Feynman Diagram Description of 2D-Raman-THz Spectroscopy Applied to Water

2D-Raman-THz spectroscopy of liquid water, which has been presented recently (Proc. Natl. Acad. Sci. USA 110, 20402 (2013)), directly probes the intermolecular degrees of freedom of the hydrogen-bond network. However, being a relatively new technique, its information content is not fully explored as to date. While the spectroscopic signal can be simulated based on molecular dynamics simulation in connection with a water force field, it is difficult to relate spectroscopic signatures to the underlying microscopic features of the force field. Here, a completely different approach is taken that starts from an as simple as possible model, i.e., a single vibrational mode with electrical and mechanical anharmonicity augmented with homogeneous and inhomogeneous broadening. An intuitive Feynman diagram picture is developed for all possible pulse sequences of hybrid 2D-Raman-THz spectroscopy. It is shown that the model can explain the experimental data essentially quantitatively with a very small set of parameters, and it is tentatively concluded that the experimental signal originates from the hydrogen-bond stretching vibration around 170 cm$^{-1}$. Furthermore, the echo observed in the experimental data can be quantified by fitting the model. A dominant fraction of its linewidth is attributed to quasi-inhomogeneous broadening in the slow-modulation limit with a correlation time of 370 fs, reflecting the lifetime of the hydrogen-bond networks giving rise the absorption band.