Ultrafast electron diffraction imaging of bond breaking in di-ionized acetylene

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Science  21 Oct 2016:
Vol. 354, Issue 6310, pp. 308-312
DOI: 10.1126/science.aah3429

Acetylene's scission visualized by selfie

Can molecules take pictures of themselves? That is more or less the principle underlying laser-induced electron diffraction (LIED): A laser field strips an electron from a molecule and then sends it back to report on the structure of the remaining ion. Wolter et al. applied this technique to acetylene to track the cleavage of its C–H bond after double ionization (see the Perspective by Ruan). They imaged the full structure of the molecule and also distinguished more rapid dissociative dynamics when it was oriented parallel rather than perpendicular to the LIED field.

Science, this issue p. 308; see also p. 283


Visualizing chemical reactions as they occur requires atomic spatial and femtosecond temporal resolution. Here, we report imaging of the molecular structure of acetylene (C2H2) 9 femtoseconds after ionization. Using mid-infrared laser–induced electron diffraction (LIED), we obtained snapshots as a proton departs the [C2H2]2+ ion. By introducing an additional laser field, we also demonstrate control over the ultrafast dissociation process and resolve different bond dynamics for molecules oriented parallel versus perpendicular to the LIED field. These measurements are in excellent agreement with a quantum chemical description of field-dressed molecular dynamics.

Ultrafast imaging of atomic motion in real time during transitions in molecular structure is a prerequisite to disentangling the complex interplay between reactants and products (1, 2) because the movements of all atoms are coupled. Ultrafast absorption and emission spectroscopic techniques have uncovered numerous insights in chemical reaction dynamics (3, 4) but are limited by their reliance on local chromophores and their associated ladders of quantum states rather than global structural characterization.

Reaction imaging at the molecular level requires a combination of few-femtosecond temporal and picometer spatial measurement resolution (5). Among the many techniques that are currently under intense development, x-ray scattering can reach few-femtosecond pulse durations at photon energies of 8.3 keV (1.5 Å) (6) with a demonstrated measurement resolution of 3.5 Å (7). Challenges for such photon-based approaches are the coarse spatial resolution and the low scattering cross sections, especially for gas-phase investigations. Electron scattering (8) provides much-larger-interaction cross sections and smaller de Broglie wavelengths but suffers from space charge broadening, which decreases the temporal resolution. Consequently, measurements have demonstrated 7-pm spatial and 100-fs temporal resolution (9, 10) in gas-phase experiments. Remedies to improve temporal resolution include relativistic electron acceleration (11) or electron bunch compression (12) with 100- and 28-fs limits, respectively. Compared with such incoherent scattering of electrons from an electron source off a molecular target, laser-induced electron diffraction (LIED) is a self-imaging method based on coherent electron scattering (1317). In LIED, one electron is liberated from the target molecule through tunnel ionization and then accelerated in the field and rescattered off its molecular ion, acquiring structural information. The electron recollision process occurs within one optical cycle of the laser field and permits the mapping of electron momenta to recollision time (18, 19).

Here, we used LIED to image an entire hydrocarbon molecule [acetylene (C2H2)] at 9 fs after ionization-triggered dissociation and visualize the departure of a proton. Our methodology combined mid-infrared (mid-IR) LIED with single-molecule coincidence detection in a reaction microscope (2022) and used an additional laser control field to impulsively align the molecule (supplementary materials). The laser control field, a 1700-nm pulse, was sent before the 3100-nm LIED pulse and oriented the rotationally cold C2H2 molecule parallel or perpendicular to the LIED field depending on the time delay. The 3100-nm pulse triggered molecular dissociation and, at the same time, collected structural snapshots of the entire C2H2 molecule. The alignment-dependent dynamics (23) were structurally imaged for both orientations. We chose C2H2 because it is one of the best-studied hydrocarbons (2427) and offers the numerous degrees of freedom and multitude of structural dynamics found also in larger and more complex molecules (1, 28, 29). Because of the strong field nature of LIED, many different fragmentation channels and ionization states occur simultaneously. Our specific implementation of mid-IR LIED with single-molecule coincidence detection provides a remedy because post-selection of data regains channel selectivity. Using this capability, we specifically chose to isolate and examine the dissociation of the C2H2 dication (C2H22+→ H+ + C2H+) because it results in a proton H+ and an ethynyl C2H+ moiety. This prototypical dissociation pathway is interesting because it presents one of the fastest expected proton motions and can proceed via two different pathways.

