A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy

Ultrafast Two-Dimensional Infrared Spectroscopy of a Quasifree Rotor: J Scrambling and Perfectly Anticorrelated Cross Peaks

Ultrafast two-dimensional infrared (2DIR) spectra of the N_{2}O ν_{3} mode in moderately dense SF_{6} gas exhibit complex line shapes with diagonal and antidiagonal features in contrast to condensed phase vibrational 2DIR spectroscopy. Observed spectra for this quasifree rotor system are well captured by a model that includes all 36 possible rovibrational pathways and treats P (ΔJ=-1) and R (ΔJ=+1) branch resonances as distinct Kubo line shape features. Transition frequency correlation decay is due to J scrambling within one to two gas collisions at each density. Studies of supercritical solvation and relaxation at high pressure and temperature are enabled by this methodology.

Monitoring equilibrium reaction dynamics of a nearly barrierless molecular rotor using ultrafast vibrational echoes

Using rapidly acquired spectral diffusion, a recently developed variation of heterodyne detected infrared photon echo spectroscopy, we observe ∼3 ps solvent independent spectral diffusion of benzene chromium tricarbonyl (C6H6Cr(CO)3, BCT) in a series of nonpolar linear alkane solvents. The spectral dynamics is attributed to low-barrier internal torsional motion. This tripod complex has two stable minima corresponding to staggered and eclipsed conformations, which differ in energy by roughly half of kBT. The solvent independence is due to the relative size of the rotor compared with the solvent molecules, which create a solvent cage in which torsional motion occurs largely free from solvent damping. Since the one-dimensional transition state is computed to be only 0.03 kBT above the higher energy eclipsed conformation, this model system offers an unusual, nearly barrierless reaction, which nevertheless is characterized by torsional coordinate dependent vibrational frequencies. Hence, by studying the spectral diffusion of the tripod carbonyls, it is possible to gain insight into the fundamental dynamics of internal rotational motion, and we find some evidence for the importance of non-diffusive ballistic motion even in the room-temperature liquid environment. Using several different approaches to describe equilibrium kinetics, as well as the influence of reactive dynamics on spectroscopic observables, we provide evidence that the low-barrier torsional motion of BCT provides an excellent test case for detailed studies of the links between chemical exchange and linear and nonlinear vibrational spectroscopy.

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.