Full Quantum and Mixed Quantum–Classical Dynamics of Hot Exciton Cooling in Semiconductor Nanocrystals

Hot-exciton relaxation in semiconductor nanocrystals (NCs) is often described using perturbative theories, but their accuracy is difficult to assess for realistic systems. Here, we benchmark the perturbative quantum master equation (QME) and several mixed quantum-classical (MQC) methods against fully quantum mechanical dynamics. Using exciton-phonon Hamiltonians for CdSe core and CdSe/CdS core-shell NCs, parametrized from electronic-structure and vibronic calculations, we find that the CdSe core exhibits an ultrafast initial decay followed by slower cooling, whereas the core-shell system is dominated by the slower component. The QME captures the initial fast decay but can fail for the slower relaxation in the diabatic representation, while the mapping approach to surface hopping (MASH) gives the most consistent agreement with both benchmark dynamics and equilibrium populations. These results establish a benchmark for exciton-cooling dynamics in NCs and clarify the validity of widely used approximate methods.