Ultrafast two-dimensional infrared (2D-IR) vibrational echo spectroscopy can probe structural dynamics under thermal equilibrium conditions on time scales ranging from femtoseconds to approximately 100 ps and longer. One of the important uses of 2D-IR spectroscopy is to monitor the dynamical evolution of a molecular system by reporting the time dependent frequency fluctuations of an ensemble of vibrational probes. The vibrational frequency-frequency correlation function (FFCF) is the connection between the experimental observables and the microscopic molecular dynamics and is thus the central object of interest in studying dynamics with 2D-IR vibrational echo spectroscopy. A new observable is presented that greatly simplifies the extraction of the FFCF from experimental data. The observable is the inverse of the center line slope (CLS) of the 2D spectrum. The CLS is the inverse of the slope of the line that connects the maxima of the peaks of a series of cuts through the 2D spectrum that are parallel to the frequency axis associated with the first electric field-matter interaction. The CLS varies from a maximum of 1 to 0 as spectral diffusion proceeds. It is shown analytically to second order in time that the CLS is the T(w) (time between pulses 2 and 3) dependent part of the FFCF. The procedure to extract the FFCF from the CLS is described, and it is shown that the T(w) independent homogeneous contribution to the FFCF can also be recovered to yield the full FFCF. The method is demonstrated by extracting FFCFs from families of calculated 2D-IR spectra and the linear absorption spectra produced from known FFCFs. Sources and magnitudes of errors in the procedure are quantified, and it is shown that in most circumstances, they are negligible. It is also demonstrated that the CLS is essentially unaffected by Fourier filtering methods (apodization), which can significantly increase the efficiency of data acquisition and spectral resolution, when the apodization is applied along the axis used for obtaining the CLS and is symmetrical about tau=0. The CLS is also unchanged by finite pulse durations that broaden 2D spectra.

A core/shell model has often been used to describe water confined to the interior of reverse micelles. The validity of this model for water encapsulated in AOT/isooctane reverse micelles ranging in diameter from 1.7 to 28 nm (w0 = 2-60) and bulk water is investigated using four experimental observables: the hydroxyl stretch absorption spectra, vibrational population relaxation times, orientational relaxation rates, and spectral diffusion dynamics. The time dependent observables are measured with ultrafast infrared spectrally resolved pump-probe and vibrational echo spectroscopies. Major progressive changes appear in all observables as the system moves from bulk water to the smallest water nanopool, w0 = 2. The dynamics are readily distinguishable for reverse micelle sizes smaller than 7 nm in diameter (w0 = 20) compared to the response of bulk water. The results also demonstrate that the size dependent absorption spectra and population relaxation times can be quantitatively predicted using a core-shell model in which the properties of the core (interior of the nanopool) are taken to be those of bulk water and the properties of the shell (water associated with the headgroups) are taken to be those of w0 = 2. A weighted sum of the core and shell components reproduces the size dependent spectra and the nonexponential population relaxation dynamics. However, the same model does not reproduce the spectral diffusion and the orientational relaxation experiments. It is proposed that, when hydrogen bond structural rearrangement is involved (orientational relaxation and spectral diffusion), dynamical coupling between the shell and the core cause the water nanopool to display more homogeneous dynamics. Therefore, the absorption spectra and vibrational lifetime decays can discern different hydrogen bonding environments whereas orientational and spectral diffusion correlation functions predict that the dynamics are size dependent but not as strongly spatially dependent within a reverse micelle.

The dynamics of water are examined using ultrafast IR stimulated vibrational echo correlation spectroscopy. The OD hydroxyl stretch of HOD in H2O is probed with 45-fs pulses that have sufficient bandwidth (>400 cm-1) to span the entire broad spectrum. High-quality 2D correlation spectra are obtained having the correct phase relations across the broad hydroxyl band. The correlation spectra are found to evolve on multiple time scales. The time evolution of the vibrational echo correlation spectrum reflects the structural evolution of the hydrogen bond networks. The extended vibrational lifetime of the OD hydroxyl stretch of HOD in H2O facilitates the measurement of hydrogen bond dynamics for longer times than possible in previous studies of the OH stretch. Molecular dynamics simulations/electronic structure calculations are used to obtain the time correlation functions (TCF) for two water models, TIP4P and SPC/E. The TCFs are inputs to full time-dependent diagrammatic perturbation theory calculations, which yield theoretical correlation spectra. Quantitative comparison with the data demonstrates that the two water models somewhat overemphasize the fast fluctuations in water and do not contain a slow enough component to account for the slowest fluctuations. Fits to the data using a phenomenological triexponential TCF yield a slowest component of ∼2 ps, and TIP4P and SPC/E have slowest components of <1 ps. The TCF obtained from the water models and the triexponential TCF reproduce the linear absorption line shape equally well, but all miss to some extent the asymmetric “wing” on the low-energy side of the line. Therefore, the time dependence of the vibrational echo correlation spectra provides a good test for the TCF, but the absorption spectrum does not.

In general, the formation and dissociation of solute-solvent complexes have been too rapid to measure without disturbing the thermal equilibrium. We were able to do so with the use of two-dimensional infrared vibrational echo spectroscopy, an ultrafast vibrational analog of two-dimensional nuclear magnetic resonance spectroscopy. The equilibrium dynamics of phenol complexation to benzene in a benzene-carbon tetrachloride solvent mixture were measured in real time by the appearance of off-diagonal peaks in the two-dimensional vibrational echo spectrum of the phenol hydroxyl stretch. The dissociation time constant tau(d) for the phenol-benzene complex was 8 picoseconds. Adding two electron-donating methyl groups to the benzene nearly tripled the value of tau(d) and stabilized the complex, whereas bromobenzene, with an electron-withdrawing bromo group, formed a slightly weaker complex with a slightly lower tau(d). The spectroscopic method holds promise for studying a wide variety of other fast chemical exchange processes.