^{1}, Carlos R. Baiz

^{1}, Jessica M. Anna

^{1}, Robert McCanne

^{1}and Kevin J. Kubarych

^{1,a)}

### Abstract

Multidimensional infrared (MDIR) spectroscopy of a strongly coupled multilevel vibrational system (dimanganese decacarbonyl) in cyclohexane solution reveals fully resolved excited vibrational state coherences that exhibit slow decay constants. Detailed analysis of the waiting-time dependence of certain cross-peak amplitudes shows modulation at multiple frequencies, providing a direct signature of excited vibrational coherences resulting from coherence transfer. A new signature of coherence transfer is observed as temporally modulated cross-peak amplitudes with more than one modulation frequency. The relative importance of different coherence transfer paths is considered in the context of the orientational response of a system which includes two vibrational modes with parallel dipole moments. Since MDIR spectroscopy enables spectral isolation of individual excited vibrational coherences (i.e., coherences between fundamental excitations), these experiments report directly on the frequency-frequency correlation functions of the excited states relative to each other as well as relative to the ground state. These results highlight the rich information contained in fully exploring three-dimensional third-order spectroscopy, particularly regarding chemically relevant slower dynamics and the importance of intramolecular interactions leading to dephasing by optically dark or low-frequency modes of the molecule.

The authors wish to thank E. Geva and N. Preketes for useful discussions regarding the general nature of coherent energy transfer. This work was funded in part by a grant from the Rackham Graduate School, by the Petroleum Research Fund of the American Chemical Society and by the National Science Foundation (No. CHE-0748501).

I. INTRODUCTION

II. EXPERIMENTAL METHODS

III. RESULTS

A. Two-dimensional spectra at

B. 2DIR spectra as a function of waiting time

IV. DISCUSSION

A. General vibrational structure

B. Evolution of 2DIR spectra with increasing waiting time

C. Coherence transfer pathways

V. CONCLUSION

### Key Topics

- Coherence
- 75.0
- Dephasing
- 17.0
- Excited states
- 15.0
- Electric dipole moments
- 11.0
- Infrared spectra
- 8.0

## Figures

(a) FTIR spectrum of the carbonyl stretching region of DMDC in cyclohexane. Three major peaks are seen, with shoulders on either side of the largest peak (labeled and ). (b) One- and two-quantum vibrational energy levels of the three main bands of DMDC labeled with the IR transition energies relative to the ground state in , highlighting the states involved in the excited state vibrational coherences. (c) Six representative double-sided Feynman diagrams corresponding to cross peaks which oscillate during the waiting time . The bottom three pathways involve coherence transfer (indicated by the dotted lines) during and (left) and during (right). (d) 2DIR pulse sequence indicating time and wave vector variables.

(a) FTIR spectrum of the carbonyl stretching region of DMDC in cyclohexane. Three major peaks are seen, with shoulders on either side of the largest peak (labeled and ). (b) One- and two-quantum vibrational energy levels of the three main bands of DMDC labeled with the IR transition energies relative to the ground state in , highlighting the states involved in the excited state vibrational coherences. (c) Six representative double-sided Feynman diagrams corresponding to cross peaks which oscillate during the waiting time . The bottom three pathways involve coherence transfer (indicated by the dotted lines) during and (left) and during (right). (d) 2DIR pulse sequence indicating time and wave vector variables.

An absolute value rephasing 2DIR spectrum of DMDC in cyclohexane at shows a large number of peaks, referenced throughout this article as indicated, and detailed in Table I. The FTIR (shown above the 2D spectrum) shows peaks in the same locations. The 2DIR is plotted with 60 evenly spaced contours ranging from 6% to 70% of the maximum intensity.

An absolute value rephasing 2DIR spectrum of DMDC in cyclohexane at shows a large number of peaks, referenced throughout this article as indicated, and detailed in Table I. The FTIR (shown above the 2D spectrum) shows peaks in the same locations. The 2DIR is plotted with 60 evenly spaced contours ranging from 6% to 70% of the maximum intensity.

