Center Line Slope Analysis in Two-Dimensional Electronic Spectroscopy

Abstract

Center line slope (CLS) analysis in 2D infrared spectroscopy has been extensively used to extract frequency–frequency correlation functions of vibrational transitions. We apply this concept to 2D electronic spectroscopy, where CLS is a measure of electronic gap fluctuations. The two domains, infrared and electronic, possess differences: In the infrared, the frequency fluctuations are classical, often slow and Gaussian. In contrast, electronic spectra are subject to fast spectral diffusion and affected by underdamped vibrational wavepackets in addition to Stokes shift. All these effects result in non-Gaussian peak profiles. Here, we extend CLS-analysis beyond Gaussian line shapes and test the developed methodology on a solvated molecule, zinc phthalocyanine. We find that CLS facilitates the interpretation of 2D electronic spectra by reducing their complexity to one dimension. In this way, CLS provides a highly sensitive measure of model parameters describing electronic–vibrational and electronic–solvent interaction.

From wavelike to sub-diffusive motion: exciton dynamics and interaction in squaraine copolymers of varying length

“…8,9 While traditional TA spectroscopy employs one pump and one probe pulse, an extension using a pair of pump pulses is offered by coherent two-dimensional electronic spectroscopy (2DES). [10][11][12][13][14][15] The resulting frequency resolution of both the pump and the probe step allows the analysis of lineshapes, 16 transition couplings, 17 coherent dynamics, 18 state-tostate population transfer kinetics, [19][20][21] and coupling to dark states such as charge-transfer states. 22 In the double-quantum coherence variant of third-order 2DES the energetic positions and lineshapes of higher excited/biexciton states can be probed as well, though their kinetic evolution is not accessible for lack of another time variable.…”

Two-dimensional UV spectroscopy: a new insight into the structure and dynamics of biomolecules

“…The eld of theoretical spectroscopy deals with developing generalized models for incorporating the above phenomena into the simulations beyond the phenomenological treatment of eqn (4) which would enable comparison with the experiment, as well as with the development of methods for extracting physical quantities associated with the phenomena responsible for the lineshapes from the raw experimental data. [75][76][77] Much less attention has been devoted to the accurate computation of the transition energies 3 i and the transition dipole moments m ij , the key ingredients required for simulating the third-order nonlinear response recorded in 2DUV maps. This aspect is addressed in the next section.…”

Measuring Ultrafast Spectral Diffusion and Correlation Dynamics by Two‐Dimensional Electronic Spectroscopy

“…It can also be seen that in general 0≤ CLSω τ ≤1, as in the partially correlated case of Figure b. Alternatively, the CLS can be obtained as CLSω t in a similar fashion as CLSω τ with the difference that the slices of 2D spectra were taken parallel to the probe frequency and the CLSω t value is the inverse of the gradient of the line connecting the maxima . Within certain approximations such as the short time approximation, where T is much longer than the coherence times τ and t , the 2D peakshape can be described by the expression, …”

“…We should note again that the above theoretical consideration applies for Gaussian fluctuation. For systems where the fluctuation is non‐Gaussian, the 2D peak will no longer present a 2D Gaussian shape and the center line will not be a straight line . The analysis mentioned above is then strictly not applicable in such cases.…”