AO-HEOM: A computational platform for non-Markovian quantum dissipative dynamics in atomic orbital spaces

Building upon our previous implementation for the hydrogen atom [Zhang, Y. and Tanimura, Y., J. Chem. Phys. 163, 184108 (2025)], we have developed source code for AO-HEOM, a quantum mechanical framework based on hierarchical equations of motion formulated within an atomic orbital basis. This method enables numerically "exact" simulations of atomic systems coupled to three independent thermal baths, under both isotropic and anisotropic conditions, while preserving rotational symmetry. AO-HEOM rigorously accounts for system-bath entanglement, which is critical for describing the quantum nature of environmental interactions. Incorporating spatial bath degrees of freedom significantly increases the computational cost in the HEOM formalism, due to the proliferation of electronic states at high temperatures and the inclusion of Matsubara frequency terms at low temperatures. To address this challenge, we developed a GPU-accelerated implementation. As a demonstration, we computed the emission spectra of He I and He II atoms. The source code is broadly applicable to atomic systems and enables detailed analysis of electronic transitions in thermal environments.