Energy and charge-transfer dynamics using projected modes

For electron-phonon Hamiltonians with the couplings linear in the phonon operators, we construct a class of unitary transformations that separate the normal modes into two groups. The modes in the first group interact with the electronic degrees of freedom directly. The modes in the second group interact directly only with the modes in the first group but not with the electronic system. These transformations can be carried out independently for different types of phonon modes, e.g., high- versus low-frequency phonon bands. This construction generalizes recently introduced transformations for systems exhibiting a conical intersection topology. The separation of the normal modes into several groups allows one to develop new approximation schemes. We apply one of such schemes to study electronic relaxation at a semiconducting polymer interface.