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

TL;DR

This paper develops a discretized hierarchical equations of motion in mixed Liouville-Wigner space to analyze vibrational spectra and energy transfer in a quantum model of liquid water, capturing non-Markovian dynamics.

Contribution

It introduces a novel numerical method (DHEOM-MLWS) combining Liouville and Wigner spaces for detailed quantum dissipative simulations of water vibrational modes.

Findings

Computed various vibrational spectra of liquid water.

Demonstrated non-Markovian quantum dissipative dynamics.

Provided a framework for analyzing energy transfer processes.

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.