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Zhuo-ran Ma, Feng-feng Qi, Dao Xiang. Probing Molecular Dynamics with Ultrafast Electron Diffraction†[J]. Chinese Journal of Chemical Physics , 2021, 34(1): 15-29. doi: 10.1063/1674-0068/cjcp2012208
Citation: Zhuo-ran Ma, Feng-feng Qi, Dao Xiang. Probing Molecular Dynamics with Ultrafast Electron Diffraction[J]. Chinese Journal of Chemical Physics , 2021, 34(1): 15-29. doi: 10.1063/1674-0068/cjcp2012208

Probing Molecular Dynamics with Ultrafast Electron Diffraction

doi: 10.1063/1674-0068/cjcp2012208
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  • Corresponding author: Dao Xiang, E-mail: dxiang@sjtu.edu.cn
  • Part of special topic on “the New Advanced Experimental Techniques on Chemical Physics”.
  • Received Date: 2020-12-11
  • Accepted Date: 2021-01-12
  • Publish Date: 2021-02-27
  • Recent progress in ultrafast lasers, ultrafast X-rays and ultrafast electron beams has made it possible to watch the motion of atoms in real time through pump-probe technique. In this review, we focus on how the molecular dynamics can be studied with ultrafast electron diffraction where the dynamics is initiated by a pumping laser and then probed by pulsed electron beams. This technique allows one to track the molecular dynamics with femtosecond time resolution and Ångström spatial resolution. We present the basic physics and latest development of this technique. Representative applications of ultrafast electron diffraction in studies of laser-induced molecular dynamics are also discussed. This table-top technique is complementary to X-ray free-electron laser and we expect it to have a strong impact in studies of chemical dynamics.
  • Part of special topic on “the New Advanced Experimental Techniques on Chemical Physics”.
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Probing Molecular Dynamics with Ultrafast Electron Diffraction

doi: 10.1063/1674-0068/cjcp2012208

Abstract: Recent progress in ultrafast lasers, ultrafast X-rays and ultrafast electron beams has made it possible to watch the motion of atoms in real time through pump-probe technique. In this review, we focus on how the molecular dynamics can be studied with ultrafast electron diffraction where the dynamics is initiated by a pumping laser and then probed by pulsed electron beams. This technique allows one to track the molecular dynamics with femtosecond time resolution and Ångström spatial resolution. We present the basic physics and latest development of this technique. Representative applications of ultrafast electron diffraction in studies of laser-induced molecular dynamics are also discussed. This table-top technique is complementary to X-ray free-electron laser and we expect it to have a strong impact in studies of chemical dynamics.

Part of special topic on “the New Advanced Experimental Techniques on Chemical Physics”.
Zhuo-ran Ma, Feng-feng Qi, Dao Xiang. Probing Molecular Dynamics with Ultrafast Electron Diffraction†[J]. Chinese Journal of Chemical Physics , 2021, 34(1): 15-29. doi: 10.1063/1674-0068/cjcp2012208
Citation: Zhuo-ran Ma, Feng-feng Qi, Dao Xiang. Probing Molecular Dynamics with Ultrafast Electron Diffraction[J]. Chinese Journal of Chemical Physics , 2021, 34(1): 15-29. doi: 10.1063/1674-0068/cjcp2012208
  • One of the dream experiments in chemistry is to observe structural changes in real time during chemical reactions, which is important for understanding, and ultimately controlling chemical reactions [1, 2]. The advent of femtosecond lasers has enabled researchers to investigate laser-induced reactions on the primary time scale on which they take place [3-6]. Laser-based ultrafast spectroscopy provides information on changes in the energy landscape of molecules, leading to the rise of the field of femtochemistry [7]. However, with the laser wavelength much longer than the bond length, ultrafast spectroscopy only provides indirect information about the atomic structural changes, and extensive quantum chemical simulations are needed to interpret the spectroscopic data, which limit its application to large molecular systems. In contrast, ultrafast diffraction techniques using pulsed X-rays and electrons (wavelength smaller than interatomic distances) provide direct information about the structural changes, making the interpretation of the data relatively easy and straightforward. Therefore, ultrafast diffraction techniques are generally considered complementary to spectroscopic methods, connecting the measured data directly with the changes of the structure.

    Over the last few decades, the sources of ultrashort X-ray pulses and ultrashort electron pulses are both under rapid development, which enabled many new experiments [8-15]. X-ray free-electron lasers now can produce $ \sim $100 fs pulses with 10$ ^{12} $ photons per pulse, and the number of electrons in a bunch with similar pulse width is 5-6 orders of magnitude lower. However, since the cross-section for electron scattering is about 5-6 orders of magnitude larger than that of X-ray scattering [16], state-of-the-art ultrafast X-ray and electron diffraction actually produce similar level of scattering signals. Furthermore, electrons are less damaging than X-ray to specimens per useful elastic scattering event [16], and the spatial resolution for electron scattering can be higher than that of X-ray scattering due to the much shorter De Broglie wavelength [11]. This together with the table-top scale of ultrafast electron diffraction (UED) facility makes UED increasingly popular in the past few years for studies of ultrafast dynamics.

