Coherent vibrational dynamics in molecular bond breaking: methyl radical umbrella mode probed by femtosecond x-ray spectroscopy

TL;DR

This work demonstrates that bond breaking can coherently excite vibrational motion in the resulting methyl radical, specifically the ν2 umbrella mode, and that ultrafast x-ray spectroscopy can track the time evolution of core-to-valence transitions to reveal real-space dynamics. A two-channel quantum model with a quartic ground-state potential maps the umbrella motion to observed C1s→SOMO energy shifts, enabling reconstruction of the methyl radical trajectories and exposing pronounced quantum beating due to high coherence and strong negative ν2 anharmonicity. The analysis shows a dominant difference-frequency near $80\,\mathrm{cm^{-1}}$ and, upon symmetry breaking, observation of fundamental ν2 frequencies, with deuteration and potential symmetry-breaking pathways offering insight into the underlying core-excited PES and vibrational coupling. These results provide a framework for probing core-excited potential energy surfaces and coherence in bond-breaking processes using femtosecond x-ray spectroscopy.

Abstract

We report on the observation of coherent molecular vibrations launched by the breaking of a molecular bond. The methyl radical, which is produced by $267\,\mathrm{nm}$ photodissociation of methyl iodide, is excited to high levels in its $ν_2$ ``umbrella" vibrational mode by the dissociation. The ensuing coherent vibrational dynamics are observed by measuring ultrafast time-dependent changes in the x-ray transition energy from the C$1s$ to the singly-occupied valence orbital. Due to symmetry, the real space vibrational motion appears predominantly in the x-ray energy shift at the difference frequencies of the $ν_2$ progression, although the fundamental frequencies of the $ν_2$ mode are also observed. By constructing a fully quantum-mechanical model of the dynamics the coherent superposition is rigorously characterized and the real-space motion of the radicals is reconstructed. The retrieved trajectories are dominated by pronounced quantum beating governed by the high degree of coherent excitation and the strong negative anharmonicity of the $ν_2$ mode.

Figures (14)

• Figure 1: (a) Dissociation of methyl iodide probed with femtosecond x-ray spectroscopy. Excitation via $267\,\mathrm{nm}$ radiation will promote the molecule onto its ${}^{3}Q_0$ surface (blue curve) from where it will evolve towards a conical intersection with the ${}^{1}Q_{1}$ surface (red). The two ensembles of radicals that are produced from the dissociation are shown as ball-and-stick models with their vibrational excitation indicated. (b) The first $100\,\mathrm{fs}$ of the transient absorption signal shows the radical peak initially appearing at $282.9\,\mathrm{eV}$ and moving to its dissociation limit value of $281.7\,\mathrm{eV}$. Black dots are the peak position. We determine a time constant of $(20.7\pm 5.4)\,\mathrm{fs}$ by fitting an exponential decay convolved with a Gaussian function of $36\,\mathrm{fs}$ width for the instrument response (black curve). The depletion of the ground state absorption near $286\,\mathrm{eV}$ is also visible. (c) Potential energy surfaces for the methyl radical along the $\nu_2$ umbrella vibrational motion for the ground state and core-excited state as a function of the bending angle $\vartheta_g$ modeled here. (d) Energetic position of the radical peak as a function of pump-probe delay time (black) decomposed into the difference frequency component due to radicals excited only along the umbrella mode (yellow dashed) and the fundamental frequencies (blue dash-dotted), which become visible due to symmetry breaking (see text). Beginning and end of the filtered data are cropped as these contain the time-domain image of the filter windows. (e) Frequency domain picture of what is shown in panel (d) with the filter windows indicated. A clear peak is seen in the region where the difference frequencies are expected (yellow, dashed), as well as a series of peaks that increase in amplitude again and closely resemble the fundamental $\nu_2$ vibrational progression (blue, dash-dotted). Other features in the low frequency region are due to noise and not associated with any significant signal.
• Figure 2: Application of the two-channel model to the experiment using the populations reported by cheng2011vibrationally. The points in the top panel is the experimental data, where adjacent points have been binned for the fit. The bold red line is the fit of our model. In all panels, blue dash dotted and red dashed lines indicate results for the $\mathrm{I^{*}}$ and $\mathrm{I}$ channel, respectively. The individual energy shifts in the $\mathrm{I}$ and $\mathrm{I^*}$ channels are also shown in the top panel, with a shift applied for visual clarity. Their weighted sum $E_{\mathrm{exp.}}(t) \approx \sigma_\mathrm{I^*} E_\mathrm{cx}^\mathrm{I^*}(t) + (1 - \sigma_\mathrm{I^*})E_\mathrm{cx}^\mathrm{I}(t)$ yields the bold red line.
• Figure 3: (a, b) Ground-state and core-excited state potential energy surfaces of ekstroem2008umbrella. The path along which the real-space motion takes place is shown as black dashed lines. (c, d) Reconstructed real-space motion of the methyl radicals with pure $\nu_2$ activation along the angular coordinate $\vartheta_g$. The radial coordinate $r_\mathrm{CH}$ follows from the black dashed lines in panels (a) and (b). The energy shift (see also fig. \ref{['img:het_fitting']}) closely follows the envelope of the vibrational trajectory. The complex nature of the trajectory in the $\mathrm{I}$ channel is due to the pronounced beating resulting from the high degree of excitation. To a lesser, yet notable extent such beating is also present in the $\mathrm{I^{*}}$ channel trajectory.
• Figure 4: Direct observation of the $\nu_2$ vibrational progression mediated by symmetry breaking. The phase of this oscillation as determined via the Fourier transform (red) is essentially flat across this region. A slight detuning of the $\nu_2$ vibration, due to the concurrent activity in the $\nu_1$ mode may be the reason for the third peak near $750\,\mathrm{cm^{-1}}$ to appear at a slightly higher frequency (see text).
• Figure S1: Relationship between hyperangle $\vartheta$ and $\nu_2$ bending angle $\vartheta_g$ (left panel). Description of the umbrella mode via the hyperangle enables factoring out the bond elongation occurring during the motion. The relationship between bending angle $\vartheta_g$ and the $\mathrm{C-H}$ bond length is shown in the right panel.