall decay, while the oscillations result from fluctuations in the electrostatic terms in the solute intramolecular potential energy. A comparison of equilibrium and nonequilibrium approaches for the calculation of the solvation response confirmed that the solvation dynamics of H33258 in water is well-described by linear response theory for both rigid and flexible models of the probe.     

Vibrational energy relaxation of a diatomic molecule in a room-temperature ionic liquid

Vibrational energy relaxation (VER) dynamics of a diatomic solute in ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI(+)PF(6) (-)) are studied via equilibrium and nonequilibrium molecular dynamics simulations. The time scale for VER is found to decrease markedly with the increasing solute dipole moment, consonant with many previous studies in polar solvents. A detailed analysis of nonequilibrium results shows that for a dipolar solute, dissipation of an excess solute vibrational energy occurs almost exclusively via the Lennard-Jones interactions between the solute and solvent, while an oscillatory energy exchange between the two is mainly controlled by their electrostatic interactions. Regardless of the anharmonicity of the solute vibrational potential, VER becomes accelerated as the initial vibrational energy increases. This is attributed primarily to the enhancement in variations of the solvent force on the solute bond, induced by large-amplitude solute vibrations. One interesting finding is that if a time variable scaled with the initial excitation energy is employed, dissipation dynamics of the excess vibrational energy of the dipolar solute tend to show a universal behavior irrespective of its initial vibrational state. Comparison with water and acetonitrile shows that overall characteristics of VER in EMI(+)PF(6) (-) are similar to those in acetonitrile, while relaxation in water is much faster than the two. It is also found that the Landau-Teller theory predictions for VER time scale obtained via equilibrium simulations of the solvent force autocorrelation function are in reasonable agreement with the nonequilibrium results.     

Measuring the change in the intermolecular Raman spectrum during dipolar solvation

We demonstrate a method to directly measure the change in the spectrum of intermolecular solvent fluctuations as a function of time after electronic excitation of a solute, and this method is applied to the dye Coumarin 102 (C102) in acetonitrile. The complete intermolecular response is captured following resonant excitation with time domain third-order Raman spectroscopy. In a previous report, we introduced this method and used it to probe one point in the intermolecular response as a function of time after solute excitation (Underwood, D. F., Blank, D. A. J. Phys. Chem. A 2003, 107 (7), 956). Here we extend this approach to recover the change in the entire intermolecular response as a function of time. To our knowledge the results provide the first direct measurement of the difference in the equilibrated intermolecular response after excitation of a solute and its evolution during a dipolar solvation event. Excitation of C102 results in a significant increase in the solvent-solute interaction due to a large increase in the dipole moment. The observed change in the intermolecular response is consistent with a rapid change in local solvent density, with intermolecular kinetic energy transfer changing the response on longer time scales. Evolution of the response exhibits a strong frequency dependence and suggests changes over longer distances at longer delay times. The measured change in the spectrum of solvent fluctuations represents a direct experimental confirmation of the breakdown of linear response and confirms predictions from molecular dynamics simulations.     

Solvent structural relaxation dynamics in dipolar solvation studied by resonant pump polarizability response spectroscopy

Resonant pump polarizability response spectroscopy (RP-PORS) was used to study the isotropic and anisotropic solvent structural relaxation in solvation. RP-PORS is the optical heterodyne detected transient grating (OHD-TG) spectroscopy with an additional resonant pump pulse. A resonant pump excites the solute-solvent system and the subsequent relaxation of the solute-solvent system is monitored by the OHD-TG spectroscopy. This experimental method allows measuring the dispersive and absorptive parts of the signal as well as fully controlling the beam polarizations of incident pulses and signal. The experimental details of RP-PORS were described. By performing RP-PORS with Coumarin 153(C153) in CH(3)CN and CHCl(3), we have successfully measured the isotropic and anisotropic solvation polarizability spectra following electronic excitation of C153. The isotropic solvation polarizability responses result from the isotropic solvent structural relaxation of the solvent around the solute whereas the anisotropic solvation polarizability responses come from the anisotropic translational relaxation and orientational relaxation. The solvation polarizability responses were found to be solvent-specific. The intramolecular vibrations of CHCl(3) were also found to be coupled to the electronic excitation of C153.     

