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

Abstract

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.