Discretized hierarchical equations of motion in mixed Liouville--Wigner space for two-dimensional vibrational spectroscopies of liquid water

Abstract

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.

14 pages 6 figures

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• Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle
• Coherent two-dimensional THz magnetic resonance spectroscopies for molecular magnets: Analysis of Dzyaloshinskii-Moriya interaction
• A Multimode Classical Hierarchical Fokker-Planck Equations Approach to Molecular Vibrations: Simulating Two-Dimensional Spectra
• Twin-Space Representation of Classical Mapping Model in the Constraint Phase Space Representation: Numerically Exact Approach to Open Quantum Systems
• System-Bath Modeling in Vibrational Spectroscopy via Molecular Dynamics: A Machine Learning Framework for Hierarchical Equations of Motion (HEOM)
• sbml4md: A computational platform for System-Bath Modeling via Molecular Dynamics powered by Machine Learning