Ultrafast solvent dynamics: Connection between time resolved fluorescence and optical Kerr measurements

Energy Dissipation into the Solvent during Proton Transfer Occurs via Acoustic Phonons

In photochemistry, rapid energy dissipation into the solvent is mandatory to prevent radiation damages. By optical pump THz spectroscopy, we are able to follow the details of the energy dissipation mechanism upon photoexcitation of the photoacid to the hydrogen-bonded network of water: Based on the frequency maps subsequent to photoexcitation, we propose that energy transfer takes place via propagation of an acoustic phonon. The dissipation into the solvent can be rationalized by an initial first hydration shell response followed by energy dissipation via an acoustic phonon. Surprisingly, for the first 10 ps, the propagation in the water network can be described by a wave packet with a constant group velocity, indicating a long-range correlation. After 300 ps, thermalization in the liquid jet is reached and the THz spectrum reflects a Boltzmann population, corresponding a temperature increase of ΔT = 0.5 °C.

The Influence of Electronic Polarization on Nonlinear Optical Spectroscopy

The environment surrounding a chromophore can dramatically affect the energy absorption and relaxation process, as manifested in optical spectra. Simulations of nonlinear optical spectroscopy, such as two-dimensional electronic spectroscopy (2DES) and transient absorption (TA), will be influenced by the computational model of the environment. We here compare a fixed point charge molecular mechanics model and a quantum mechanical (QM) model of the environment in computed 2DES and TA spectra of Nile red in water and the chromophore of photoactive yellow protein (PYP) in water and protein environments. In addition to simulating these nonlinear optical spectra, we directly juxtapose the computed excitation energy correlation function to the dynamic Stokes shift function often used to analyze environment dynamics. Overall, we find that for the three systems studied here the mutual electronic polarization provided by the QM environment manifests in broader 2DES signals, as well as a larger reorganization energy and a larger static Stokes shift due to stronger coupling between the chromophore and the environment.

Ultrafast vibrational dynamics of a solute correlates with dynamics of the solvent

Two-dimensional infrared (2D-IR) spectroscopy is used to measure the spectral dynamics of the metal carbonyl complex cyclopentadienyl manganese tricarbonyl (CMT) in a series of linear alkyl nitriles. 2D-IR spectroscopy provides direct readout of solvation dynamics through spectral diffusion, probing the decay of frequency correlation induced by fluctuations of the solvent environment. 2D-IR simultaneously monitors intramolecular vibrational energy redistribution (IVR) among excited vibrations, which can also be influenced by the solvent through the spectral density rather than the dynamical friction underlying solvation. Here, we report that the CMT vibrational probe reveals solvent dependences in both the spectral diffusion and the IVR time scales, where each slows with increased alkyl chain length. In order to assess the degree to which solute-solvent interactions can be correlated with bulk solvent properties, we compared our results with low-frequency dynamics obtained from optical Kerr effect (OKE) spectroscopy-performed by others-on the same nitrile solvent series. We find excellent correlation between our spectral diffusion results and the orientational dynamics time scales from OKE. We also find a correlation between our IVR time scales and the amplitudes of the low-frequency spectral densities evaluated at the 90-cm^-1 energy difference, corresponding to the gap between the two strong vibrational modes of the carbonyl probe. 2D-IR and OKE provide complementary perspectives on condensed phase dynamics, and these findings provide experimental evidence that at least at the level of dynamical correlations, some aspects of a solute vibrational dynamics can be inferred from properties of the solvent.

Optical Kerr Effect of Liquid Acetonitrile Probed by Femtosecond Time-Resolved X-ray Liquidography

