Extracting The Frequency Fluctuation Correlation Function From Two-Dimensional Electronic Spectra Via The Dynamic Stokes Shift

The dynamic Stokes shift is a common means to characterize the ultrafast solvation dynamics of excited electronic states. Under the linear response approximation, the extracted dynamic Stokes shift is equivalent to the normalized frequency fluctuation correlation function (FFCF). Two-dimensional electronic spectroscopy is a powerful tool for investigating the ultrafast solvation dynamics as it provides both high temporal and spectral resolution. General procedures for extracting the dynamic Stokes shift from 2DES spectra have been developed by our group and I extend the procedures to systems with prominent vibrational coherences. Cresyl violet, a well-studied test system for the ultrafast community, exhibits strong oscillatory components and a larger Stokes shift and as such was chosen as a model system to test and extend the analysis of the dynamic Stokes shift to 2DES with oscillatory features. For the 2DES of cresyl violet, the well-characterized oscillatory modes are incorporated into the fitting of the Stokes shift function so as to extract the ultrafast timescale associated solvation dynamics. The excitation frequency dependence of the ultrafast response is examined through analysis of the Stokes shift function obtained from slices taken at different excitation frequencies of the 2DES spectra. Through comparison of the extracted timescales, we find that the fastest timescales are extracted over a range of excitation frequencies, where contributions from vibrational relaxation and spectral diffusion can be minimized. In addition, we conduct a comparison to test our procedure for extracting the FFCF from analysis of the dynamic Stokes shift against other spectral line shape analysis methods, such as the center line slope, ellipticity and inhomogeneity index. To test the analysis procedures 2DES spectra were simulated with varying Stokes shifts and with the incorporation of vibrational relaxation. The simulated spectra were analyzed using different lineshape analysis procedures and the extracted FFCF were compared to the FFCF from the input model. We find that the analysis of the dynamic Stokes shift from a slice taken from the center of the 2DES spectra was generally more effective for extracting the correlation function from 2DES for systems with larger Stokes shifts. To conclude, the dynamic Stokes shift is an effective method to extract FFCF from the 2DES when the system has a larger Stokes shift