System-Bath Modeling in Vibrational Spectroscopy via Molecular Dynamics: A Machine Learning Framework for Hierarchical Equations of Motion (HEOM)

TL;DR

This work addresses the challenge of accurately simulating vibrational spectroscopy in solution by marrying a physically principled multimode anharmonic Brownian (MAB) open-quantum-system model with a data-driven parameterization from MD trajectories. A fixed HEOM-compatible form for spectral distribution functions (Drude and Brownian Oscillator components) is learned to capture anharmonic mode coupling and non-Markovian dissipation, enabling quantum dynamics of ultrafast relaxation and dephasing. The approach is demonstrated on liquid water, with a two-stage ML training pipeline, cross-validation, and separate Drude-only and BO+Drude bath configurations, yielding interpretable parameters for three intramolecular modes and their couplings. Linear IR spectra computed via HEOM illustrate distinct peaks that are not fully captured by MD alone, while the framework paves the way for rigorously simulating nonlinear 2D spectra (e.g., 2D IR, 2D Raman) by integrating HEOM with learned bath models. Overall, the methodology provides a general, transferable route to quantify system–bath interactions from MD and to perform spectroscopic predictions that are consistent with microscopic dynamics.

Abstract

Molecular vibrations in solutions, especially OH stretching and bending in water, drive ultrafast energy relaxation and dephasing in chemical and biological systems. We present a machine learning approach for constructing system-bath models of intramolecular vibrations in solution, compatible with quantum simulations via the hierarchical equations of motion (HEOM). Using classical molecular dynamics trajectories generated with a force field specifically developed for quantum molecular dynamics, the model captures anharmonic mode coupling and non-Markovian dissipation through spectral distribution functions (SDFs). These features, in turn, enable quantum mechanical treatment of ultrafast energy relaxation, vibrational dephasing, and thermal excitation within the HEOM framework.. The trained model yields physically interpretable parameters, validated against infrared spectra. Notably, combining Brownian oscillator and Drude SDFs -- representing inter- and intramolecular vibrational modes -- significantly improves learning performance and supports rigorous simulation of nonlinear vibrational spectroscopy.

Figures (5)

• Figure 1: Flowchart of the algorithm used to optimize the parameters of the MAB model based on atomic trajectories obtained from MD simulations.
• Figure 2: Schematic workflow for spectral calculation. Starting from MD trajectories, we first train the bath parameters and mode–mode coupling strength. The trained parameters are then passed to HEOM propagation, and the Fourier transform yields the final IR absorption spectrum.
• Figure 3: Infrared absorption spectra obtained from HEOM calculations using the optimized MAB model parameters for (a) Drude SDF case (blue curves) and (b) BO+Drude case (green curves). For comparison, each figure also includes results from MD simulations (orange lines) and experimental data.(black dotted curve).IRexp2011
• Figure 4: Training and testing losses were evaluated by comparing predicted model trajectories with actual MD trajectories, using two coordinate systems: atomic coordinates in Cartesian space and normal-mode coordinates. In both cases, the system's time evolution was governed by the corresponding MD Liouvillian.
• Figure 5: The left panel shows training losses for the OH symmetric and OH asymmetric stretch modes, while the right panel displays the loss for the HOH bending mode. The bending mode demonstrates a more rapid learning process compared to the stretch modes.