with α aa ′ tt ′ the atomic polarizability on each site. To avoid effects of spurious overpolarization, a damped version of the interaction tensor (Thole damping ) is used. Then, the static and induced multipoles in the MM region also interact with the electron density in QM region via an additional external potential to Eq. (2). At the same time, the explicit electrostatic field from the QM density is included in polarizing the MM region. The total density of excited state S is evaluated from the excited-state wavefunction χ S as