Waiting Time Dynamics in Two-Dimensional Infrared Spectroscopy

We review recent work on the waiting time dynamics of coherent two-dimensional infrared (2DIR) spectroscopy. This dynamics can reveal chemical and physical processes that take place on the femto- and picosecond time scale, which is faster than the time scale that may be probed by, for example, nuclear magnetic resonance spectroscopy. A large number of chemically relevant processes take place on this time scale. Such processes range from forming and breaking hydrogen bonds and proton transfer to solvent exchange and vibrational population transfer. In typical 2DIR spectra, multiple processes contribute to the waiting time dynamics and the spectra are often congested. This makes the spectra challenging to interpret, and the aid of theoretical models and simulations is often needed. To be useful, such models need to account for all dynamical processes in the sample simultaneously. The numerical integration of the Schrödinger equation (NISE) method has proven to allow for a very general treatment of the dynamical processes. It accounts for both the motional narrowing resulting from solvent-induced frequency fluctuations and population transfer between coupled vibrations. At the same time, frequency shifts arising from chemical-exchange reactions and changes of the transition dipoles because of either non-Condon effects or molecular reorientation are included in the treatment. This method therefore allows for the disentanglement of all of these processes. The NISE method has thus far been successfully applied to study chemical-exchange processes. It was demonstrated that 2DIR is not only sensitive to reaction kinetics but also to the more detailed reaction dynamics. NISE has also been applied to the study of population transfer within the amide I band (CO stretch) and between the amide I and amide II bands (CN stretch and NH bend) in polypeptides. From the amide I studies, it was found that the population transfer can be used to enhance cross-peaks that act as structural markers for β-sheet structure in proteins. From the amide I/II investigation, it was found that the amide II band and the hydrogen-bond stretch vibration are important parts of the relaxation pathway for the amide I vibration. With the development of simple approximations, it becomes possible to apply the NISE method even to very big systems, such as the OH stretch of bulk water, which can only be described well when large numbers of coupled vibrations are taken into account.