HEOM-Based Numerical Framework for Quantum Simulation of Two-Dimensional Vibrational Spectra in Molecular Liquids (HEOM-2DVS)

The multi-mode anharmonic Brownian motion model provides a universal framework for simulating molecular vibrations in condensed phases. When vibrational energy surpasses thermal excitation, quantum effects become significant, necessitating a rigorous treatment of system-bath entanglement. The hierarchical equations of motion (HEOM) provide a powerful methodology for simulating such open quantum systems. In this context, two-dimensional vibrational spectroscopy (2DVS) constitutes a powerful probe for elucidating the complex dynamics of molecular processes, both experimentally and theoretically. This work introduces a computational implementation, HEOM-2DVS, for treating non-Markovian open quantum dynamics that encompass energy relaxation, dephasing, thermal excitation, and related processes arising from non-perturbative and nonlinear interactions between selected vibrational modes and their thermal environments. To validate the theoretical framework, we computed 2D correlation infrared spectra for three coupled intramolecular vibrational modes of water. The HEOM-2DVS program developed for both CPU and graphics processing unit (GPU) is provided as supplementary material.