Derivation of Lorentz-Drude undamped oscillator hierarchical equations of motion

Here we present a derivation of the hierarchical equations of motion (HEOM) for an overdamped Lorentz-Drude environment containing an undamped oscillator (LDUO-HEOM). The new approach avoids the artifact of superfluous damping inherent in underdamped spectral densities. We show that the new HEOM is a useful model for intramolecular vibrations in condensed phase molecules.