  A model of a bulk water system describing the vibrational motion of
intramolecular and intermolecular modes is constructed, enabling analysis of
its linear and nonlinear vibrational spectra, as well as the energy transfer
processes between the vibrational modes. The model is described as a system of
four interacting anharmonic oscillators nonlinearly coupled to their respective
heat baths. To perform a rigorous numerical investigation of the non-Markovian
and nonperturbative quantum dissipative dynamics of the model, we derive
discretized hierarchical equations of motion in mixed Liouville-Wigner space
(DHEOM-MLWS), with Lagrange-Hermite mesh discretization being employed in the
Liouville space of the intramolecular modes and Lagrange-Hermite mesh
discretization and Hermite discretization in the Wigner space of the
intermolecular modes. One-dimensional infrared and Raman spectra and
two-dimensional terahertz-infrared-visible and infrared-infrared-Raman spectra
are computed as demonstrations of the quantum dissipative description provided
by our model.
