Ultrafast imaging of spontaneous symmetry breaking in a photoionized molecular system

The Jahn-Teller effect is an essential mechanism of spontaneous symmetry breaking in molecular and solid state systems, and has far-reaching consequences in many fields. Up to now, to directly image the onset of Jahn-Teller symmetry breaking remains unreached. Here we employ ultrafast ion-coincidence Coulomb explosion imaging with sub-10 fs resolution and unambiguously image the ultrafast dynamics of Jahn-Teller deformations of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{CH}}}_{4}^{+}$$\end{document}CH4+ cation in symmetry space. It is unraveled that the Jahn-Teller deformation from C3v to C2v geometries takes a characteristic time of 20 ± 7 fs for this system. Classical and quantum molecular dynamics simulations agree well with the measurement, and reveal dynamics for the build-up of the C2v structure involving complex revival process of multiple vibrational pathways of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{CH}}}_{4}^{+}$$\end{document}CH4+ cation.


I. COULOMB MOMENTUM MAPPING 1
To calculate the momentum distribution of three-body breakup channel (CH + 2 +H + +H + ) 2 from different configurations, the Coulomb explosion is simulated by the classical Hamilto-3 nian of three point charged particles [1] 4 H = T + V Coul (r 1 , r 2 , r C ) (1) V Coul (r 1 , r 2 , r C ) = 1 r 12 where T is the kinetic energy, r 1 , r 2 and r C are coordinates of two ionized H + and the mass 5 point of CH + 2 , respectively. Molecular dynamics is carried out for 2500 fs, with the initial 6 positions set to equilibrium geometry of C 3v , C 2v , D 2d and initial momentum set to zero.

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The configuration evolution of CH + 4 can be revealed by momentum distribution of CH another H + ion is set to be (1, 0). The distance between the i-th event and one of the C 3v 12 configurations is defined by The distance between event i and C 3v is defined by the minimum value of its distance to 14 each different C 3v configuration and so do C 2v and D 2d . Each exploded CH + 4 is classified To demonstrate the fragmentation channel from the C 2v geometry of methane cation to 1 CH + 2 + H + 2 , we calculate the pathway of the Coulomb explosion after double ionization in the 1 A 1 ground state of C 2v symmetry. The structures along the path were determined for each is shown in Fig. S3. The total amplitude fluctuates due to their commensurate frequencies. 1 The peaks of total vibration means CH + 4 approaches C 2v configuration, which indicates more The initial condition of the classical MD simulation is taken for the geometries in the

III. THE CORRESPONDENCE OF VIBRATIONAL MODES AND SYMMETRY
Here we analyse the distorted geometry of Jahn-Teller molecules under specified vibra- All these symmetry operations form a group C 3v . Similarly, under distortion Q 2 = z, 2 symmetry operations such as C 2 and σ v will conserve which corresponds to point group C s . In conclusion, So there exist some special distortions, such that the distorted geometry can remain in 5 higher symmetry. Thus we know that f 2 mode leads to C 3v and C 2v distorted geometry and 6 the maximal symmetric C 3v is preferred.  Hence, CH + 4 is distorted to D 2d geometry due to e bending mode, and f 2 mode leads 12 to C 3v and C 2v distorted geometry, as shown in Fig.4  To understand the dynamics of the JT distortion, we carried out wave packet dynamics 2 simulation using the multi-configuration time-dependent Hartree (MCTDH) method [5], where θ and φ are the parameterized coordinates and d = 0.373Å is a parametrized distor- The linear JT effect of f 2 vibration produces methane cation in C 3v , which contributes =T +V (θ, φ) where t = 10 cm −1 is the pseudo-rotation parameter, the potential parameters are chosen configuration is much smaller than that in the C 2v configuration. Moreover, the population 9 of the C 2v configurations peaks at ∼18.7 fs, which is almost consistent with the measurement.

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Using this time delay between the two breakup channels, we can reproduce the experimental 11 data shown in Fig. 2 of the main text. The KER of the fragments from the Coulomb explosion 12 is related to the distance R between the centers of mass for the CH + 2 + H + 2 and CH + 3 + H + 13 fragments at the moment of separation by KER ≈ 1/R. We assume that the reduced mass 14 of the nuclei starts moving with constant velocity, thus the distance R can be expressed as where R 0 is the initial distance and v 0 is the velocity adjusted to best fit with 16 the experiment. With a time delay of 18.7 fs between the two breakup channels, we achieve 17 a good agreement between the simulation and the measurement, as shown in Fig. 2  intensity and b reduced pump pulse of intensity ∼ 0.7 × 10 14 W/cm 2 with mean absolute error, the delays between C 3v to C 2v peaks are 20 fs (3 × 10 14 W/cm 2 pump) and 22 fs (0.7 × 10 14 W/cm 2 pump), respectively. The configuration evolution from C 3v to C 2v as well as the delay between these two peaks are both insensitive to the change of pump pulse intensity.
pulse must be substantially reduced. As a result, the relative portion of dication after the 1 pump pulse should become smaller, i.e., the pathway (ii) is suppressed under this condition. 2 We present the result of the temporal evolution for configurations of specific symmetries to charge ratio (m/q) spectra of ionic species for the pump laser pulse alone with various 8 intensities, from which the yields of CH 2+ 4 and CH + 4 can be directly determined. Because part