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2D THz-THz-Raman Photon-Echo Spectroscopy of Molecular Vibrations in Liquid Bromoform Ian A. Finneran, Ralph Welsch, Marco A. Allodi, Thomas Francis Miller, and Geoffrey A. Blake J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02106 • Publication Date (Web): 06 Sep 2017 Downloaded from http://pubs.acs.org on September 7, 2017

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tion that matches the experimental spectrum (labeled X in Fig. 3(a)). These peaks are much weaker, since the Raman detection scheme is depolarized, while the ν3 vibration is polarized and ν6 is depolarized. Finally, a third set of peaks near f2 =5.3 THz (labeled IX in Fig. 3(a)) is observed in the experimental spectrum that is absent from the simulation; it is speculated that these features come from the coupling of vibrational levels with E/h>15 THz. The off-diagonal couplings recovered from the fit confirm the differences between the THz and Raman transitions (see SI). All of the multiquantum polarizability couplings fit to values of near zero, while the multi-quantum dipole couplings are relatively large. To further illustrate the effect of the couplings on the 2D spectrum, a simulation with the fit multi-quantum dipole and polarizability couplings switched is shown in Fig. 3(c)). In this case, strong peaks are predicted at f2 = ±1.9 THz, in complete disagreement with the experiment. Although the RDM simulations indicate the existence of multi-quantum THz (dipole) transitions, they are agnostic as to the atomistic origins of these couplings. The simplest cause of multi-quantum transitions is perhaps vibrational (mechanical) anharmonicity, which arises from the shape of the molecular potential energy surface as a function of the normal mode coordinates. 8,16 However, the intramolecular modes measured here may be expected to be relatively harmonic, 6 and indeed, previous combination and overtone measurements in the linear Raman spectrum of CHBr3 have shown that the vibrational anharmonicity is small for the ν6 and ν3 manifolds. 23 Additional calculations employing vibrational second-order perturbation theory (VPT2) 24 at the Hartree-Fock level also hint to this assumption (see SI). Other possible origins of multi-quantum transitions are coherence transfer (CT) and the ‘through space’ coupling of nearby monomers in the liquid. 25,26 However, such intermolecular coupling only leads to multi-quantum transitions in highly anharmonic modes, which is not the case for the ν6 and ν3 manifolds. 23,26 CT processes result from the spontaneous transfer of vibrational coherences from

many off-diagonal peaks in the first and second quadrants. We note that peaks VII and VIII were observed in our previous low-bandwidth experiment, 7 while all other features are new. Peaks in the first quadrant, (f1 =±,f2 =±), are due to non-rephasing pathways, while peaks in the second quadrant, (f1 =±,f2 =∓), arise from rephasing pathways. The frequencies of the fundamental 1-quantum transitions ν6 and ν3 have been marked with dashed gray lines in Fig. 3(a). Qualitatively, we find that the strongest peaks align with the expected 1-quantum transitions on the f2 axis, while the f1 positions are distributed between 0.5-8.5 THz, likely due to multi-quantum transitions. To interpret these results, we fit the experimental data to a previously developed reduced density matrix (RDM) simulated spectrum with vibrational eigenstates up to 15 THz (Fig. 3(b,d)). 7 The fundamental eigenstate energies and relative intensities were taken from the linear spectrum, 7 while the excited eigenstate energies and 1-quantum dipole/polarizability couplings were fixed at values consistent with a harmonic oscillator. Multi-quantum dipole and polarizability couplings were fit with a basin hopping algorithm 21 and quasi-Newton local minimizer. 22 The fitness function was calculated with an L2-norm and regularization. Alternative models for the couplings were additionally considered and found to poorly fit the experimental spectra. The full details of the RDM modeling are given in the SI. The simulated RDM spectrum, Fig. 3(b), is in qualitative agreement with the experimental spectrum. A representative set of the pathways that contribute to the experimental peaks are highlighted with Feynman diagrams in Fig. 3(e). This analysis indicates that the strongest non-rephasing and rephasing peaks I-VIII are due to multi-quantum ν6-ν3 difference band transitions with the THz pulses, and 1-quantum ν6 transitions with the Raman pulse. No ν6 overtone transitions are observed, likely due to the limited bandwidth of the THz pulses. If the THz bandwidth were to exceed 9.4 THz, these transitions should appear at f1 =4.7, 9.4 THz and f2 =4.7 THz. The simulation also shows a set of peaks near the 1-quantum ν3 transi-

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To gain better insight into the molecular origin(s) of these effects, we performed ab initio calculations on the dipole and polarizability surfaces of an isolated bromoform molecule. The resulting dipole coupling elements are given in the SI. In these calculations, no significant nonlinearities in either the dipole or polarizability surface were found. These results suggest that the nonlinearities are a property of the liquid and not of the single molecule. We therefore performed additional ab initio calculations of the dipole and polarizability surfaces of a bromoform molecule surrounded by seven bromoform monomers. The employed configuration was sampled from a molecular dynamics simulation. Again, no significant nonlinearities were found. Due to the large computational cost of these calculations, however, only a central bromoform and its first solvation shell were treated. Thus, no longer range effects were included. Further, only a single representative configuration of the cluster was selected from an MD simulation of the liquid, and coupled motions between the central bromoform and its first solvation shell were not considered. Since 2D TTR is only sensitive to pathways containing a multi-quantum transition, it is possible that the experiments are strongly selective to relatively rare configurations of the local liquid structure that exhibit large dipole nonlinearities; it is also possible that coupled intramolecular motions originate the 2D TTR signal in this case. To explore the effect of conformational sampling, dipole and polarizability transition matrix elements were calculated using a dipole-induced dipole (DID) 28 model averaging over 2560 cluster configurations. As before, the clusters included only a central CHBr3 and its first solvation shell, and only the motions of the central bromoform were considered. Again, no significant nonlinearities in the coupling elements were found, which might be due either to inaccuracies in the employed force field and the DID model or to the neglect of coupled intramolecular motions. In conclusion, we have measured the broadband 2D THz-THz-Raman spectrum of room temperature liquid bromoform. Many offdiagonal peaks are observed in the spectrum,

