Theoretical Insights on Nonlinear Response Theory of Fluorescence Spectroscopy in Liquids

Correlations between the nonequilibrium solvation dynamics upon the photon excitation of the chromophore and a system's equilibrium fluctuations are deeply studied. As the linear response of the solvent has been linked with Gaussian statistics of the energy fluctuations in the literature, we specifically explore the cases beyond the regime of the linear response theory due to deviation from Gaussian fluctuations. As a continuation of our previous work, an analytical formalism is presented to project the energy shift with various order moments, where the non-Gaussian statistics arise from the overlap of the energy basins on the perturbed potential energy surface. It is shown that the nonequilibrium dynamics still correlate with the spontaneous regressions at equilibrium and are controlled by the decay rates of those higher order components with the prevailing contributions to the energy shift. Molecular dynamics simulations were performed in the protein Staphylococcus nuclease, in which even the dynamics of the high order moments are available. The results further verify the above relationship. Our scheme is used to evaluate Stokes shift using the information on non-Gaussian statistics at equilibrium, thus presenting a broad picture on the correlation between the nonequilibrium process and equilibrium properties in liquids.

Efficient Criterion To Evaluate Linear Response Theory in Optical Transitions

The role of the Gaussian statistics on the solvation dynamics upon the photon excitation of the chromophore is deeply explored. The linear response theory for the fluorescence Stokes shift is investigated. An analytical formulism is presented to recast Stokes shift into the contributions of the equilibrium time correlation functions of the solute-solvent interactions on the excited-state surface, and the latter is further reformed and depicted by the time relaxation of the moment. As the first application of the formulism in the molecular dynamics simulations, it is verified that the efficiency of the linear response theory relies on the Gaussian characteristics of the dominant moments in terms of the Stokes shift, which is identified by the same relaxation dynamics between those moments and the linear order one. The comparisons between the above observations on the linearity of Stokes shift and the explanations in the literature are discussed. The key finding is the development of explicit criterion to measure the appropriateness of applying linear response theory.

Vibrational energy transport in molecules studied by relaxation-assisted two-dimensional infrared spectroscopy

This review presents an overview of the relaxation-assisted two-dimensional infrared (RA 2DIR) spectroscopy method for measuring structures and energy transport dynamics in molecules. The method strongly enhances the range of accessible distances compared to traditional 2DIR and offers new structural reporters, such as the energy transport time, cross-peak amplification factors, and connectivity patterns. The use of the method for assigning vibrational modes with various levels of delocalization is illustrated. RA 2DIR relies on vibrational energy transport in molecules; as such, the transport mechanism can be conveniently studied by the method. Applications to identify diffusive and ballistic energy transport are demonstrated.

Vibrational energy relaxation of large-amplitude vibrations in liquids

Given the limited intermolecular spaces available in dense liquids, the large amplitudes of highly excited, low frequency vibrational modes pose an interesting dilemma for large molecules in solution. We carry out molecular dynamics calculations of the lowest frequency ("warping") mode of perylene dissolved in liquid argon, and demonstrate that vibrational excitation of this mode should cause identifiable changes in local solvation shell structure. But while the same kinds of solvent structural rearrangements can cause the non-equilibrium relaxation dynamics of highly excited diatomic rotors in liquids to differ substantially from equilibrium dynamics, our simulations also indicate that the non-equilibrium vibrational energy relaxation of large-amplitude vibrational overtones in liquids should show no such deviations from linear response. This observation seems to be a generic feature of large-moment-arm vibrational degrees of freedom and is therefore probably not specific to our choice of model system: The lowest frequency (largest amplitude) cases probably dissipate energy too quickly and the higher frequency (more slowly relaxing) cases most likely have solvent displacements too small to generate significant nonlinearities in simple nonpolar solvents. Vibrational kinetic energy relaxation, in particular, seems to be especially and surprisingly linear.

Coherent fifth-order visible-infrared spectroscopies: ultrafast nonequilibrium vibrational dynamics in solution

Obtaining a detailed description of photochemical reactions in solution requires measuring time-evolving structural dynamics of transient chemical species on ultrafast time scales. Time-resolved vibrational spectroscopies are sensitive probes of molecular structure and dynamics in solution. In this work, we develop doubly resonant fifth-order nonlinear visible-infrared spectroscopies to probe nonequilibrium vibrational dynamics among coupled high-frequency vibrations during an ultrafast charge transfer process using a heterodyne detection scheme. The method enables the simultaneous collection of third- and fifth-order signals, which respectively measure vibrational dynamics occurring on electronic ground and excited states on a femtosecond time scale. Our data collection and analysis strategy allows transient dispersed vibrational echo (t-DVE) and dispersed pump-probe (t-DPP) spectra to be extracted as a function of electronic and vibrational population periods with high signal-to-noise ratio (S/N > 25). We discuss how fifth-order experiments can measure (i) time-dependent anharmonic vibrational couplings, (ii) nonequilibrium frequency-frequency correlation functions, (iii) incoherent and coherent vibrational relaxation and transfer dynamics, and (iv) coherent vibrational and electronic (vibronic) coupling as a function of a photochemical reaction.

Ballistic energy transport along PEG chains: distance dependence of the transport efficiency

Dual-frequency relaxation-assisted two-dimensional infrared (RA 2DIR) spectroscopy was used to investigate energy transport in polyethylene glycol (PEG) oligomers of different length, having 0, 4, 8, and 12 repeating units and end-labeled with azido and succinimide ester moieties (azPEGn). The energy transport initiated by excitation of the N≡N stretching mode of the azido group in azPEGn in CCl(4) at ca. 2100 cm(-1) was recorded by probing the C=O stretching modes (reporters) of the succinimide ester moiety. Sensitive to the excess energy delivered to the reporter modes, RA 2DIR permits observation of both the through-bond and through-solvent energy transport contributions. The cross-peak data involving the reporter modes with different thermal sensitivity and the data for mixtures of compounds permitted concluding that through-bond energy transport is the dominant mechanism for most cross peaks in all four azPEGn compounds. The through-bond energy transport time, evaluated as the waiting time at which the cross peak maximum is reached, was found to be linearly dependent on the chain length of up to 60 Å, suggesting a ballistic energy transport regime. The through-bond energy transport speed determined from the chain-length dependence of T(max) in CCl(4) is found to be ca. 450 m s(-1). The cross-peak amplitude at the maximum decays exponentially with the chain length; a characteristic decay distance is found to be 15.7 ± 1 Å. The cross-peak amplitude at zero waiting time, determined by the end-to-end distance distribution, is found to decay with the chain length (L) as ∼L(-1.4), which is close to predictions of the free flight chain model. The match indicates that the end-group interaction does not strongly perturb the end-to-end distribution, which is close to the ideal random coil distribution with the Gaussian probability density.

Solvation dynamics and proton transfer in nanoconfined liquids

Nanoconfined liquids are of interest because of both their fundamental properties and their potential utility in an array of applications. The structure and dynamics of the liquid can be dramatically impacted by the geometrical constraints and the interactions with the interface. Understanding the molecular-level origins of these changes and how they are determined by the characteristics of the confining framework is the subject of ongoing experimental and theoretical studies. The progress and remaining challenges in these efforts are reviewed in the context of solvation dynamics and proton transfer reactions, processes that are strongly affected by nanoscale confinement.