The relevant cuts through the potential energy surface (PES) of C2H2 along one C–H direction are shown in Fig. 1A, including states that are relevant for the desired dissociation channel of C2H22+ (30, 31) at the present experimental conditions by using a 65-fs (6.3 cycle), 3100-nm pulse (32, 33) with a peak intensity of (65 ± 16) TW/cm2. The pulse parameters were chosen in order to position the experiment in the sequential double ionization (SDI) regime in which the LIED imaging electron is ejected independently from the first electron in a second tunnel ionization step before scattering off the C2H2 dication (supplementary materials). It is known (26, 30, 31) that the resulting pair of proton H+ and ethynyl C2H+ moiety originates via different possible pathways from the C2H22+ dication: (i) The first dissociative excited singlet and triplet states, the 1Πu and the 3Πu states, can be reached through ionization from the σg type highest occupied molecular orbital (HOMO)–1 of the neutral ground state (1σg2, 1σu2, 2σg2, 2σu2, 3σg2, 1πu2, 1πu2) followed by tunnel ionization from the πu type HOMO of the excited cationic 2Σg+ state (26, 34); (ii) the dication possesses a long-lived metastable triplet state [3Σg lifetime 108 ns (35)] and two metastable singlet states (1Σg+ and 1Δg) that can be reached via sequential tunnel ionization of two πu electrons. In this case, first one electron tunnels from the HOMO of the neutral ground state (1Σg+), populating the singly ionic doublet 2Πu state; then, a second electron tunnels from the HOMO of the singly ionic ground state to populate one of the aforementioned dicationic states. We were interested in the direct dissociation channel that leads to fast proton loss. A simple estimation of the initial speed of the C–H bond elongation, which is based on the curvature of the 3Πu PES, yields an initial elongation velocity of 9 pm/fs from the initial C–H bond length of 1.07 Å in the Frank-Condon region.

Fig. 1 Identification of the relevant states leading to proton ejection.

(A) The calculated relevant energy levels and possible pathways (34) leading to dissociation of C2H2 and departure of one proton (26, 35). The calculation is detailed in the supplementary materials. Two main pathways are identified, one leading to dissociative PES and fast dissociation (i), the other via metastable states to slow dissociation (ii). (B) These pathways are identified in the PIPICO analysis and (C) exhibit alignment-dependent fragment yields. (B) is shown here for perpendicularly oriented C2H2; the parallel case is provided in fig. S4.

To obtain the clearest possible conditions for imaging the direct proton loss channel, and to investigate its dependence on the LIED field, we impulsively aligned the C2H2 molecule with an additional 1700-nm, 98-fs pulse focused to a peak intensity of (20 ± 5) TW/cm2 into the interaction region of the 3100-nm LIED pulse. Having ensured that the 1700-nm pulse did not induce ionization, we could distinguish between the different pathways from a photo-ion/photo-ion coincidence (PIPICO) analysis of our data, which is shown in Fig. 1B (here for perpendicularly oriented C2H2). The diagonally sloping line (Fig. 1B, top left to bottom right) shows a very pronounced section [Fig. 1B, top left corner, (i) centered around 0.8 μs/4.1 μs], which corresponds to direct dissociation of the dication from its excited 1Πu and 3Πu states. Section (ii) of this line [Fig. 1B, top left corner 1.0 μs/4.0 μs to bottom right corner 2.6 μs/3.1 μs] is much weaker and is identified with the dication’s meta-stable states 3Σg, 1Δg, and 1Σg+ (35). The proton-ethynyl pairs of the fast deprotonation channel are accompanied by two shallow lines, above and below, respectively associated with reactions involving a 13C atom and a neutral product that is not detected with the reaction microscope: C2H22+ → H+ + C2+ + H. Both of these processes, as well as the slow proton loss channel, occur with a probability two orders of magnitude lower than that for the fast proton loss channel. Nevertheless, we explicitly excluded those channels by isolating the three-dimensional (3D) momentum distribution of the electrons that correspond to the reaction moieties originating from the fast proton loss channel. This permits extraction of structural information only from electrons that rescattered off the H+ and C2H+ fragment pairs from direct dissociation. Additional support to identify population of the fast proton ejection channel (i) stems from measurements of the fragment pair ion yield (H+ + C2H+) as a function of delay between alignment and LIED pulse. The results are shown in Fig. 1C and are in excellent agreement with previous work (36) in which this temporal dependence was used to identify the two different dication fragmentation channels.

