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An Observation of Structural Wavepacket Motion: the Umbrella Mode in Rydberg-Excited N-Methyl Morpholine Yao Zhang, Sanghamitra Deb, Hannes Jonsson, and Peter M. M. Weber J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b01274 • Publication Date (Web): 25 Jul 2017 Downloaded from http://pubs.acs.org on July 27, 2017

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The Journal of Physical Chemistry Letters

An Observation of Structural Wavepacket Motion: the Umbrella Mode in Rydberg-Excited N-Methyl Morpholine

Yao Zhang1, Sanghamitra Deb2, Hannes Jónsson1,3, Peter M. Weber1,# 1

Department of Chemistry, Brown University, Providence, RI 02912, USA.

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Beckman Institute for Advanced Science and Technology, University of Illinois at

Urbana-Champaign, Urbana, IL 61801, USA. 3

Faculty of Physical Sciences, University of Iceland, 107 Reykjavík, Iceland.

#

Corresponding Author: [email protected]

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Abstract: We have observed time-resolved, structural dynamics of a coherent vibrational wavepacket in Rydberg-excited N-methyl morpholine, a molecule with 48 internal degrees of freedom. The molecular structure was established by associating the timedependent Rydberg electron binding energy, obtained from time-resolved photoionization-photoelectron spectroscopy, to the molecular structure using selfinteraction corrected density functional calculations. Optical excitation at 226 nm launches an oscillatory wavepacket in the amine umbrella coordinate with a 650 fs period. Even though the Franck-Condon excitation is at an angle of 17°, the wavepacket settles into an oscillation between 4° and -10° within a fraction of a vibrational period and then dephases with a time constant of 750 fs.

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The structural dynamics of molecular systems, i.e. the temporal evolution of the spatial arrangements of atoms and functional groups, plays a central role in our understanding of chemistry. As quantum mechanical systems, the structural dynamics of molecules entails the propagation of vibrational wavepackets, i.e. time-evolving superpositions of vibrational eigenstates (1,2). Most experimental observations have, therefore, utilized some form of vibrationally resolved spectroscopy (3,4,5,6,7). Yet, our understanding of chemistry rests on the visualization of chemical reactions as the structural motion of atoms and functional groups. While a vibrationally resolved spectrum of a wavepacket certainly has projections onto structural dimensions that describe the chemical dynamics, the relation between a vibrational spectrum and structure is generally only indirect. Prior studies that observed wavepacket dynamics and structural motions are mostly focused on small molecules with only few degrees of freedom where the structural dynamics can be correlated to the spectra (8,9,10,11,12,13,14). That approach remains challenging for polyatomic molecular systems. With many vibrational degrees of freedom, the features in vibrational are likely overlapped and difficult to resolve, making any connection to the molecular structure and its dynamics difficult. There remains, therefore, a desire to develop ways for observing the structural motion more directly, in particular in polyatomic molecular systems with many vibrational degrees of freedom. Molecular structure can be observed using diffraction methods or structural spectroscopy. Recent advances in ultrafast time resolved x-ray (15,16,17) and electron scattering (18,19,20) hold out the promise to observe structural motion in polyatomic molecules in real time with diffraction methods. Traditional structural spectroscopy, in particular NMR, microwave or rotational spectroscopy, cannot be applied with ultrafast time resolution, but the recently developed method of photoionization/photoelectron spectroscopy via Rydberg states offers an approach that can be implemented with

