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

Abstract

Building upon our previous implementation for the hydrogen atom [Y. Zhang and Y. Tanimura, J. Chem. Phys. 163, 184108 (2025)], we have developed source code for atomic orbital–hierarchical equations of motion (AO-HEOM), a quantum mechanical framework based on HEOM formulated within an AO 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 because of 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 graphics processing unit-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.