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.     

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.     

Solvation and rotational dynamics of coumarin 153 in ionic liquids: comparisons to conventional solvents

Steady-state and time-resolved emission spectroscopy with 25 ps resolution are used to measure equilibrium and dynamic aspects of the solvation of coumarin 153 (C153) in a diverse collection of 21 room-temperature ionic liquids. The ionic liquids studied here include several phosphonium and imidazolium liquids previously reported as well as 12 new ionic liquids that incorporate two homologous series of ammonium and pyrrolidinium cations. Steady-state absorption and emission spectra are used to extract solvation free energies and reorganization energies associated with the S0 <--> S1 transition of C153. These quantities, especially the solvation free energy, vary relatively little in ionic liquids compared to conventional solvents. Some correlation is found between these quantities and the mean separation between ions (or molar volume). Time-resolved anisotropies are used to observe solute rotation. Rotation times measured in ionic liquids correlate with solvent viscosity in much the same way that they do in conventional polar solvents. No special frictional coupling between the C153 and the ionic liquid solvents is indicated by these times. But, in contrast to what is observed in most low-viscosity conventional solvents, rotational correlation functions in ionic liquids are nonexponential. Time-resolved Stokes shift measurements are used to characterize solvation dynamics. The solvation response functions in ionic liquids are also nonexponential and can be reasonably represented by stretched-exponential functions of time. The solvation times observed are correlated with the solvent viscosity, and the much slower solvation in ionic liquids compared to dipolar solvents can be attributed to their much larger viscosities. Solvation times of the majority of ionic liquids studied appear to follow a single correlation with solvent viscosity. Only liquids incorporating the largest phosphonium cation appear to follow a distinctly different correlation.     

Electronic excitation energies of molecules in solution: state specific and linear response methods for nonequilibrium continuum solvation models

We present a formal comparison between the two different approaches to the calculation of electronic excitation energies of molecules in solution within the continuum solvation model framework, taking also into account nonequilibrium effects. These two approaches, one based on the explicit evaluation of the excited state wave function of the solute and the other based on the linear response theory, are here proven to give formally different expressions for the excitation energies even when exact eigenstates are considered. Calculations performed for some illustrative examples show that this formal difference has sensible effects on absolute solvatochromic shifts (i.e., with respect to gas phase) while it has small effects on relative (i.e., nonpolar to polar solvent) solvatochromic shifts.     

Continuous medium theory for nonequilibrium solvation: I. How to correctly evaluate solvation free energy of nonequilibrium

Considering the influences of electrostatic potential Phi upon the change of solute charge distribution deltarho and rho upon the change deltaPhi at the same time, a more reasonable integral formula of dG = (1/2) integral (V) (rhodeltaPhi + Phideltarho)dV is used to calculate the change of the electrostatic free energy in charging the solute-solvent system to a nonequilibrium state, instead of the one of dG = integral (V) PhideltarhodV used before. This modification improves the expressions of electrostatic free energy and solvation free energy, in which no quantity of the intermediate equilibrium state is explicitly involved. Detailed investigation reveals that the solvation free energy of nonequilibrium only contains the interaction energy between the field due to the solute charge in vacuum, and the dielectric polarization at the nonequilibrium state. The solvent reorganization energies of forward and backward electron transfer reactions have been redefined because the derivations lead to a remarkable feature that these quantities are direction-dependent, unlike the theoretical models developed before. The deductions are given in the electric field-displacement form. Relevant discussions on the reliability of theoretical models suggested in this work have also been presented.     