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sufficiently fine time resolution to resolve molecular motions. The method rests on the fact that photoionization from a Rydberg state largely retains the vibrational energy of a molecule, so that the entire vibrational Franck-Condon envelope is contained in a relatively sharp spectral line with energy that depends on the structure of the molecule (21,22). The binding energy of the Rydberg electron has been found to be very sensitive to the structure of the molecule as was verified in a variety of molecules (23,24). Theoretical calculations are now sufficiently advanced to connect the observed Rydberg electron binding energy spectrum to the molecular structure (25,26). In the present communication we report that an ultrafast time-resolved measurement of the timedependent Rydberg electron binding energy can also reveal the structural projection of a dynamical wavepacket in a polyatomic molecule. We chose N-methyl morpholine (NMM, C5H11NO), a molecule with 48 degrees of freedom providing a dense set of vibrational states acting as an effective bath. NMM has several conformers in its electronic ground state: the six-membered ring can be in chair, boat or twisted form, and the methyl group on the nitrogen atom can be in equatorial or axial position (See SI). The most stable form is the chair-equatorial configuration, which was calculated to be lower in energy than the chair-axial and twisted forms by 0.193 eV and 0.383 eV, respectively. Consequently, the chair-equatorial conformer is the dominant form of NMM at both room temperature and in the molecular beam of our experiment. Optical excitation of NMM by ultrashort pump laser pulses at 226 nm promotes an electron from the highest occupied molecular orbital, mostly a nitrogen lone-pair, to the 3s Rydberg orbital in which the amine group assumes a near planar geometry. (See SI for details regarding the experimental methods). The sudden switch from sp3 to sp2 hybridization launches a wavepacket along the amine umbrella coordinate. The time-

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resolved photoelectron spectrum, Figure 1a, was obtained by ionizing the molecules with 404 nm (3.06 eV) laser pulses. A spectral feature spanning a binding energy range between 2.80 eV and 3.06 eV is assigned to the 3s Rydberg state by analogy to similar tertiary amine systems (27,28,29,30). This assignment is confirmed by theoretical calculations as discussed below.

Figure 1: (a) Time-resolved photoelectron spectrum of NMM pumped at 226 nm (5.49 eV) and probed with 404 nm (3.06 eV). The color encodes the intensity in arbitrary units. (b) The time trace of a high binding energy slice (2.975 eV to 3.025 eV). The experimental data (blue symbols) are fitted using Eq. 1, with the rising and oscillatory components shown as green and red curves, respectively. (c) The oscillatory component of the spectrum, with the peak centers marked for each time slice between 50 fs and 2250 fs. (d) The steady state spectrum at large delay times, averaged over the range of 2.75 to 3.4 ps.

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The spectrum shown in Figure 1a reveals oscillations in the binding energy that persist for about 1 ps before gradually converging into a broad, steady state feature shown in Figure 1d. Given the well-documented structure sensitivity of the Rydberg electron binding energy (21,22,28,31), we infer that this time dependence reveals the wavepacket dynamics, i.e. that it directly shows the changing molecular structure with time. To determine the dynamic parameters of the oscillation, we integrated the intensity in an energy slice between 2.975 and 3.025 eV and fitted the results to a damped sinusoidal function with period T, phase φ and damping time constant τd: ௧ ݂ሺ‫ݐ‬ሻ = ቀ‫ܥ‬ଵ + ‫ܥ‬ଶ ∙ ݁ ି ൗఛ೏ ∙ sin൫2ߨ‫ݐ‬ൗܶ + ߶൯ቁ ∙ ‫ܫ‬௧வ଴

(Eq. 1)

Here, It>0 is a step function rising at time zero. For the fit, the function f(t) was convoluted with a Gaussian instrument response function measured to be 118 fs (FWHM). This yields an oscillation period of T = 650 (13) fs, a phase of φ = 0.52 (0.11) radian, and a damping time constant of τd = 750 (90) fs (3σ uncertainty is shown in parentheses). The structural wavepacket dynamics was further identified by deconstructing the binding energy spectrum into two components: the time-dependent binding energy oscillations that reveal the wavepacket motion and a fixed-spectrum component that reflects the approach to a steady state. The latter was taken to be the spectrum at long delay times (Figure 1d), with an exponential rise that equals the damping of the wavepacket oscillations, τd. Subtracting this rising, fixed-spectrum component from the experimental data yields the purely oscillatory component shown in Figure 1c. Even though visual inspection of Figure 1a might suggest the oscillation amplitude to decrease over time, that is merely an artifact arising from the decaying intensity of the