Optical Kerr effect (OKE) spectroscopy is a method that measures the time-dependent change of the birefringence induced by an optical laser pulse using another optical laser pulse and has been used often to study the ultrafast dynamics of molecular liquids. Here we demonstrate an alternative method, femtosecond time-resolved X-ray liquidography (fs-TRXL), where the microscopic structural motions related to the OKE response can be monitored using a different type of probe, i.e., X-ray solution scattering. By applying fs-TRXL to acetonitrile and a dye solution in acetonitrile, we demonstrate that different types of molecular motions around photoaligned molecules can be resolved selectively, even without any theoretical modeling, based on the anisotropy of two-dimensional scattering patterns and extra structural information contained in the q-space scattering data. Specifically, the dynamics of reorientational (libration and orientational diffusion) and translational (interaction-induced motion) motions are captured separately by anisotropic and isotropic scattering signals, respectively. Furthermore, the two different types of reorientational motions are distinguished from each other by their own characteristic scattering patterns and time scales. The measured time-resolved scattering signals are in excellent agreement with the simulated scattering signals based on a molecular dynamics simulation for plausible molecular configurations, providing the detailed structural description of the OKE response in liquid acetonitrile.

Ultrafast Solvation Dynamics and Vibrational Coherences of Halogenated Boron-Dipyrromethene Derivatives Revealed through Two-Dimensional Electronic Spectroscopy

Boron-dipyrromethene (BODIPY) chromophores have a wide range of applications, spanning areas from biological imaging to solar energy conversion. Understanding the ultrafast dynamics of electronically excited BODIPY chromophores could lead to further advances in these areas. In this work, we characterize and compare the ultrafast dynamics of halogenated BODIPY chromophores through applying two-dimensional electronic spectroscopy (2DES). Through our studies, we demonstrate a new data analysis procedure for extracting the dynamic Stokes shift from 2DES spectra revealing an ultrafast solvent relaxation. In addition, we extract the frequency of the vibrational modes that are strongly coupled to the electronic excitation, and compare the results of structurally different BODIPY chromophores. We interpret our results with the aid of DFT calculations, finding that structural modifications lead to changes in the frequency, identity, and magnitude of Franck-Condon active vibrational modes. We attribute these changes to differences in the electron density of the electronic states of the structurally different BODIPY chromophores.

Enhanced vibrational solvatochromism and spectral diffusion by electron rich substituents on small molecule silanes

Fourier transform infrared and two-dimensional IR (2D-IR) spectroscopies were applied to two different silanes in three different solvents. The selected solutes exhibit different degrees of vibrational solvatochromism for the Si-H vibration. Density functional theory calculations confirm that this difference in sensitivity is the result of higher mode polarization with more electron withdrawing ligands. This mode sensitivity also affects the extent of spectral diffusion experienced by the silane vibration, offering a potential route to simultaneously optimize the sensitivity of vibrational probes in both steady-state and time-resolved measurements. Frequency-frequency correlation functions obtained by 2D-IR show that both solutes experience dynamics on similar time scales and are consistent with a picture in which weakly interacting solvents produce faster, more homogeneous fluctuations. Molecular dynamics simulations confirm that the frequency-frequency correlation function obtained by 2D-IR is sensitive to the presence of hydrogen bonding dynamics in the surrounding solvation shell.

Resolving and Controlling Photoinduced Ultrafast Solvation in the Solid State

Solid-state solvation (SSS) is a solid-state analogue of solvent-solute interactions in the liquid state. Although it could enable exceptionally fine control over the energetic properties of solid-state devices, its molecular mechanisms have remained largely unexplored. We use ultrafast transient absorption and optical Kerr effect spectroscopies to independently track and correlate both the excited-state dynamics of an organic emitter and the polarization anisotropy relaxation of a small polar dopant embedded in an amorphous polystyrene matrix. The results demonstrate that the dopants are able to rotationally reorient on ultrafast time scales following light-induced changes in the electronic configuration of the emitter, minimizing the system energy. The solid-state dopant-emitter dynamics are intrinsically analogous to liquid-state solvent-solute interactions. In addition, tuning the dopant/polymer pore ratio offers control over solvation dynamics by exploiting molecular-scale confinement of the dopants by the polymer matrix. Our findings will enable refined strategies for tuning optoelectronic material properties using SSS and offer new strategies to investigate mobility and disorder in heterogeneous solid and glassy materials.

