Mo-heom Achieves Exact Molecular Excitation Dynamics, Capturing 3D Rotational Invariance

Understanding how molecules respond to light and heat requires accurately modelling their complex behaviour, a challenge often hampered by oversimplified computational approaches. Yankai Zhang, Yoshitaka Tanimura, and So Hirata, from Kyoto University, address this limitation with a new theoretical framework, MO-HEOM, which extends existing methods to incorporate the crucial role of molecular orbitals. This innovative approach models molecules in three dimensions, accounting for both their internal vibrations and the surrounding environment, offering a significantly more realistic representation of molecular excitation dynamics. By applying MO-HEOM to simple molecules like hydrogen and its ion, the researchers successfully predict their light absorption spectra, demonstrating the potential of this method to unlock a deeper understanding of chemical processes in complex systems. Current theoretical treatments of molecular systems often rely on simplified potential energy surfaces that inadequately represent the complexity of real chemical environments. Molecules are, in reality, spatially extended and exist within anisotropic surroundings where molecular orbitals decisively govern quantum behaviour. To overcome these limitations, researchers propose a three-dimensional rotationally invariant system-bath (3D-RISB) model, operating within the molecular orbital framework, and explicitly incorporating intramolecular vibrational motion. This molecular orbital foundation allows for the derivation of numerically exact hierarchical equations of motion (MO-HEOM), which the team used to analyse hydrogen molecules and hydrogen molecular ions, including vibrational degrees of freedom, and successfully reveals their linear absorption spectra. Hierarchy Equations of Motion for Open Systems This work represents a significant body of research in quantum dynamics and spectroscopy, with a strong emphasis on the hierarchy equation of motion (HEOM) method and its applications to complex systems. The research encompasses theoretical and computational chemistry, specifically related to open quantum systems, non-adiabatic dynamics, and methods for calculating excited states and molecular properties. Key areas of investigation include simulating dynamics with dissipation and dephasing, modelling environments using various spectral distributions, combining HEOM with molecular dynamics for condensed-phase simulations, and accelerating HEOM calculations with machine learning. Specific techniques explored include coupled cluster theory, path integrals, Redfield theory, and Padé spectrum decomposition. These methods are applied to a wide range of problems, including electron transfer, exciton dynamics, vibrational dynamics, spin relaxation, and the dynamics of liquid water. The research also incorporates open-source quantum chemistry software, such as Psi4, and computational platforms for system-bath modelling, like SBML4MD. 3D Model Accurately Simulates Molecular Dynamics Scientists have developed a new theoretical framework, the three-dimensional rotationally invariant system-bath (3D-RISB) model, to accurately simulate the behavior of molecules in thermal environments. This work addresses a longstanding challenge in modelling molecular excitation dynamics, which often relies on oversimplified representations of complex chemical systems.

The team constructed numerically exact hierarchical equations of motion (MO-HEOM) derived from molecular orbital calculations, enabling a detailed analysis of how molecules absorb light and respond to thermal fluctuations. Experiments reveal that the 3D-RISB model accurately predicts the linear absorption spectra of hydrogen molecules and hydrogen molecular ions, demonstrating its ability to capture intricate vibrational effects. The model accounts for the interplay between electronic and nuclear motion, crucial for understanding molecular dynamics, and accurately represents potential energy surfaces derived from quantum chemical calculations. The breakthrough preserves quantum entanglement between the molecule and its surrounding environment, a critical factor often lost in traditional simulations, and avoids classical behavior resulting from symmetry mismatches. Tests prove that even with weak interactions, repeated interactions necessitate a non-perturbative treatment, which the MO-HEOM framework provides, accurately predicting the suppression of transitions from high-energy states in hydrogen atoms due to strong rotational relaxation. Molecular Response to Thermal Fluctuations Modelled This research presents a new theoretical framework, molecular orbital hierarchical equations of motion, for accurately modelling how molecules respond to thermal fluctuations and energy dissipation.

The team developed a three-dimensional rotationally invariant system-bath model that moves beyond simplified approaches by explicitly incorporating the complex vibrational motions within molecules and their surrounding environments. Applying this method to hydrogen molecules and ions, scientists successfully calculated linear absorption spectra, demonstrating the model’s ability to predict molecular behaviour under thermal conditions. The achievement establishes a robust and versatile method for investigating quantum thermodynamic phenomena, with potential applications extending across spectroscopy, quantum chemistry, and cavity quantum electrodynamics. While the current work focuses on harmonic vibrations, the researchers acknowledge that more complex, anharmonic vibrations require additional computational techniques. Future work may benefit from incorporating more detailed representations of the interactions between molecules and their environments, potentially through machine learning models, and integrating the method with time-dependent density functional theory for even greater accuracy. 👉 More information 🗞 MO-HEOM: Extending Hierarchical Equations of Motion to Molecular Orbital Space 🧠 ArXiv: https://arxiv.org/abs/2512.22962 Tags: