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arXiv · 2509.25840

A Multimode Classical Hierarchical Fokker-Planck Equations Approach to Molecular Vibrations: Simulating Two-Dimensional Spectra

Ryotaro Hoshino·Yoshitaka Tanimura
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Abstract

The multimode Brownian model with nonlinear system-bath coupling offers a flexible framework for studying both intra- and intermolecular vibrational modes in condensed-phase molecular systems. This approach allows us to calculate linear and nonlinear spectra of molecular vibrations and to examine thermal effects-such as anharmonicity, energy relaxation, and dephasing-as reflected in the spectral peak profiles. In this study, we present a computer program based on classical hierarchical Fokker-Planck equations applied to three vibrational modes of a molecular liquid. The primary objective of developing this code was to simulate the two-dimensional correlation spectrum of the intramolecular modes of liquid water. [R. Hoshino and Y. Tanimura, J. Chem. Phys. 162, 044105 (2025)]. The code has been further refined to optimize grid selection and numerical integration routines for graphics processing units (GPUs). As a demonstration, we apply this setup to simulate three interacting modes representing intermolecular vibrations in water, and calculate the resulting two-dimensional terahertz-Raman signals. The code and example routines are available in the supplementary material.

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Ryotaro Hoshino, Yoshitaka Tanimura. 2025-09-30. A Multimode Classical Hierarchical Fokker-Planck Equations Approach to Molecular Vibrations: Simulating Two-Dimensional Spectra. https://doi.org/10.1063/5.0294181

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