  We explore and describe the roles of inter-molecular vibrations employing a
Brownian oscillator (BO) model with linear-linear (LL) and square-linear (SL)
system-bath interactions, which we use to analyze two-dimensional (2D)
THz-Raman spectra obtained by means of molecular dynamics (MD) simulations. In
addition to linear absorption (1D IR), we calculated 2D Raman-THz-THz,
THz-Raman-THz, and THz-THz-Raman signals for liquid formamide, water, and
methanol using an equilibrium non-equilibrium hybrid MD simulation. The
calculated 1D IR and 2D THz-Raman signals are compared with results obtained
from the LL+SL BO model applied through use of hierarchal Fokker-Planck
equations with non-perturbative and non-Markovian noise. We find that all of
the qualitative features of the 2D profiles of the signals obtained from the MD
simulations are reproduced with the LL+SL BO model, indicating that this model
captures the essential features of the inter-molecular motion. We analyze the
fitted 2D profiles in terms of anharmonicity, nonlinear polarizability, and
dephasing time. The origins of the echo peaks of the librational motion and the
elongated peaks parallel to the probe direction are elucidated using optical
Liouville paths.
