Full Characterization of Vibrational Coherence in a Porphyrin Chromophore by Two-Dimensional Electronic Spectroscopy

In this work we present experimental and calculated two-dimensional electronic spectra for a 5,15-bisalkynyl porphyrin chromophore. The lowest energy electronic Qy transition couples mainly to a single 380 cm(-1) vibrational mode. The two-dimensional electronic spectra reveal diagonal and cross peaks which oscillate as a function of population time. We analyze both the amplitude and phase distribution of this main vibronic transition as a function of excitation and detection frequencies. Even though Feynman diagrams provide a good indication of where the amplitude of the oscillating components are located in the excitation-detection plane, other factors also affect this distribution. Specifically, the oscillation corresponding to each Feynman diagram is expected to have a phase that is a function of excitation and detection frequencies. Therefore, the overall phase of the experimentally observed oscillation will reflect this phase dependence. Another consequence is that the overall oscillation amplitude can show interference patterns resulting from overlapping contributions from neighboring Feynman diagrams. These observations are consistently reproduced through simulations based on third order perturbation theory coupled to a spectral density described by a Brownian oscillator model.