Symmetry-dependent solvation of donor-substituted triarylboranes

Donor-substituted triarylboranes are investigated by femtosecond absorption spectroscopy to study the influence of molecular symmetry on solvation. In solvents of varying polarity and differently fast solvation response, the solvation dynamics of a highly symmetric triple carbazole-substituted triarylborane (TCB) is compared to a single carbazole-substituted triarylborane (CB). The decomposition of the transient absorption spectra allows us to measure the solvation time by means of the time-dependent solvatochromic shift of the excited-state absorption (ESA) and the stimulated emission (SE). For all polar solvents under study we find an accelerated solvation process for TCB compared to the less symmetric CB. The difference is particularly large for solvents with a slow response. In order to explain these findings we propose that the electronic excitation is mobile in the symmetric molecule and can change between the three carbazole chromophores probably by a hopping mechanism. The excited-state dipole moment of TCB can thereby respond to the solvent relaxation and changes its direction according to the local field of the solvation shell. Thus, in a symmetric solute the possibility of an intramolecular charge delocalization over equivalent sites accelerates the approach of the minimum-energy configuration.     

Two-dimensional measurements of the solvent structural relaxation dynamics in dipolar solvation

Resonant-pump polarizability response spectroscopy (RP-PORS) is based on an optical heterodyne detected transient grating (OHD-TG) method with an additional resonant pump pulse. In RP-PORS, the resonant pump pulse excites the solute-solvent system and the subsequent relaxation of the solute-solvent system is monitored by the OHD-TG spectroscopy. RP-PORS is shown to be an excellent experimental tool to directly measure the solvent responses in solvation. In the present work, we extended our previous RP-PORS (Park et al., Phys. Chem. Chem. Phys., 2011, 13, 214-223) to measure time-dependent transient solvation polarizability (TSP) spectra with Coumarin153 (C153) in acetonitrile. The time-dependent TSP spectra showed how the different solvent intermolecular modes were involved in different stages of the solvation process. Most importantly, the inertial and diffusive components of the solvent intermolecular modes in solvation were found to be spectrally and temporally well-separated. In a dipolar solvation of C153, high-frequency inertial solvent modes were found to be driven instantaneously and decay on a subpicosecond timescale while low-frequency diffusive solvent modes were induced slowly and decayed on a picosecond timescale. Our present result is the first experimental manifestation of frequency-dependent solvent intermolecular response in a dipolar solvation.     

Absorption and emission lineshapes and solvation dynamics of NO in supercritical Ar

We perform a theoretical study of electronic spectroscopy of dilute NO in supercritical Ar fluid. Absorption and emission lineshapes for the A(2)Sigma(+)<--X(2)Pi Rydberg transition of NO in argon have been previously measured and simulated, which yielded results for the NO/Ar ground- and excited-state pair potentials [Larregaray et al., Chem. Phys. 308, 13 (2005)]. Using these potentials, we have performed molecular dynamics simulations and theoretical statistical mechanical calculations of absorption and emission lineshapes and nonequilibrium solvation correlation functions for a wide range of solvent densities and temperatures. Theory was shown to be in good agreement with simulation. Linear response treatment of solvation dynamics was shown to break down at near-critical temperature due to dramatic change in the solute-solvent microstructure upon solute excitation to the Rydberg state and the concomitant increase of the solute size.     

Nonequilibrium solvation for vertical photoemission and photoabsorption processes using the symmetry-adapted cluster-configuration interaction method in the polarizable continuum model

In this paper, we present the theory and implementation of a nonequilibrium solvation model for the symmetry-adapted cluster (SAC) and symmetry-adapted cluster-configuration interaction (SAC-CI) method in the polarizable continuum model. For nonequilibrium solvation, we adopted the Pekar partition scheme in which solvent charges are divided into dynamical and inertial components. With this nonequilibrium solvation scheme, a vertical transition from an initial state to a final state may be described as follows: the initial state is described by equilibrium solvation, while in the final state, the inertial component remains in the solvation for the initial state; the dynamical component will be calculated self-consistently for the final state. The present method was applied to the vertical photoemission and absorption of s-trans acrolein and methylenecyclopropene. The effect of nonequilibrium solvation was significant for a polar solvent.     