Having identified the direct proton ejection channel (via 1Πu and 3Πu), we turned to extracting structural information from its scattered electrons. Our LIED methodology (20) permits use of momentum coincidence arguments to associate the scattering electron to only the moieties of the fast proton loss channel. Applying such constraints to the data analysis reduces the event rate by a factor of 83, but the elimination of the general electron scattering background ensures that the resulting momentum map of the electrons bears only structural information of the dissociating C2H2 dication (Fig. 2A); the left half of the image shows data for parallel oriented C2H2, and the right half of the image shows data for perpendicularly oriented C2H2. These momentum maps correspond to the doubly differential electron scattering cross section measured under the influence of the mid-IR LIED field. However, molecular structure is extracted from the field-free molecular differential cross section (mDCS), which is to say that we need to correct for the influence of the mid-IR field. Operating LIED with the 3100-nm pulse in the deep tunneling regime permits application of the semiclassical model (18, 37) in order to determine the vector potential of the LIED field at the time of rescattering for a given electron energy. The vector potential presents the LIED field’s influence on the rescattering electron as an offset from zero (field-free) momentum that is simply subtracted from the measurement. The mDCS is then extracted by recording the number of counts along the circumference of a circle whose radius corresponds to the scattering momentum and whose origin is shifted by the vector potential from zero momentum; we show an example in black in Fig. 2A for an electron kinetic energy of 50 eV. Information about the position of the molecule’s nuclei is encoded as energy modulations onto the mDCS due to scattering interference. To make these oscillations directly visible, we calculated the molecular contrast factor (MCF), a renormalized quantity, from the mDCS (supplementary materials).

Fig. 2 Measurement of bond distances with LIED.

(A) The electron momentum distribution in coincidence with the moieties corresponding to the fast proton loss channel. The left half shows data for parallel aligned C2H2, and the right half shows data for perpendicularly aligned C2H2. (B) The MCF for both cases, parallel (top, blue) and perpendicular (bottom, red). Error bars are derived from the experiment based on Poissonian statistics (supplementary materials). (C and D) Experimental data (white data points with error bars extracted from the MCF fit) overlaid with numerical results (density plot) for cuts through the 3D solution space at the location of its minima. The locations of these cuts correspond to C–C distances of 1.48 Å for the parallel case (C) and 1.38 Å for the perpendicular case (D). (C) shows elongation of one C–H bond to more than twice the equilibrium bond length, corresponding to bond breakage, whereas the other C–H bond is still bound. (D) represents a more symmetric scenario, nearing heterolytic cleavage of one of the two C–H bonds.

Shown in Fig. 2B are the resulting MCFs for both perpendicularly oriented (Fig. 2B, red circles) and parallel oriented (Fig. 2B, blue squares) C2H2. Striking differences are immediately apparent between the MCFs of both orientations, indicating that different structures are observed. The positions of the individual scattering centers, and hence atomic distances, are extracted by calculating MCF patterns for a wide range of possible positions. Comparing the measured MCF with these patterns, we obtained the full 3D solution space (minimum fitted χ2 value as a function of the C–C distance and two C–H distances) of the instant condition of the molecular wave packet at the time of the electron’s return. The solution space is obtained without assumptions such as partially frozen nuclei or linear elongation and includes independent symmetric as well as asymmetric elongation of C–H bonds.

We obtained two different solutions, one for the parallel and one for the perpendicular case, and present 2D cuts through the 3D solution space at those positions: The solution for the parallel case for which we measure a C–C bond length of (1.48 ± 0.11) Å, a value 23% greater than the 1.204 Å equilibrium bond length (38) in neutral C2H2, is shown in Fig. 2C. Associated C–H distances are (2.31 ± 0.15) Å and (1.19 ± 0.10) Å, corresponding to 118 and 12% elongations, respectively, relative to the 1.06 Å equilibrium value (38). This difference, in which one proton has more than doubled its distance to its neighbor, is a clear signature of departure of a proton and hence bond cleavage. The scenario is markedly different for the perpendicular case, in which we measured a C–C bond elongation of 16% from the equilibrium value to (1.38 ± 0.06) Å. The measured C–H distances of (1.94 ± 0.10) Å and (1.54 ± 0.06) Å are shown in Fig. 2D. The more symmetric scenario of C–H bond elongations by 83 and 45% from their equilibrium value is understandable considering that the molecule is aligned perpendicular to the control field when being imaged with the LIED electrons; the molecule is not asymmetrically pulled apart by the strong laser field. This approximates an imaging scenario under quasi–field-free conditions (Fig. 3B). The measured disparity of C–H distances for different alignments provides a means of controlling bond cleavage and proton loss, depending on molecular orientation.