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signal. Tracing the peak centers shows that the amplitudes of the swings in the binding energy remain nearly constant, Figure 1c, and span the range from 2.87 eV to 2.97 eV. We note that this binding energy range closely conforms to the broad spectrum at long delay time. This suggests that the wavepacket created by the excitation to the Rydberg state propagates back and forth for several periods, and then disperses into an incoherent superposition of structures. The ability to observe the coherent wavepacket motion so clearly, albeit for only a picosecond, for this large molecule containing 48 internal degrees of freedom, is due to the fact that the Rydberg electron binding energy is only minimally affected by thermal vibrations (21,28,31,32). The time-dependent spectrum is connected to the structural dynamics by calculating the 3s Rydberg electron binding energy using self-interaction corrected density functional theory for a series of molecular geometries that were obtained by scanning the amine umbrella angle of the molecular ion while relaxing other coordinates (the structure of the cation approximates well the structure of the Rydberg state and is easier to calculate). Depending on the structure, the calculated binding energy spans the range from 2.92 to 3.04 eV, which is in close agreement with the experimental data ranging from 2.87 to 2.97 eV. A systematic deviation of 0.07 eV between experimental and computed binding energy is typical for tertiary amines (25,26) and has also been found for the 3p states of the methyl radical (33). The close agreement between experimentally measured and computed binding energy further confirms the assignment of the spectrum to the 3s Rydberg state. As depicted in Figure 2, the 3s binding energy depends strongly on the amine umbrella angle. At time zero, the molecule is lifted to 3s in the equatorial Franck-Condon geometry with a positive value for the umbrella angle. The ensuing dynamics toward a planar (~0°) and then an axial (negative umbrella angle) geometry is expected to be

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associated with a decrease in the binding energy. After reaching the turning point at a negative umbrella angle, the binding energy should again increase until reaching the initial value at the Franck-Condon geometry. A comparison with the observed dynamics, Figure 1, shows that this is exactly what was observed. The oscillations in the measured binding energy spectrum indeed capture this structural motion of the vibrating molecule. Although the optical excitation of NMM initially excites a coherent umbrella motion, the analysis of Figure 1 suggests that the oscillation fades within 2 ps. NMM has 48 internal degrees of freedom, so the coupling of the umbrella motion to the bath modes leads to loss of coherence. The lack of binding energy oscillations beyond the one associated with the umbrella motion suggests that the loss of coherence leads to a statistical distribution of vibrationally excited states. For such a distribution, the majority of vibrational energy goes into modes where the Rydberg electron binding energy is independent of the vibrational excitation (22). Using a classical model treating the modes as harmonic oscillators, we find that once thermalized, about 60 meV of energy remain in the amine umbrella coordinate. As illustrated in figure 2 using red dashed lines, the classical turning points are at +5 and -10°, corresponding to binding energies of 3.03 and 2.97 eV, closely reflecting the observed values. The binding energy spectrum at long time delays, Figure 1d, therefore is seen to reflect the statistical population of the umbrella vibration after dephasing, where a larger population of molecular structures are around the turning points of the incoherent superposition of vibrationally excited eigenstates. Other possible explanations, in particular the involvement of other conformers, have been considered but rejected (see SI).

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Figure 2: The computed potential energy of NMM in the 3s Rydberg state as a function of the amine umbrella angle coordinate (a), and the binding energy of the 3s Rydberg electron as a function of the umbrella angle (b). The calculations used the self-interaction corrected PW91 functional. The dashed red lines illustrate the vibrational amplitude for a thermalized distribution in 3s at the excitation conditions.

In order to further examine the molecular motion and test our model, molecular dynamics (MD) simulations were performed for the NMM cation. Figure 3(a) shows an example of a trajectory projected on the amine umbrella coordinate. Optical excitation places the molecule on the steeply sloping side of the potential surface and induces a vibration that remains active on a picosecond time scale. Other vibrations, for instance the ring twisting motion, are silent or have very small vibrational amplitude (not shown).

