^{1,a)}, Franz Milota

^{2}, Tomáš Mančal

^{3}, Vladimír Lukeš

^{4}, Jürgen Hauer

^{1}, Harald F. Kauffmann

^{1,5}and Jaroslaw Sperling

^{6}

### Abstract

This is the first in a series of two papers investigating the effect of electron-phonon coupling in two-dimensional Fourier transformed electronic spectroscopy. We present a series of one- and two-dimensional nonlinear spectroscopic techniques for studying a dye molecule in solution. Ultrafast laser pulse excitation of an electronic transition coupled to vibrational modes induces a propagating vibrational wave packet that manifests itself in oscillating signal intensities and line shapes. For the two-dimensional electronic spectra we can attribute the observed modulations to periodic enhancement and decrement of the relative amplitudes of rephasing and nonrephasing contributions to the total response. Different metrics of the two-dimensional signals are shown to relate to the frequency-frequency correlation function which provides the connection between experimentally accessible observations and the underlying microscopic molecular dynamics. A detailed theory of the time-dependent two-dimensional spectralline shapes is presented in the accompanying paper [T. Mančal *et al.*, J. Chem. Phys.132, 184515 (2010)].

This work was supported by the Austrian Science Foundation (FWF) within the Project Nos. P22331 and F016/18 *Advanced Light Sources* (ADLIS). A.N. and J.S. thank the Austrian Academy of Sciences for partial financial support by the Doctoral Scholarship Programs (DOCfFORTE and DOC). T.M. acknowledges the kind support by the Czech Science Foundation through Grant No. GACR 202/07/P278 and by the Ministry of Education, Youth, and Sports of the Czech Republic through Research Plan No. MSM0021620835. J.H. gratefully acknowledges support by the Lise Meitner Project No. M1080-N16. The quantum-chemical calculations were performed in part on the Schrödinger III cluster at the University of Vienna.

I. INTRODUCTION

II. QUANTUM-CHEMICAL CALCULATIONS

III. EXPERIMENTAL

IV. RESULTS AND DISCUSSION

A. Two-dimensional electronic spectra

B. Rephasing and nonrephasing signal parts

C. Frequency-frequency correlation function

V. CONCLUSION

### Key Topics

- Absorption spectra
- 12.0
- Electron spectroscopy
- 9.0
- Fourier transforms
- 7.0
- Nonlinear spectroscopy
- 7.0
- Four wave mixing
- 6.0

## Figures

(a) Linear absorption spectrum of PERY in toluene (black solid line) and spectrum of the excitation pulses (green dashed line). The red line indicates the position of the lowest energy transition obtained from ZINDO/S calculations. The inset shows the chemical structure of PERY. (b) Huang–Rhys factors determined from semiemprical AM1 calculations. Only modes that posses Huang–Rhys factors larger than 0.005 are plotted.

(a) Linear absorption spectrum of PERY in toluene (black solid line) and spectrum of the excitation pulses (green dashed line). The red line indicates the position of the lowest energy transition obtained from ZINDO/S calculations. The inset shows the chemical structure of PERY. (b) Huang–Rhys factors determined from semiemprical AM1 calculations. Only modes that posses Huang–Rhys factors larger than 0.005 are plotted.

(a) Side and front views on the B3LYP/SV(P) optimal structure of PERY in the electronic ground state. (b) Visualization of the HOMO (bottom) and LUMO (top) obtained from ZINDO/S//B3LYP/SV(P) calculations.

(a) Side and front views on the B3LYP/SV(P) optimal structure of PERY in the electronic ground state. (b) Visualization of the HOMO (bottom) and LUMO (top) obtained from ZINDO/S//B3LYP/SV(P) calculations.

(a) Schematic setup for recording 2D electronic spectra. (BS) beamsplitter, (CP) compensation plate, (SM) spherical mirror, (DOE) diffractive optical element, (WP) wedge pair, (ND) neutral density filter, (S) sample, (L) lens, (CCD) charge-coupled-device camera. (b) Designation of pulses and time delays in four wave mixing experiments.

(a) Schematic setup for recording 2D electronic spectra. (BS) beamsplitter, (CP) compensation plate, (SM) spherical mirror, (DOE) diffractive optical element, (WP) wedge pair, (ND) neutral density filter, (S) sample, (L) lens, (CCD) charge-coupled-device camera. (b) Designation of pulses and time delays in four wave mixing experiments.