A series of four 2DIR spectra of DMDC in cyclohexane, taken at different waiting times . Integrating the volume of the circled peak as a function of time delay shows oscillatory behavior caused by the waiting-time excited-state coherence. Oscillation arises because of the two Liouville paths contributing to that 2DIR peak; one involves a ground-state population during while the other contains a coherence between states and . The circled peak is peak 19, which oscillates at ( period).

A series of four 2DIR spectra of DMDC in cyclohexane, taken at different waiting times . Integrating the volume of the circled peak as a function of time delay shows oscillatory behavior caused by the waiting-time excited-state coherence. Oscillation arises because of the two Liouville paths contributing to that 2DIR peak; one involves a ground-state population during while the other contains a coherence between states and . The circled peak is peak 19, which oscillates at ( period).

Peak volumes of the diagonal peaks (a) and the peaks directly beneath them (b) as a function of waiting time. The peaks with the lower value of correspond to paths which go through an overtone in the mode whose diagonal peak has the same value of . The largest peaks in each panel (peaks 13 and 9) have been scaled by a factor of 3 to show the relative intensities on the same plot. As tabulated in the supplemental information, biexponential fits to the decays show fast decay times ranging between 2.5 and for all peaks shown here (Ref. 39).

Peak volumes of the diagonal peaks (a) and the peaks directly beneath them (b) as a function of waiting time. The peaks with the lower value of correspond to paths which go through an overtone in the mode whose diagonal peak has the same value of . The largest peaks in each panel (peaks 13 and 9) have been scaled by a factor of 3 to show the relative intensities on the same plot. As tabulated in the supplemental information, biexponential fits to the decays show fast decay times ranging between 2.5 and for all peaks shown here (Ref. 39).

Peak volumes and respective Fourier transform amplitudes of peaks 5 and 11 [(a) and (b)], 6 and 19 [(c) and (d)], and 15 and 21 [(e) and (f)] as a function of waiting time. Each pair oscillates at a frequency as shown in the absolute value of the Fourier transform of the time-domain volumes.

Peak volumes and respective Fourier transform amplitudes of peaks 5 and 11 [(a) and (b)], 6 and 19 [(c) and (d)], and 15 and 21 [(e) and (f)] as a function of waiting time. Each pair oscillates at a frequency as shown in the absolute value of the Fourier transform of the time-domain volumes.

Peak volumes and their respective Fourier transforms of some of the peaks accessing combination bands. Peak 3 (a) clearly oscillates at the same two frequencies [Fourier transform in (b)] seen in Fig. 4. Peaks 10 [(c) and (d)] and 2 [(d) and (e)], however, show at best only a single broad peak.

Peak volumes and their respective Fourier transforms of some of the peaks accessing combination bands. Peak 3 (a) clearly oscillates at the same two frequencies [Fourier transform in (b)] seen in Fig. 4. Peaks 10 [(c) and (d)] and 2 [(d) and (e)], however, show at best only a single broad peak.

Representative double-sided Feynman diagrams involving single (1CT) and double (2CT) coherence transfers. 1CT paths can lead to additional oscillations beyond what would be expected by neglecting coherence transfer. Paths leading to these oscillations give rise to peaks 3 (a), 10 (b), and 1 (c). While less likely than 1CT paths, 2CT paths contribute significantly to peak 3, as in (d) and (e), but much less to the other peaks.

Representative double-sided Feynman diagrams involving single (1CT) and double (2CT) coherence transfers. 1CT paths can lead to additional oscillations beyond what would be expected by neglecting coherence transfer. Paths leading to these oscillations give rise to peaks 3 (a), 10 (b), and 1 (c). While less likely than 1CT paths, 2CT paths contribute significantly to peak 3, as in (d) and (e), but much less to the other peaks.

## Tables

Peaks present in the 2DIR spectrum of DMDC in cyclohexane. Transition dipoles listed reference the energy level diagram in Fig. 1(b); Liouville paths involving coherence transfer effects are neglected in the assignments.

Peaks present in the 2DIR spectrum of DMDC in cyclohexane. Transition dipoles listed reference the energy level diagram in Fig. 1(b); Liouville paths involving coherence transfer effects are neglected in the assignments.

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