  Two-dimensional spectroscopic techniques combining terahertz (THz), infrared
(IR), and visible pulses offer a wealth of information about coupling among
vibrational modes in molecular liquids, thus providing a promising probe of
their local structure. However, the capabilities of these spectroscopies are
still largely unexplored due to experimental limitations and inherently weak
nonlinear signals. Here, through a combination of equilibrium-nonequilibrium
molecular dynamics (MD) and a tailored spectrum decomposition scheme, we
identify a relationship between the tetrahedral order of liquid water and its
two-dimensional IR-IR-Raman (IIR) spectrum. The structure-spectrum relationship
can explain the temperature dependence of the spectral features corresponding
to the anharmonic coupling between low-frequency intermolecular and
high-frequency intramolecular vibrational modes of water. In light of these
results, we propose new experiments and discuss the implications for the study
of tetrahedrality of liquid water.