(a) Real and (b) imaginary part of the 2D spectra of PERY in toluene for -delays of 100, 200, 300, 450, 550, 650, and 800 fs. The first, second, and third column of each panel display the corresponding total signal, the rephasing, and the nonrephasing part, respectively. All total spectra are normalized to their absolute maximum value, whereas the rephasing and nonrephasing parts are plotted with their respective contribution to the total signal. Contour lines are drawn at 5% intervals starting at ±10%. Red lines indicate positive signals, blue lines negative ones. The solid line in the real part indicates the diagonal, whereas the black lines in the imaginary part are drawn at the zero crossings between the positive and negative features.

(a) Real and (b) imaginary part of the 2D spectra of PERY in toluene for -delays of 100, 200, 300, 450, 550, 650, and 800 fs. The first, second, and third column of each panel display the corresponding total signal, the rephasing, and the nonrephasing part, respectively. All total spectra are normalized to their absolute maximum value, whereas the rephasing and nonrephasing parts are plotted with their respective contribution to the total signal. Contour lines are drawn at 5% intervals starting at ±10%. Red lines indicate positive signals, blue lines negative ones. The solid line in the real part indicates the diagonal, whereas the black lines in the imaginary part are drawn at the zero crossings between the positive and negative features.

(a) Amplitude and (b) phase of the 2D spectra of PERY in toluene recorded at -delays of 100, 200, 300, 450, 550, 650, and 800 fs. The first, second, and third column of each panel display the corresponding total signal, the rephasing and the nonrephasing part, respectively. The amplitude part total spectra are normalized to their absolute maximum value, whereas the rephasing and nonrephasing parts are plotted with their respective contribution to the total signal. Contour lines are drawn at 5% intervals starting at 10% in the amplitude part spectra and at intervals in the phase spectra. The zero-phase line is indicated in each phase spectrum. Note the different spectral range in the representation of the phase spectra.

(a) Amplitude and (b) phase of the 2D spectra of PERY in toluene recorded at -delays of 100, 200, 300, 450, 550, 650, and 800 fs. The first, second, and third column of each panel display the corresponding total signal, the rephasing and the nonrephasing part, respectively. The amplitude part total spectra are normalized to their absolute maximum value, whereas the rephasing and nonrephasing parts are plotted with their respective contribution to the total signal. Contour lines are drawn at 5% intervals starting at 10% in the amplitude part spectra and at intervals in the phase spectra. The zero-phase line is indicated in each phase spectrum. Note the different spectral range in the representation of the phase spectra.

The four Feynman diagrams graphically illustrating the Liouville space pathways for a two-level system within the rotating wave approximation. and denote ground and excited state, respectively.

The four Feynman diagrams graphically illustrating the Liouville space pathways for a two-level system within the rotating wave approximation. and denote ground and excited state, respectively.

Oscillating features extracted from the 2D spectra of PERY in toluene. (a) Ellipticity (filled circles) and CLS (open circles) of the peak in the real 2D spectra. (b) Relative amplitudes of the rephasing (filled circles) and the nonrephasing (open circles) part of the real 2D spectra. (c) Inhomogeneity index extracted from the real part 2D spectra as defined in Eq. (4). (d) Slope of the nodal line separating the positive and negative feature in the imaginary 2D spectra. (e) Slope of the phase line in the phase 2D spectra.

Oscillating features extracted from the 2D spectra of PERY in toluene. (a) Ellipticity (filled circles) and CLS (open circles) of the peak in the real 2D spectra. (b) Relative amplitudes of the rephasing (filled circles) and the nonrephasing (open circles) part of the real 2D spectra. (c) Inhomogeneity index extracted from the real part 2D spectra as defined in Eq. (4). (d) Slope of the nodal line separating the positive and negative feature in the imaginary 2D spectra. (e) Slope of the phase line in the phase 2D spectra.

One-dimensional four-wave mixing signals of PERY in toluene. Top and bottom panels share the same abscissa, color scales are shown as insets in the bottom panels. (a) Three-pulse photon echo peak-shift trace (top) and the corresponding frequency integrated three-pulse photon echo signal as a function of delay and . (b) Frequency integrated (top) and frequency resolved (bottom) TG signal. (c) Frequency integrated (top) and frequency resolved (bottom) PP signal.

One-dimensional four-wave mixing signals of PERY in toluene. Top and bottom panels share the same abscissa, color scales are shown as insets in the bottom panels. (a) Three-pulse photon echo peak-shift trace (top) and the corresponding frequency integrated three-pulse photon echo signal as a function of delay and . (b) Frequency integrated (top) and frequency resolved (bottom) TG signal. (c) Frequency integrated (top) and frequency resolved (bottom) PP signal.

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