MO-HEOM: Extending Hierarchical Equations of Motion to Molecular Orbital Space

Studies of quantum thermal effects on molecular excitation dynamics have often relied on oversimplified models, such as energy eigenstates or low-dimensional potentials, which fail to capture the complexity of real chemical systems. In reality, molecules are spatially extended and embedded in anisotropic environments, where molecular orbitals (MOs) play a central role in determining quantum behavior. To advance beyond these limitations, we propose a three-dimensional rotationally invariant system-bath (3D-RISB) model within the MO framework, with explicit inclusion of intramolecular vibrational motion. From this MO foundation, we derive numerically ``exact'' hierarchical equations of motion (MO-HEOM). As a demonstration, we analyze hydrogen molecules and hydrogen molecular ions with vibrational degrees of freedom, revealing their linear absorption spectra.