interactions with the surrounding ‘bath’, without the loss of phase memory, 25 via dynamical processes, not to their direct excitation during the light-matter interaction via modifications of the dipole and/or polarizability surfaces. The transfer energetics are limited to ∼kT, or 6.3 THz at 300 K. 27 To investigate this mechanism, CT processes were included phenomenologically in our RDM model; while they were found to yield multi-quantum transitions on both the f1 and f2 axes, it was not found that they lead to transitions along only one of the axes, as is seen experimentally. Since CT only changes the relaxation dynamics of the density matrix, it cannot prefer dipole versus polarizability coupling elements in the Hamiltonian. Therefore, CT effects cannot explain the observed multi-quantum dipole and 1-quantum polarizability transitions. Further details are given in the SI. A remaining possibility is that the TTR signatures arise from nonlinearities in the molecular dipole moment (~µ) and polarizability (˜ α) as a function of the vibrational coordinates (q), which lead to multi-quantum THz and Raman transitions, respectively. For example, dipole nonlinearity can be described with 8,16

µ ~ =~µ(q0 ) +

X ∂~µ i

∂qi

qi q0

1 X ∂ 2µ ~ qi qj + ... + 2 i,j ∂qi ∂qj q0

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(2)

where the Taylor expansion summations run over the normal modes. The first term is due to the permanent dipole moment, giving rise to rotational spectra, while the second corresponds to the first dipole derivative and 1-quantum vibrational transitions. It is the higher order terms that generate multi-quantum transitions. This is a likely source of the transitions in the bromoform spectrum, assuming large nonlinearities in the dipole surface and small nonlinearities in the polarizability surface. Particular multi-quantum couplings appear to be strongly favored over others in the RDM simulations, suggesting an interesting underlying mechanism.


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which we have assigned to coupling between the ν3 and ν6 modes. The most prominent features correspond to multi-quantum dipole and 1-quantum polarizability transitions, which are not predicted by electronic structure theory calculations of isolated bromoform molecules or from a cluster model of a representative solvation structure. A more extensive theoretical investigation of the ensemble of solvent configurations and coupled motions will be needed to reveal the molecular origin of the multi-quantum transitions from first principles.

(3) Shim, S.-H.; Gupta, R.; Ling, Y. L.; Strasfeld, D. B.; Raleigh, D. P.; Zanni, M. T. Two-dimensional IR Spectroscopy and Isotope Labeling Defines the Pathway of Amyloid Formation with Residue-Specific Resolution. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 6614–6619. (4) Woerner, M.; Kuehn, W.; Bowlan, P.; Reimann, K.; Elsaesser, T. Ultrafast TwoDimensional Terahertz Spectroscopy of Elementary Excitations in Solids. New J. Phys. 2013, 15, 025039.

Acknowledgement The authors acknowledge Dr. Mostafa Shalaby (Paul Scherrer Institut, Switzerland) for suggesting the use of a diamond window and polarizer beam combiner, and the National Science Foundation (Grants CHE-1214123 and CHE-1057112) for financial support. We also thank Matt Welborn, Ioan Magdau, Brett Savoie, and Feizhi Ding for helpful discussions. R.W. acknowledges financial support from the Deutsche Forschungsgemeinschaft under grant number WE 5762/1-1. M.A.A. acknowledges current support from a Yen Postdoctoral Fellowship from the Institute for Biophysical Dynamics at the University of Chicago.

(5) Lu, J.; Zhang, Y.; Hwang, H. Y.; Ofori-Okai, B. K.; Fleischer, S.; Nelson, K. A. Nonlinear Two-Dimensional Terahertz Photon Echo and Rotational Spectroscopy in the Gas Phase. Proc. Natl. Acad. Sci. U.S.A. 2016, 113, 11800– 11805. (6) Savolainen, J.; Ahmed, S.; Hamm, P. Two-Dimensional Raman-Terahertz Spectroscopy of Water. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 20402–20407. (7) Finneran, I. A.; Welsch, R.; Allodi, M. A.; Miller, T. F.; Blake, G. A. Coherent TwoDimensional Terahertz-Terahertz-Raman Spectroscopy. Proc. Natl. Acad. Sci. U.S.A. 2016, 113, 6857–6861.

Supporting Information Available: Experimental Setup, Reduced Density Matrix (RDM) Modeling, Coherence Transfer, Anharmonic Vibrational Calculations, Calculation of Dipole and Polarizability Non-Linearities. This material is available free of charge via the Internet at http://pubs.acs.org/.

(8) Tokmakoff, A.; Lang, M.; Larsen, D.; Fleming, G.; Chernyak, V.; Mukamel, S. Two-Dimensional Raman Spectroscopy of Vibrational Interactions in Liquids. Phys. Rev. Lett. 1997, 79, 2702–2705.

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