Molecular density functional theory of solvation: from polar solvents to water

A classical density functional theory approach to solvation in molecular solvent is presented. The solvation properties of an arbitrary solute in a given solvent, both described by a molecular force field, can be obtained by minimization of a position and orientation-dependent free-energy density functional. In the homogeneous reference fluid approximation, limited to two-body correlations, the unknown excess term of the functional approximated by the angular-dependent direct correlation function of the pure solvent. We show that this function can be extracted from a preliminary MD simulation of the pure solvent by computing the angular-dependent pair distribution function and solving subsequently the molecular Ornstein-Zernike equation using a discrete angular representation. The corresponding functional can then be minimized in the presence of an arbitrary solute on a three-dimensional cubic grid for positions and Gauss-Legendre angular grid for orientations to provide the solvation structure and free-energy. This two-step procedure is proved to be much more efficient than direct molecular dynamics simulations combined to thermodynamic integration schemes. The approach is shown to be relevant and accurate for prototype polar solvents such as the Stockmayer solvent or acetonitrile. For water, although correct for neutral or moderately charged solute, it tends to underestimate the tetrahedral solvation structure around H-bonded solutes, such as spherical ions. This can be corrected by introducing suitable three-body correlation terms that restore both an accurate hydration structure and a satisfactory energetics.     

A time-dependent polarizable continuum model: theory and application

This work presents an extention of the polarizable continuum model to explicitly describe the time-dependent response of the solvent to a change in the solute charge distribution. Starting from an initial situation in which solute and solvent are in equilibrium, we are interested in modeling the time-dependent evolution of the solvent response, and consequently of the solute-solvent interaction, after a perturbation in this equilibrium situation has been switched on. The model introduces an explicit time-dependent treatment of the polarization by means of the linear-response theory. Two strategies are tested to account for this time dependence: the first one employs the Debye model for the dielectric relaxation, which assumes an exponential decay of the solvent polarization; the second one is based on a fitting of the experimental data of the solvent complex dielectric permittivity. The first approach is simpler and possibly less accurate but allows one to write an analytic expression of the equations. By contrast, the second approach is closer to the experimental evidence but it is limited to the availability of experimental data. The model is applied to the ionization process of N,N-dimethyl-aniline in both acetonitrile and water. The nonequilibrium free-energy profile is studied both as a function of the solvent relaxation coordinate and as a function of time. The solvent reorganization energy is evaluated as well.     

Solution reaction space Hamiltonian based on an electrostatic potential representation of solvent dynamics

Quantum chemical solvation models usually rely on the equilibrium solvation condition and is thus not immediately applicable to the study of nonequilibrium solvation dynamics, particularly those associated with chemical reactions. Here we address this problem by considering an effective Hamiltonian for solution-phase reactions based on an electrostatic potential (ESP) representation of solvent dynamics. In this approach a general ESP field of solvent is employed as collective solvent coordinate, and an effective Hamiltonian is constructed by treating both solute geometry and solvent ESP as dynamical variables. A harmonic bath is then attached onto the ESP variables in order to account for the stochastic nature of solvent dynamics. As an illustration we apply the above method to the proton transfer of a substituted phenol-amine complex in a polar solvent. The effective Hamiltonian is constructed by means of the reference interaction site model self-consistent field method (i.e., a type of quantum chemical solvation model), and a mixed quantum/classical simulation is performed in the space of solute geometry and solvent ESP. The results suggest that important dynamical features of proton transfer in solution can be captured by the present approach, including spontaneous fluctuations of solvent ESP that drives the proton from reactant to product potential wells.