What can we learn from three-dimensional infrared spectroscopy?

The low-frequency part of the vibrational spectrum of a liquid is dominated by intermolecular degrees of freedom. Hence, it reports on the motion of solvent molecules with respect to each other rather than on the intramolecular details of individual molecules. In hydrogen-bonded liquids, in particular water, a detailed understanding of the low-frequency spectrum is enormously complicated because of the complex hydrogen-bond network, which constantly rearranges on an ultrafast femtosecond to picosecond time scale. Many of the peculiar properties of water have their origin in these processes. Conventional far-infrared (far-IR) or Raman spectroscopy, as well as two-dimensional IR (2D-IR) spectroscopy, are all linear with respect to the intermolecular (solvent) degrees of freedom. These spectroscopies tell us much about the density of states in the low-frequency range but little about the dynamics of the hydrogen-bond making and breaking. In this Account, we propose three-dimensional IR (3D-IR) spectroscopy as a novel tool that is nonlinear with respect to these low-frequency degrees of freedom; hence, it may provide much more detailed insights into intermolecular dynamics. The first experimental realizations of 3D-IR spectroscopy have been demonstrated in the literature; the information it affords is similar to that of 2D-Raman spectroscopy. Three-dimensional IR spectroscopy will, for the first time, reveal whether the low-frequency part of the vibrational spectrum of liquids has to be considered mostly homogeneously or inhomogeneously broadened. Alternately, we may find that either of these classifications is completely wrong because the normal mode picture fails when thermal energy is of the same order of magnitude as the ruggedness of the intramolecular potential energy surface. We briefly introduce the theoretical background of 3D-IR spectroscopy and discuss two of its most promising applications: (a) the more thorough characterization of non-Gaussian stochastic processes such as the hydrogen-bond dynamics of water and (b) non-Markovian ultrafast exchange processes. In the ultrafast regime, many of the otherwise valid simplifying assumptions of nonequilibrium statistical mechanics (for example, linear response and Markovian dynamics) are likely to fail; 3D-IR spectroscopy will allow us for the first time to experimentally explore their range of validity