    Actually since picosecond electron beams became available in late 1980s [17], Zewail and co-workers did pioneering work in resolving non-equilibrium molecular structures [18], transient molecular structures [14] and radiationless dark structures [15] with keV electron scattering, and established the field of ultrafast gas electron diffraction (UGED). In the past few years, mega-electron-volt (MeV) electron beams were used in gas-phase UED and enhanced the temporal resolution to sub-200 fs resolution [19]. A series of experiments, e.g. rotational dynamics in N$ _2 $ [20], vibrational dynamics in I$ _2 $ [21], nuclear wave packet crossing a conical intersection in CF$ _3 $I [22], and ring-opening in 1, 3-cyclohexadiene (CHD) [23], have been carried out. However, a higher temporal resolution is still needed to capture the motion of atoms in real time, in particular for the dynamics in the first 100 femtoseconds following laser excitation. Very recently, 50 fs FWHM temporal resolution in MeV UED has been achieved by a novel bunch compression scheme based on a double bend achromat (DBA) [24], which opens up many new opportunities in capturing the ultrafast and probing the ultrasmall with UED.

    In this review, we discuss recent advances in gas phase UED experiments. The time-resolved electron diffraction in the gas phase are introduced. The gas-phase keV UED experiments with picosecond resolution is discussed, and the recent advances in UED with MeV electron pulses are described, and the resent progress of gas phase UED experiment in our laboratory at Shanghai Jiao Tong University are also shown.

  • In gas-phase UED, the diffraction pattern is an incoherent sum of the coherent diffraction from individual molecules [25]. This is because that the spatial coherence of the electron beam (i.e. the ratio of electron's wavelength to the beam divergence) is typically larger than the size of a molecule, but smaller than the intermolecular distance. Hence, only a single molecular diffraction, composing of elastic and inelastic scattering, is needed to calculate the gas diffraction pattern, and the nuclear structural information is encoded in the elastic signals.

    In general, the diffraction pattern is expressed as a function of the momentum transfer $ \bf{s} $:

    where $ |\bf{k}_0 | $ = $ |\bf{k}_ {\rm{s}}| $ = $ 2\pi/\lambda $ is the wave vector of the incident electron, and $ \bf{k}_ {\rm{s}} $ is the wave vector of the scattered electron, as shown in FIG. 1.

    Figure 1.  Schematic of gas phase electron diffraction experiment.

    For randomly oriented molecules with $ N $ atoms, the total intensity scattered by them can be expressed as Ref.[26]:

    where $ I_0 $ is the intensity of the incident electron beam, $ R $ is the distance between the electron-molecule scattering point and the detector, $ f $ is the atomic scattering amplitude, $ \Delta\eta_{ij}(s) $ is the phase shift for the scattered electrons which equals to the phase difference between $ f_i $ and $ f_j^* $, $ \bf{r}_{ij} $ = $ \bf{r}_i $-$ \bf{r}_j $ is the vector between atom $ i $ and $ j $ as shown in FIG. 1. $ I_ {\rm{a}}(\bf{s}) $ describes the atomic scattering, which depends only on the species and number of atoms in the molecule and acts as a background. $ I_ {\rm{m}}(\bf{s}) $ contains the interference terms where the structural information is encoded.

    As an example, FIG. 2 shows the simulated results of carbon dioxide (CO$ _2 $), and the structure of this molecule is shown in FIG. 2(a). FIG. 2(b) shows the scattering intensity, where the blue, red and yellow lines represent $ I_ {\rm{m}} $, $ I_ {\rm{a}} $ and $ I $, respectively. As can be seen from FIG. 2(b), the scattering intensity decreases rapidly as $ s $ is increased. In order to compensate for the steep decrease of the total intensity with $ s $ and enhance oscillations imparted by the $ \sin(sr_{ij})/sr_{ij} $ term, it is convenient to convert the measured scattering intensity into a modified scattering intensity,

    Figure 2.  Simulated gas electron diffraction of CO$ _2 $ molecule. (a) Bond length information of CO$ _2 $ molecule. (b) Scattering intensity for $ I_ {\rm{m}} $ (blue), $ I_ {\rm{a}} $ (red) and $ I $ (yellow). (c) Modified scattering intensity $ s $$ \cdot $$ M(s) $. (d) Radial distribution function $ f_ {\rm{r}} $.

    FIG. 2(c) shows $ s $$ \cdot $$ M(s) $ for CO$ _2 $ calculated from FIG. 2(b), where the interference pattern from multiple atoms can be clearly seen. Further analysis shows that the radial distribution function which contains the information of the intermolecular distance can be calculated by taking a sine-transform of $ s $$ \cdot $$ M(s) $,

    where $ k $ is a damping factor to avoid edge effects in the transform. The peaks of $ f_ {\rm{r}}(r) $ correspond to the distance between each atom pair in the molecule and thus contain the one-dimensional information of the molecule. As can be seen in FIG. 2(d), the radial distribution function for CO$ _2 $ has two peaks at 1.16 and 2.32 Å, corresponding to the distance between C-O atoms and that between O-O atoms.

