We employ a system-bath (SB) model for vibrational spectroscopy of liquid water, which was created to fit two-dimensional (2D) vibrational spectra obtained from full molecular dynamics (MD) simulation using the polarizable water model for intermolecular and intramolecular vibrational spectroscopy (POLI2VS).1,2 Assuming the classical SB Hamiltonian constructed from the classical MD with POLI2VS is capable of simulating 2D vibrational spectrum in a quantum regime when we solve it quantum mechanically, we compute various 2D vibrational spectra including 3D-IR, and 2D-IR-Raman-Raman-IR spectra using the numerically “exact” hierarchal equations of motion (HEOM) approach developed for the investigation of open quantum dynamics.3,4 For example, the response of 2D IR-Raman-Raman-IR spectroscopies can be expressed as3,4 RIR-R-R-IR(t1, t2, t3)=tr{μG(t3)ΠXG(t2)ΠXG(t1)μXρeq}, where AXρ=Aρ-ρA with the dipole operator A=μ and Raman polarizability A=Π at time intervals of t1, t2, and t3, respectively. This response function can be evaluated by simulating a time evolution of the density operator G(t) from the thermal equilibrium described by ρeq. Then, 2D spectrum I(ω1, t2, ω3) is obtained from the double Fourier transformation along t1 and t3. A significant point in calculating 2D spectra is that, due to the non-Markovian and non-perturbative SB interaction, the system and the bath are quantum-mechanically entangled. If we ignore such an effect, the 2D profile will exhibit unphysical results.4 The HEOM approach has the capability of treating such entanglement dynamics numerically rigorously. We will present some aspects of the theoretical calculation of various 2D spectra, and thoroughly discuss to what extent it is now possible to simulate and analyze 2D spectra using HEOM theory.

Modeling, calculating, and analyzing, multi-dimensional spectra: Hierarchical equations of motion approach

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