A notorious problem for the external GW -BSE/MM approaches with polarization is related to the self-consistency procedure in the quantum-classical iterations cycle. Evaluation of the QM density as in Eq. (90) or Eq. (92) (and the respective energies) depending on the calculation route can be tricky as electronic energy levels can swap between iterations. Following the "correct" state is not always trivial, especially if polarization effects cause significant changes to the nature of the excitation, as they do in the example of Figure . Issues like these are well-known also for instance in geometry optimizations in excited states.