Polarizability response spectroscopy: Formalism and simulation of ultrafast dynamics in solvation

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.

Topical Review: Molecular reaction and solvation visualized by time-resolved X-ray solution scattering: Structure, dynamics, and their solvent dependence

Time-resolved X-ray solution scattering is sensitive to global molecular structure and can track the dynamics of chemical reactions. In this article, we review our recent studies on triiodide ion (I3 (-)) and molecular iodine (I2) in solution. For I3 (-), we elucidated the excitation wavelength-dependent photochemistry and the solvent-dependent ground-state structure. For I2, by combining time-slicing scheme and deconvolution data analysis, we mapped out the progression of geminate recombination and the associated structural change in the solvent cage. With the aid of X-ray free electron lasers, even clearer observation of ultrafast chemical events will be made possible in the near future.

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.

New insights into response functions of liquids by electric field-resolved polarization emission time measurements

We resolve information about the dynamics of simple liquids that has been obscured in prior frequency and time-domain measurements by way of full field-resolved polarization emission time (FR-PET) measurements of carbon disulfide. The amplitude and phase of the field-resolved transient-grating signal is used to calculate a spectrogram of the signal field at each delay between the transient-grating (TG) pump and probe pulses. The temporal maximum of the spectrogram, defined to be the signal emission time, varies with pump-probe delay; it follows the convolution of the TG pulses while the pulses overlap and exhibits recurrences at times when the nuclear dynamics are the main component of the liquid material response. Since this is a third-order nonlinear spectroscopic method, the isotropic and anisotropic signals are constructed from the polarization tensor components. The frequency-integrated anisotropic component of the signal is equivalent to the signal measured in optical Kerr Effect (OKE) experiments. The FR-PET determination of the signal emission times is a direct measurement of the third-order nonlinear (polarizability) polarization and, hence provides new strong constraints on appropriate models of the liquid dynamics. Models for the material response function are used to calculate the signal emission times. In particular, we show that the proper treatment of the time-correlation function for orientational motion gives the best fit to the FR-PET data for rotational diffusional motion. We also establish that librational motion is not a short-time (coherent) motion that leads to rotational diffusion. Finally, we find that the Bucaro-Litovitz form for interaction-induced dynamics is not entirely correct for the CS(2) liquid we study. We suggest that the failing may result from the implicit assumption of two-body interactions, which is only appropriate for gases.

Femtosecond stimulated Raman scattering for polyatomics with harmonic potentials: application to rhodamine 6G

The perturbation theory of stimulated Raman scattering (SRS), with Raman pump on minus pump off and heterodyne detection along the probe direction, is reviewed. It has four third-order polarization terms, labeled as SRS or inverse Raman scattering (IRS): SRS(I), SRS(II), IRS(I), and IRS(II). These four polarizations have a wave packet interpretation. The polarizations, with homogenous and inhomogeneous broadening included, can be written as integrals over four-time correlation functions, and analytic formulas are derived for the latter for multidimensional harmonic potential surfaces with Franck-Condon displacements in the modes which facilitates the calculation of the SRS cross sections. The theory is applied to understand recent experimental results on the femtosecond SRS (FSRS) of a fluorescent dye, rhodamine 6G (R6G), where the Raman pump pulse is about 1 ps long, and the probe pulse is about 10 fs. The calculations compared very well with the R6G experimental results for off-resonance and resonance FSRS spectra spanning both Stokes and anti-Stokes bands, and for negative and positive pump-probe delay times on resonance.

Efficient calculation of time- and frequency-resolved four-wave-mixing signals

"Four-wave-mixing" is the generic name for a family of nonlinear electronic and vibrational spectroscopies. These techniques are widely used to explore dissipation, dephasing, solvation, and interstate coupling mechanisms in various material systems. Four-wave-mixing spectroscopy needs a firm theoretical support, because it delivers information on material systems indirectly, through certain transients, which are measured as functions of carrier frequencies, durations, and relative time delays of the laser pulses. The observed transients are uniquely determined by the three-pulse-induced third-order polarization. There exist two conceptually different approaches to the calculation of the nonlinear polarization. In the standard perturbative approach to nonlinear spectroscopy, the third-order polarization is expressed in terms of the nonlinear response functions. As the material systems become more complex, the evaluation of the response functions becomes cumbersome and the calculation of the signals necessitates a number of approximations. Herein, we review alternative methods for the calculation of four-wave-mixing signals, in which the relevant laser pulses are incorporated into the system Hamiltonian and the driven system dynamics is simulated numerically exactly. The emphasis is on the recently developed equation-of-motion phase-matching approach (EOM-PMA), which allows us to calculate the three-pulse-induced third-order polarization in any phase-matching direction by performing three (with the rotating wave approximation) or seven (without the rotating wave approximation) independent propagations of the density matrix. The EOM-PMA is limited to weak laser fields (its domain of validity is equivalent to the approach based on the third-order response functions) but allows for arbitrary pulse durations and automatically accounts for pulse-overlap effects. As an illustration, we apply the EOM-PMA to the calculation of optical three-pulse photon-echo two-dimensional (2D) signals for a generic model system, which represents a characteristic photophysical dynamics of large molecules or chromophores in condensed phases. The EOM-PMA is easy to implement and can straightforwardly be incorporated into any computational scheme, which provides the time-dependent density matrix or wave function of the material system of interest. In particular, EOM-PMA-based computer codes can efficiently be implemented on parallel computers. The EOM-PMA facilitates considerably the computation of four-wave-mixing signals and 2D spectra, in both vibrational and electronic spectroscopy. The EOM-PMA can be extended to higher order optical responses, e.g., heterodyned 3D IR, transient 2D IR, and other six-wave-mixing techniques.

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.

Controlling multidimensional off-resonant-Raman and infrared vibrational spectroscopy by finite pulse band shapes

Closed expressions are derived which incorporate pulse shaping effects in femtosecond nonlinear optical signals involving various combinations of temporally well-separated vibrationally resonant infrared and electronically off-resonant Raman pulses. Combinations of broadband and narrow band pulses that yield multidimensional extensions of coherent anti-Stokes Raman and sum frequency generation spectroscopy are presented.