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A careful inspection of the trajectory in Figure 3a reveals two vibrational frequencies: a fast component with a 100 fs period and a slower one with a 345 fs period. These periods, obtained by Fourier transformation of the trajectory, are faster than the ones observed in the experiment. This is likely because the MD simulations are, for computational reasons, performed for the ion instead of the 3s Rydberg-excited neutral molecule. The flatness of the potential energy surface (Figure 2a) and the strong dependence of the binding energy on the structure (Figure 2b) indicate that the 3s Rydberg electron could significantly affect the potential energy surface and thus the oscillation period. Indeed, separate experiments using time-resolved x-ray scattering reveal a period of about 420 fs for the ion. It is therefore rational to associate the 345 fs period calculated for the ion with the 650 fs period observed for the Rydberg state. The fast component found in the MD simulation was not experimentally resolved, presumably because the experimental time resolution was not sufficient. The slow frequency vibrational motion of Figure 3a spans a range in umbrella angle between +4° and -10°. Referring to the structure-dependent binding energy curve, Figure 2b, this would imply a range in the computed binding energy from 3.03 to 2.97 eV. Application of the standard correction of 0.07 eV to the DFT-SIC predictions yields values of 2.97 and 2.90 eV, respectively, which is in good agreement with the experimentally observed values of 2.97 and 2.87 eV. Even though the fast oscillation is too fast to be directly observed in our experiment it has a significant effect on the observed spectrum since it changes the molecular structure in a short amount of time: the combined motion of the fast and the slow vibrations leads to a rapid decrease of the umbrella angle, Figure 3a, which is manifest as an apparent phase shift when the slow component is considered alone. The red curve in Figure 3a is a fit of the simulated trajectory with a single sinusoidal function with 345

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(2) fs period and a 1.00 (0.10) radian phase angle. A fit of the experimental oscillation of the binding energy, Figure 1c, gives a phase shift of 0.68 (0.15) radian, which is in reasonable agreement, again considering that the MD calculation of the cation should not be expected to fully match the experiment of the Rydberg state dynamics. By repeating the MD calculations for 50 trajectories with different random initial kinetic energy assignments among internal degrees of freedom, the average shown in Figure 3b is obtained. The trajectories are seen to travel in step early on but gradually lose their phase coherence. This suggests that the structure becomes dispersed on a picosecond time scale, which agrees well with the observed 750 fs dephasing of the oscillation in the Rydberg state.

Figure 3: (a) The time-dependent amine umbrella angle in a single MD trajectory. The red curve in panel (a) is a fit to a single sinusoidal function. (b) At each time step, the median, minimum, and maximum umbrella angles among the 50 trajectories are selected and depicted. This

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illustrates the dephasing of the wavepacket as a smearing out of the oscillations.

In summary, the time-resolved binding energy spectra of Rydberg-excited NMM molecules reveal a real-time view of the coherent structural dynamics. Optical excitation launches a wavepacket that undergoes coherent oscillatory motion along the umbrella coordinate until it dephases into a set of bath states. The time-dependent binding energy spectra reflect the wavepacket dynamics of the active mode, even though a total of 48 vibrational degrees of freedom are present in the NMM molecule. It is ultimately the strong dependence of the binding energy on the amine umbrella angle that enables us to observe the structural dynamics in the time-resolved binding energy spectrum. The Rydberg electron binding energy calculated with the self-interaction corrected DFT is in good agreement with the experimental measurements and helps identify the time-dependent molecular structure. The calculations enable us to relate the binding energy measurements to the structural molecular dynamics. Upon excitation to the 3s Rydberg state by an ultrashort laser pulse at 226 nm, a wavepacket is created at the Franck-Condon geometry. Since the excitation places the wavepacket in the steep, repulsive part of the potential energy surface, it activates the amine umbrella motion. The planarization of the amine group drives the wavepacket motion from the equatorial position towards the axial position and launches oscillations with a period of 650 fs. The coherence is gradually lost with a 750 fs damping time constant, leaving the molecule in a statistical distribution of dispersed structures. The amine umbrella motion in NMM is likely not a unique phenomenon and we expect to find coherent structural dynamics in other molecular systems as well. Yet previous studies on other tertiary amines, including trimethylamine (27), N,Ndimethylisopropylamine (29), and triethylamine (28), have not uncovered such

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wavepacket motion. These systems have much faster vibrational frequencies and flexible side chains that could, conceivably, cause the coherent motion to dampen out more quickly. It is, therefore, likely that the limited time resolution of those experiments has prevented the discovery of the coherent dynamics in the other tertiary amines.

This study was supported by the National Science Foundation (grant number CBET1336105) and by the Icelandic Science Fund. This research was conducted using computational resources and services at the Center for Computation and Visualization, Brown University.

Supporting Information Available: Details about experimental and computational methods; Figure SI-1, showing molecular structures of NMM in the chair-equatorial geometry, the chair-axial geometry and the twisted geometry; and considerations regarding the involvement of other conformeric structures in the observed NMM dynamics.

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