Fig. 3 PES of the C2H2 dication with the mid-IR LIED field.

(A and B) The field-free case is shown in red. (A) shows how the PESs Stark-shift when dressed by a mid-IR LIED field aligned with the molecular axis. For one field direction (E > 0), all dication PESs are strongly dissociative (blue), whereas for the other field direction (E < 0), the PESs present a bound scenario. The trend is exactly reversed for the other C–H bond. (B) shows the doubly degenerate scenario for alignment perpendicular to the mid-IR LIED field, for which we find slight PES shifts but not the dramatic Stark shifts shown in (A).

Next, we sought to explain the difference in imaged structures between the parallel and perpendicularly aligned molecules. We turned to mixed quantum chemistry and semiclassical ab initio molecular dynamics calculations so as to realistically describe the molecular wave packet in the dressing mid-IR field with varying polarization direction as a function of time (supplementary materials). Shown in Fig. 3 is how the PESs of the dication are modified for parallel (Fig. 3A) and perpendicularly oriented (Fig. 3B) molecules in the presence of the LIED field. In Fig. 3, A and B, only the dication’s ground states (3Σg and the near-degenerate singlet states 1Δg, 1Σg+) and the 1Πu and 3Πu excited states are shown, for clarity. For the parallel case (Fig. 3A), we found a stable equilibrium when the LIED field is directed to pull the hydrogen atom toward the carbon atom (Fig. 3A, green). Once the LIED field direction reverses, half a cycle later, all PESs (Fig. 3A, blue) become strongly dissociative, and the C–H bond is broken within 8 fs. Internuclear separation for only one of the two C–H bonds is shown in Fig. 3; the exact opposite scenario occurs at the same time for the other C–H bond (exchange blue with green PESs). In total, during one LIED field cycle (10.3 fs for 3100 nm), one C–H is always broken, whereas the other C–H bond is only elongated. We found excellent agreement with our measured C–C bond length, which is elongated during both half cycles of the LIED field. The calculation yields a C–C bond length of 1.45 Å, which is in excellent agreement with our measured value of (1.48 ± 0.11) Å. The perpendicular case is different because no preferential axis is induced by the LIED field, and hence there are two degenerate cases. Thus, no LIED field direction dependence and only minimal modification of the field-free PESs are exhibited in Fig. 3B. This scenario leads to slower bond dynamics, with eventual breakup. The computed smaller C–C elongation to 1.40 Å agrees with the measured bond length of (1.38 ± 0.06) Å. The simulations show that the C–C bond and the second C–H bond undergo vibration throughout the course of the LIED pulse, yet they stay bound within the temporal range of one optical cycle (10.3 fs).

Because the LIED field does not noticeably distort the PESs in the perpendicular orientation, the C2H2 dication behaves like a quasi–field-free electronic system and can be imaged as such. Moreover, the dependence of proton loss dynamics on alignment permits control over the speed and visualization of molecular dissociation.

Having corroborated the dependence of proton loss on alignment, we next linked the measured structures to the times when the snapshots were taken. In our experiment, we analyzed electrons with 50 eV return energy because they yielded the highest number of counts for the largest angular coverage and hence the best scattering momentum transfer. On the basis of the semiclassical model (18, 37), which pertains well for our Keldysh parameter of γ = 0.31, we can determine the time of return and the backscattering energy for the scattering electron. We only have to consider the long trajectory pathway because of its much higher ionization probability as compared with the short trajectory. We show in Fig. 4A that these electrons have reencountered the target after 9.15 fs (10.3 fs correspond to one optical cycle at 3100 nm) and backscatter with a maximum energy of 188 eV. We additionally analyzed our measurement for two closely neighboring energies of 48 and 52 eV, which correspond to backscattering energies of 181 and 195 eV and for which we achieve high count rates with excellent signal-to-noise ratio. The overall temporal spread is negligible because these three measurements interrogated the molecular structure during a short span between 9.1 and 9.2 fs, as indicated by the vertical gray bars in Fig. 4. The experimental results for the three scattering energies (Fig. 4, circles with error bars) are overlaid with calculated values for all bond distances and for all orientations. The calculated values are based on modeling the experimental conditions with ab initio molecular dynamics simulations that take the modification of the dication states of C2H2 by the LIED field fully into account. The simulated evolution of the corresponding probability distribution on the dissociative excited dication state over a time span of 20 fs is shown in Fig. 4, B to G. For parallel orientation (Fig. 4, B, D, and F), the molecule experiences the full LIED field strength along its molecular axis and gets maximally distorted. This scenario corresponds to rapid elongation of one C–H bond (Fig. 4B) and breakage, which is defined at twice its equilibrium distance, after 8 fs. The other C–H bond (Fig. 4D) experiences elongation in the presence of the LIED field, and the C–C bond (Fig. 4F) moves with a period longer than the LIED field’s optical cycle. The dynamics change markedly for perpendicular orientation (Fig. 4, C, E, and G), which closely approximates a quasi–field-free imaging scenario (Fig. 3B). We found that the C–C bond undergoes a very similar excursion as that of the parallel case because of the stiffness of the bond. The two C–H bonds, however, show strong probabilities to both oscillate in phase with the LIED field, with some small probability for dissociation. This behavior makes sense, over the shown time range, because there is no preferential direction of the external field that would bias the dynamics of one C–H bond as compared with the other.

