Correlated vibrational coherence and spectral diffusion analysis of multi-level systems using two-dimensional electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) is used to theoretically and experimentally study a minimal three level “V” system (3LVS) with one ground state and two excited states coupled to common displaced harmonic oscillator modes. The third order non-linear optical response functions with frequency fluctuation correlation functions and frequency fluctuation cross correlation functions were derived using the displaced harmonic oscillator model to characterize the diagonal and cross-peaks. The two lowest vibronic transitions of a 6,13-bis(triisopropylsilylethynyl)-pentacene (TIPS-Pn) molecule serve as a model system for the 3LVS considered above. TIPS-Pn’s 2DES spectra were measured and analyzed using the center line slope (CLS) method. The CLSs of both the diagonal and cross-peaks consist of an exponential decay and an underdamped mode oscillating at a frequency of 264 cm−1, corresponding to the long axis breathing mode of the pentacene moiety of TIPS-Pn. The CLS oscillations’ amplitude and phase of both the diagonal and cross-peaks were measured to have a specific relationship with each other, which is well predicted and simulated by our theory for the 3LVS of TIPS-Pn. We estimate an effective Huang-Rhys factor of ∼0.27, which quantifies the coupling of the two vibronic transitions to the long axis breathing mode of the pentacene moiety of TIPS-Pn. We show that such simultaneous CLS analysis recovering the amplitudes and phase relationships between diagonal peaks and cross-peaks measures the correlated vibrational coherences of different states. This can be used to quantify how different excited states or multi-chromophoric states are coupled to common modes in more complex multistate systems.