Broad-Band Pump-Probe Spectroscopy Quantifies Ultrafast Solvation Dynamics of Proteins and Molecules

In this work, we demonstrate the use of broad-band pump-probe spectroscopy to measure femtosecond solvation dynamics. We report studies of a rhodamine dye in methanol and cryptophyte algae light-harvesting proteins in aqueous suspension. Broad-band impulsive excitation generates a vibrational wavepacket that oscillates on the excited-state potential energy surface, destructively interfering with itself at the minimum of the surface. This destructive interference gives rise to a node at a certain probe wavelength that varies with time. This reveals the Gibbs free-energy changes of the excited-state potential energy surface, which equates to the solvation time correlation function. This method captures the inertial solvent response of water (∼40 fs) and the bimodal inertial response of methanol (∼40 and ∼150 fs) and reveals how protein-buried chromophores are sensitive to the solvent dynamics inside and outside of the protein environment.

Empirical rules of molecular photophysics in the light of ultrafast spectroscopy

The advent of ultrafast laser spectroscopy has allowed entirely new possibilities for the investigation of the ultrafast photophysics of inorganic metal-based molecular complexes. In this review we show different regimes where non-Kasha behavior shows up. We also demonstrate that while ultrafast intersystem crossing is a common observation in metal complexes, the ISC rates do not scale with the magnitude of the spin-orbit coupling constant. Structural dynamics and density of states play a crucial role in such ultrafast ISC processes, which are not limited to molecules containing heavy atoms.

Nonlinear spectroscopic theory of displaced harmonic oscillators with differing curvatures: a correlation function approach

We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.

Polarization caging in diffusion-controlled electron transfer reactions in solution

In some bimolecular diffusion-controlled electron transfer (ET) reactions such as ion recombination (IR), both solvent polarization relaxation and the mutual diffusion of the reacting ion pair may determine the rate and even the yield of the reaction. However, a full treatment with these two reaction coordinates is a challenging task and has been left mostly unsolved. In this work, we address this problem by developing a dynamic theory by combining the ideas from ET reaction literature and barrierless chemical reactions. Two-dimensional coupled Smoluchowski equations are employed to compute the time evolution of joint probability distribution for the reactant (P((1))(X,R,t)) and the product (P((2))(X,R,t)), where X, as is usual in ET reactions, describes the solvent polarization coordinate and R is the distance between the reacting ion pair. The reaction is described by a reaction line (sink) which is a function of X and R obtained by imposing a condition of equal energy on the initial and final states of a reacting ion pair. The resulting two-dimensional coupled equations of motion have been solved numerically using an alternate direction implicit (ADI) scheme (Peaceman and Rachford, J. Soc. Ind. Appl. Math. 1955, 3, 28). The results reveal interesting interplay between polarization relaxation and translational dynamics. The following new results have been obtained. (i) For solvents with slow longitudinal polarization relaxation, the escape probability decreases drastically as the polarization relaxation time increases. We attribute this to caging by polarization of the surrounding solvent. As expected, for the solvents having fast polarization relaxation, the escape probability is independent of the polarization relaxation time. (ii) In the slow relaxation limit, there is a significant dependence of escape probability and average rate on the initial solvent polarization, again displaying the effects of polarization caging. Escape probability increases, and the average rate decreases on increasing the initial polarization. Again, in the fast polarization relaxation limit, there is no effect of initial polarization on the escape probability and the average rate of IR. (iii) For normal and barrierless regions the dependence of escape probability and the rate of IR on initial polarization is stronger than in the inverted region. (iv) Because of the involvement of dynamics along R coordinate, the asymmetrical parabolic (that is, non-Marcus) energy gap dependence of the rate is observed.

Dynamics of the solvent around a solute: generalized Langevin theory

The generalized Langevin theory for a solution has been derived as the infinite dilution limit of the theory for a two component mixture. Following a similar formalism, the mode coupling approximations of the memory kernel have been also obtained. We have applied this method for one component bulk liquid of Lennard-Jones spheres and proved this approximation theoretically. The analysis of the space and time pair correlation proposed by Van Hove has been carried out as a function of solute particle sizes. It is found that the size of the solute particle is deeply related to the relaxation process of the solvation structure characterized around a solute particle at equilibrium. We have also investigated the relation between the different thermodynamic environments and relaxation process. From these studies, we have obtained the useful information about the rapidity of the relaxation of the solvation structure around a solute at equilibrium.

