One experimental observable that can probe the spectral density directly is resonance Raman. Within the transform theory of Raman scattering, the first order resonance Raman intensity for the displaced harmonic oscillators with the same vibrational frequencies on the ground and excited electronic state is approximately proportional to the spectral density. The approximations invoked include the Condon approximation and the neglect of the average thermal population of vibrational modes, which are valid for our system and the frequency window of interest.