  Nonlinear THz-THz-Raman (TTR) liquid spectroscopy offers new possibilities
for studying and understanding condensed-phase chemical dynamics. Although TTR
spectra carry rich information about the systems under study, the response is
encoded in a three-point correlation function comprising of both dipole and
polarizability elements. Theoretical methods are necessary for the
interpretation of the experimental results. In this work, we study the
liquid-phase dynamics of bromoform, a polarizable molecule with a strong TTR
response. Previous work based on reduced density matrix (RDM) simulations
suggests that unusually large multi-quanta dipole matrix elements are needed to
understand the measured spectrum of bromoform. Here, we demonstrate that a
self-consistent definition of the time coordinates with respect to the
reference pulse leads to a simplified experimental spectrum. Furthermore, we
analytically derive a parametrization for the RDM model by integrating the
dipole and polarizability elements to the 4th order in the normal modes, and we
enforce inversion symmetry in the calculations by numerically cancelling the
components of the response that are even with respect to the field. The
resulting analysis eliminates the need to invoke large multi-quanta dipole
matrix elements to fit the experimental spectrum; instead, the experimental
spectrum is recovered using RDM simulations with dipole matrix parameters that
are in agreement with independent ab initio calculations. The fundamental
interpretation of the TTR signatures in terms of coupled intramolecular
vibrational modes remains unchanged from the previous work.