Ultrafast dynamics in reverse micelles

Recent advances in ultrafast laser technology have spurred investigations of microheterogeneous solutions. In particular, researchers have explored details of reverse micelles (RMs), which present isolated droplets of polar solvent sequestered from a continuous nonpolar phase by a surfactant layer. This review explores recent studies utilizing a variety of ultrafast laser techniques to uncover details about structure and dynamics in various RMs. Using ultrafast vibrational spectroscopy, researchers have probed hydrogen-bond dynamics and vibrational energy relaxation in RMs. These studies have developed our understanding of reverse micellar structure, identifying varying water environments in the RMs. In a plethora of experiments employing probe molecules, researchers have explored the confined environment presented by RMs and their impact on a range of chemical reactions. These studies have shown that confinement, rather than the specific interactions with surfactants, is an important factor determining the impact of the reverse micellar environment on the chemistry.

Limiting ionic conductivity and solvation dynamics in formamide

A self-consistent microscopic theory has been used to calculate the limiting ionic conductivity of unipositive rigid ions in formamide at different temperatures. The calculated results are found to be in good agreement with the experimental data. The above theory can also predict successfully the experimentally observed temperature dependence of total ionic conductivity of a given uniunivalent electrolyte in formamide. The effects of dynamic polar solvent response on ionic conductivity have been investigated by studying the time dependent progress of solvation of a polarity probe dissolved in formamide. The intermolecular vibration (libration) band that is often detected in the range of 100-200 cm(-1) in formamide is found to play an important role in determining both the conductivity and the ultrafast polar solvent response in formamide. The time dependent decay of polar solvation energy in formamide has been studied at three different temperatures, namely, at 283.15, 298.15, and 328.15 K. While the predicted decay at 298.15 K is in good agreement with the available experimental data, the calculated results at the other two temperatures should be tested against experiments.

Photoinduced intramolecular charge separation in a polymer solid below the glass transition temperature

Photoinduced intramolecular charge separation (CS) in a polar polymer glass, cyanoethylated pullulan (CN-PUL), was studied below the glass transition temperature (Tg=395 K). A series of three carbazole (Cz: donor)-cyclohexane (S: spacer)-acceptor (A: acceptor) molecules (Cz-S-A) was used as intramolecular donor-acceptor dyads. The photoinduced CS rate was evaluated by the fluorescence decay measurement at temperatures from 100 to 400 K. The CS rate (kCS) increased above 200 K even far below Tg where micro-Brownian motions of the whole polymer chain are frozen. Below 200 K, on the other hand, kCS showed weak dependence on temperature. The temperature dependence of kCS is discussed in terms of the dielectric relaxation time of the polymer matrix. Consequently, CS below Tg was well explained by a thermally nonequilibrium electron transfer (ET) formula above 200 K and by a two-mode quantum-mechanical ET formula below 200 K. The increase in kCS above 200 K is mainly caused by a thermally activated low-frequency matrix mode originating from the side-chain relaxation of polar cyano groups. The weak temperature dependence of kCS can be explained by a nuclear-tunneling effect caused by a high-frequency matrix mode (variant Planck's over 2piomegH=250 cm-1) and an intramolecular vibrational mode (variant Planck's over 2piomegaQ=1300 cm-1). The high-frequency mode of the polymer matrix was attributed to a vibrational or librational motion of polar groups in the CN-PUL glassy solid.

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

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

Subpicosecond solvent dynamics in charge-transfer transitions: challenges and opportunities in resonance Raman spectroscopy

Resonance Raman spectroscopy is an established tool for the determination of structure and dynamics in electronically excited states. In condensed-phase systems, Raman excitation profiles and electronic absorption spectra depend on changes in molecular geometry and solvation structure induced by electronic excitation. Recent studies of solvent isotope effects on resonance Raman intensities in charge-transfer excitations reveal solvent dynamics taking place on a subpicosecond time scale and vibrational mode-specific solute-solvent interactions. These discoveries present challenges to the current working theories for analysis of resonance Raman and absorption spectra.