Extracting the Frequency-Dependent Dynamic Stokes Shift from Two-Dimensional Electronic Spectra with Prominent Vibrational Coherences

Abstract

The dynamic Stokes shift is a common means for characterizing ultrafast solvation dynamics of electronically excited states. Here we extract the excitation frequency-dependent dynamic Stokes shift from two-dimensional electronic spectra (2DES) of cresyl violet, a molecule with a well-defined vibronic progression. The extracted dynamic Stokes shift function, S(t), exhibits oscillatory behavior, and the oscillatory components are assigned to intramolecular vibrational modes through DFT and TD-DFT calculations. The well-characterized oscillations are incorporated into the fitting procedure of S(t). The excitation frequency dependence of the ultrafast response is examined through the analysis of S(t) obtained from slices taken at different excitation frequencies of the 2DES spectra. The extracted ultrafast timescales range from 36 to 98 fs, and we interpret the frequency dependence of the timescales in the context of other dynamic processes that also lead to lineshape changes in the 2DES spectrum, such as vibrational energy relaxation and spectral diffusion. 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.

The Influence of Electronic Polarization on Nonlinear Optical Spectroscopy

“…In the SI, we show that with a short-time expansion for g ( t ) in eq around t 2 to the first order in t 1 and t 3 and the use of the harmonic QCF for the excitation energy fluctuation quantum TCF, the Stokes shift function directly gives the normalized excitation energy fluctuation classical TCF, namely This well-known result for time-resolved fluorescence spectroscopy within linear response theory and the high-temperature (classical) limit has also been applied to other nonlinear spectroscopies. ,,− With the short-time approximation, the static Stokes shift is simply twice the reorganization energy, λ, defined in eq (see the SI for details), and with the harmonic QCF, the static Stokes shift is equal to βC cl (0).…”

“…If we assume that the GB peak initially overlaps with the SE peak and does not shift during t 2 , the splitting between the GB and SE peaks along the ω 3 axis (see Figure d), Δω ( t 2 ), is a good proxy for ω SE (0) – ω SE ( t 2 ), and the Stokes shift function can then be approximated by Note that Δω (∞) is equal here to the static Stokes shift. For a 2DES experiment, due to the limited bandwidth of the laser pulses, the GB and SE peaks may not be well-resolved, and more sophisticated procedures have been devised to extract the dynamic Stokes shift based on the frequencies at half of the maximum in the normalized projections of the 2DES signal onto the probe frequency axis. , …”

“…One of the methods used for analyzing environment dynamics in nonlinear spectroscopy is extracting the dynamic Stokes shift, which measures the evolving shift in frequency between absorption and emission, e.g., from time-resolved fluorescence spectroscopy and more recently from 2DES. 4 The long-time scale of this dynamic Stokes shift signal reports on the solvent-induced relaxation of the electronic excitation, revealing the time scale of the underlying solvation dynamics of the system. If the time resolution of the nonlinear spectroscopic experiment is sufficiently high (e.g., subpicosecond resolution), oscillations may also be observed in the dynamic Stokes shift signal due to the vibrational coherences arising from the intramolecular vibrations of the chromophore.…”

“…Ultrafast nonlinear optical spectroscopy, such as transient absorption (TA) and two-dimensional electronic spectroscopy (2DES), deepens our understanding of electronic excited states and energy-transfer processes by revealing changes in absorption and emission as a function of time. The dynamic Stokes shift reports on the ultrafast solvation dynamics that occur upon chromophore excitation, − both from fast solvent inertial response and slower solvent reorganization. For nonlinear optical spectra, both vibrational coherences and relaxation and the solvent dynamics manifest through peaks shifting in energy and intensity over time as the excited state evolves. − Theoretical simulations offer the opportunity to connect these complex signals to atomistic and electronic dynamics.…”

“…One of the methods used for analyzing environment dynamics in nonlinear spectroscopy is extracting the dynamic Stokes shift, which measures the evolving shift in frequency between absorption and emission, e.g., from time-resolved fluorescence spectroscopy and more recently from 2DES . The long-time scale of this dynamic Stokes shift signal reports on the solvent-induced relaxation of the electronic excitation, revealing the time scale of the underlying solvation dynamics of the system.…”