Fig. 4 Temporal dynamics of C2H2 resolved for the different bonds and as a function of alignment.

(A) Temporal range imaged for electron energies ranging up to 195 eV, in accordance with the semiclassical rescattering model. (B to G) Mixed quantum-classical dynamical calculations are shown below for [(B), (D), and (F)] parallel and [(C), (E), and (G)] perpendicularly aligned C2H2. Extracted bond distances from the snapshots taken between 9.1 and 9.2 fs are overlaid onto the calculations and exhibit excellent agreement by being well positioned within the theoretical distribution; the results corresponding to Fig. 2 are shown in pink, and error bars are determined based on the semiclassical rescattering model (supplementary materials). Differences for bond elongation between the [(B) and (D)] parallel and [(C) and (E)] perpendicular cases are clearly resolved.

The measured snapshots are overlaid (Fig. 4, B, D, and F, circles) with all figures for the parallel case and exhibit excellent agreement with the expected behavior of the molecule. The result from Fig. 2C is indicated by the pink solid circle. Similarly, we show the perpendicular case in Fig. 4, C, E, and G, and found equally excellent agreement with the measurement shown in Fig. 2D.

On the basis of these findings, we can corroborate the full spatiotemporal structure of dicationic C2H2 9 fs after ionization. The snapshots of the spatiotemporal structure were taken with an estimated 0.6-fs temporal resolution and are capable of distinguishing the different kinetic behaviors of the molecule when field-ionized parallel or perpendicular to the LIED field. In the parallel case, the snapshots show that one of the hydrocarbon bonds is heterolytically cleaved with the proton 1.24 Å away from its equilibrium position. The perpendicular case snapshots reveal the molecular structure in the quasi–field-free scenario for the dissociative dication.

As a future step, we envision application of our implementation of LIED to triggering and imaging of ultrafast structural transformations over a longer time scale—for example, with two separate pulses as pump and probe, and with molecules with more complex structures. Prospects include structural and spatial isomerization and especially proton tautomerization, a key chemical and biological process that is largely obscured from x-ray scattering techniques.

Supplementary Materials

Supplementary Text

Figs. S1 to S5

References (3962)

References and Notes

  1. Acknowledgments: We acknowledge financial support from the Spanish Ministry of Economy and Competitiveness (MINECO), through the “Severo Ochoa” Programme for Centres of Excellence in R&D (SEV-2015-0522), grants FIS2014-56774-R and FIS2014-51478-ERC; the Catalan Institució Catalana de Recerca I Estudis Avançats; Agencia de Gestió d’Ajuts Universitaris i de Recerca (AGAUR) with grant SGR 2014-2016; the Fundació Cellex Barcelona; the European Union’s Horizon 2020 research and innovation program under LASERLAB-EUROPE (EU-H2020 654148); COST Actions MP1203, XUV/X-ray light and fast ions for ultrafast chemistry (XLIC); the Marie Sklodowska-Curie grant agreement 641272; and the European Research Council through ERC-2013 Advanced Grant 338580. B.W. was supported by AGAUR (FI-DGR 2013–2015). M.G.P. was supported by the ICFONEST+ program, partially funded by the Marie Curie cofunding of Regional, National and International Programs—COFUND (FP7-PEOPLE-2013-COFUND) action of the European Commission. A.-T.L. and C.D.L. are supported by the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy, under grant DE-FG02-86ER13491. We thank D. Zalvidea, M. Sclafani, and A. Stolow for helpful and inspiring discussions.
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