Molecular Bond Breaking Achieves Coherent Vibrations in Methyl Radical Umbrella Mode

Researchers have, for the first time, directly observed coherent molecular vibrations triggered by the breaking of a chemical bond. Christian A. Schröder, John H. Hack, and Joshua L. Edwards, all from the University of California, Berkeley and Lawrence Berkeley National Laboratory, alongside Zhiyu Zhang, J. Tyler Kenyon, and Qiyue Wang et al., used femtosecond X-ray spectroscopy to probe the ‘umbrella’ vibrational mode of the methyl radical created by photodissociation. This work is significant because it provides direct insight into how energy flows during bond breaking, revealing pronounced quantum beating governed by the molecule’s strong anharmonicity and demonstrating a rigorous characterisation of the coherent superposition of vibrational states?

Experiments show that impulsive excitation, typically achieved with laser pulses, can also be induced by the rapid geometric changes inherent in bond breaking. Previous ultrafast studies primarily focused on the iodine atom produced during methyl iodide dissociation, examining the transition state region or conical intersection. This work complements those studies by selectively probing the methyl radical, enabling the identification of vibrational coherence and offering a unique perspective on the dissociation process.

The team achieved a temporal instrument response of (36 ±6) fs and a spectral resolution of approximately 300 meV, allowing for precise measurements of the ultrafast dynamics. The research establishes a clear link between bond breaking and the initiation of coherent vibrational dynamics, demonstrating that the dissociation of methyl iodide can effectively transfer energy to the resulting methyl radicals. By tracking the initial energy shift of the C1s to SOMO x-ray absorption peak, scientists determined a dissociation time constant of (20.7 ±5.4) fs. Furthermore, the observed vibrational coherence is attributed to the energy partitioning during dissociation, with radicals originating from different pathways exhibiting varying levels of excitation. This breakthrough opens avenues for controlling molecular fragmentation and manipulating chemical reactions through the precise excitation of vibrational modes.

X-ray Spectroscopy of Methyl Radical Vibrations reveals key

This technique allowed researchers to monitor the vibrational motion through shifts in x-ray energy at frequencies corresponding to the vibrational progression and fundamental mode. The team utilised a Hamiltonian, expressed as H(θ) = − 1/2mr2eq0.1 sin θ ∂/∂θ sin θ ∂/∂θ + V(θ), to represent the ν2 progression in the CH3 radical, where θ is the hyperangle and req is the equilibrium C-H bond hyperradius. Discretisation on a 512-point grid, using the ‘eigs’ function from the scipy. sparse module in Python, enabled numerical diagonalisation of this Hamiltonian. The potential energy function, V(θ) = αθ2 + βθ4, was optimised to match published data for the umbrella progression, achieving accurate representation of the vibrational energy levels.

The experimental setup involved measuring the core-to-valence transition energy as a function of time, accounting for contributions from both the I and I∗ dissociation channels of methyl iodide. The observed transition energy, Eexp. cx(t), was modelled as a weighted sum of the transition energies from each channel, defined by Eexp. (t) ≈σI∗EI∗ cx(t) + (1 −σI∗)EI cx(t), where σI∗ represents the relative population of radicals originating from the I∗ channel. This approach allowed for accurate determination of the momentary transition energy at each time step, revealing the influence of the coherent vibrational motion on the x-ray absorption spectrum. A coherent superposition was assembled from the eigenfunctions, described by ψ(θ, t) = νmax Σi=0 |ai| φi(θ)e−iωite−iφi, where ai and φi represent the amplitudes and phases of the contributing eigenfunctions. The expectation value of the bending angle was then calculated, revealing the time-dependent modulation of the molecular geometry due to the coherent vibrational dynamics, and providing a direct link between the spectroscopic measurements and the underlying molecular motion.

Molecular bond breaking reveals coherent vibrational dynamics

Applying a two-channel model to the experimental data, the researchers achieved a robust fit, demonstrating the model’s ability to accurately capture the time-dependence of the radical’s x-ray absorption peak over the entire range of time delays. This confirms the model provides an appropriate description of the microscopic dynamics for pump-probe delays greater than 75 fs, strengthening the claim that coherent vibrational dynamics are induced via the dissociation of the molecular bond. Data shows that the oscillatory trajectories exhibit pronounced beating in the I channel, leading to large excursions of the bending angle at approximately 250 fs, 830 fs, and 1.1ps. While beating is also present in the I∗ channel, it is significantly less pronounced, and the angular displacement is smaller, consistent with a lower degree of vibrational excitation.

Scientists evaluated the displacement of the angle θ −θ0, finding that the energy shift closely follows the envelope of the vibrational trajectory. The model determined a value of Ecx 1 = (−9.0 ±2.2) eV/rad2 for the quadratic expansion of the core-excited state energy, indicating a double-well structure in the potential energy surface. Tests prove that despite discrepancies with calculations from Ekstr om et al., which yielded Ecx 1 = (−2.89 ±0.01) eV/rad2, the model captures the essential aspects of the observed phenomena. The researchers acknowledge that the overlap of signals from the I and I∗ channels in the experiment introduces approximations in the determination of the peak position, potentially contributing to the observed discrepancies.

Methyl radical motion via quantum beating reveals complex

The observed dynamics map the real-space vibrational motion onto an observable energy shift at frequencies related to the vibrational progression. The authors acknowledge that the complex dissociation process of methyl iodide presents challenges for analysis. However, the developed modelling approach could be extended to determine the curvature of potential energy surfaces in future studies, provided vibrational populations and frequencies are known. Future research may also explore the mechanisms responsible for symmetry breaking, which currently remain unclear, but represent a promising area for investigation.