System−Bath Correlation Function Probed by Conventional and Time-Gated Stimulated Photon Echo

We show how in the framework of the multimode Brownian oscillator model the system−bath correlation function can be derived from conventional and time-gated stimulated photon echo experiments and consideration of the linear optical spectra. Experiments are performed on the infrared dye DTTCI in room temperature solutions of ethylene glycol, methanol, and acetonitrile. The obtained correlation function is the sum of several Brownian oscillators, of which four are attributed to intrachromophore vibrational dynamics and the other three to solute−solvent dynamics. The ultrafast part of the correlation function on the time scale of the excitation pulses is interpreted as a free induction decay-like effect due to impulsive excitation of spectrally broad underlying vibrational structure in the dye's electronic transition. The slower parts are assigned to multiple time scale solute−solvent dynamics. The effect of vibrational coherences on the echo measurements is also analyzed; this analysis permits the dissection of the correlation function into a part due to intrachromophore dynamics and a part due to solvation dynamics. The spectral densities associated with these latter oscillators are located in the far infrared, in the same spectral region as probed by the optical Kerr effect. The measurements, however, provide no definite answer to the question of whether these spectral densities are the same.