    In principle, the spatial resolution in diffraction measurement is only limited by the wavelength of electrons. However, in reality the diffraction pattern is only measured within limited range of scattering vector, and thus the shortest distance that may be resolved is determined by the maximal scattering vector as $ \delta $ = $ 2\pi/s_\max $.

    In a pump-probe experiment, only a minority of the species will participate in the chemical reaction triggered by a laser pulse, while the majority remains unchanged. In UED, however, all species will scatter the incident electrons regardless of their participation in the reaction. Furthermore, there is always dark current noise, readout noise, etc. Therefore, extracting the desired signal produced by the reacting species from all these background signals is essential for data analysis. A general approach is the diffraction-difference method implemented as follows [27]:

    where $ t_{ {\rm{ref}}} $ refers to the reference time and generally is time before time zero. In the difference data, the contributions from background noise and from species that are not excited are canceled, and the difference is between the signals at two different time from the same fraction of species. In this way, the change introduced by the pump laser is effectively differentiated from the total scattering signal. For example, a negative signal in $ \Delta f_ {\rm{r}} $ reflects the disappearance of some distance between atom pairs, an indication for breaking of a specific chemical bond.

  • Since the pioneering work by Mark and Wierl in the 1930's [28], gas phase electron diffraction (in continuous wave mode) has become a powerful tool for studying the static molecular structure. To capture the structural dynamics during a transition, time resolution must be introduced into the diffraction measurement. In 1983, electron diffraction pattern of the dissociative product from CF$ _3 $I molecule after laser excitation was captured by an experimental setup with microsecond temporal resolution [29]. This landmark experiment represented the first use of a laser-pump electron-probe scheme to capture structural dynamics in gas phase. A decade later, electron diffraction with temporal resolution of 15 ns was used to investigate the photolysis of 1, 3-dichloroethenes with UV laser pulses [30]. Later on, a breakthrough of temporal resolution to picosecond regime was achieved by the group of Zewail [31] who received Nobel Prize in Chemistry in 1999. With a laser of 300 fs pulse duration, a 19 keV electron pulse with 15 ps pulse width was generated [31] and accordingly the time resolution is limited by the electron pulse width to about 15 ps. Later on, by increasing electron beam energy to 30 keV for mitigating the space charge effect, electron beam with 1 ps pulse width was generated [14]. As the electron pulse width is gradually reduced to sub-picosecond level, the group velocity mismatch (VM) became another limiting factor, which will be discussed in next section.

    The improvement of time resolution allows determination of transient structures [14, 31, 32] during a chemical reaction that occurs on picosecond time scale. A representative work by keV UED is the ultrafast dynamics of chemical reactions of 1, 2-diiodotetrafluoroethane (C$ _2 $F$ _4 $I$ _2 $) to produce tetrafluoroethene and iodine carried out by Zewail's group [14]. In that work, a spatiotemporal resolution in the order of 0.01 Å and 1 ps was achieved, where the spatial resolution is defined as square of the standard deviations of the least-squares refinement based on theoretical molecular structural information.

    FIG. 3(a) shows the process of the two-step reaction in photodissociation. The first step (C$ _2 $F$ _4 $I$ _2 $$ \rightarrow $C$ _2 $F$ _4 $I+I) completes within 5 ps. Then the second step (C$ _2 $F$ _4 $I$ \rightarrow $ C$ _2 $F$ _4 $+I) takes place on a time scale of about 30 ps. The time constants of the reaction were measured previously with femtosecond laser time-of-flight mass spectrometry [33], but the structure of the C$ _2 $F$ _4 $I transient (classical or bridged structure) was still under debate. FIG. 3(b) shows the ground-state molecular diffraction image obtained at -95 ps for C$ _2 $F$ _4 $I$ _2 $. Then the experimental differential radial distributions $ \Delta f_ {\rm{r}} $ ($ t $, -95 ps, $ r $) = $ f(t; r) $-$ f $(-95 ps; $ r $) at different delay time are measured and shown in FIG. 3(c). The negative peak at about 5 Å corresponds to the loss of the I-I pair, and remains constant after 5 ps. This result confirms that the loss of the first I atom is completed within 5 ps. The negative peaks at 2 Å to 3 Å corresponding to the depletion of F-I and C-I bonds, however, keep decreasing until about 30 ps, which yields a 30 ps time scale for the second step, consistent with a previous measurement with spectroscopic methods [33].

    Figure 3.  (a) Schematic of the photodissociation process following a pump laser excitation. (b) The ground-state molecular diffraction images for C2F4I2. (c) Measured ∆fr (t, −95 ps, r) at various delay time. Reprinted with permission from Ref.[14] ©2001 American Association for the Advancement of Science.

    FIG. 4 (a) and (b) are the experimental differential radial distribution curves $ \Delta f $($ \infty $, 5 ps, $ r $) of bridged and classical structures, overlaid with their corresponding theoretical curves. The figure shows that the theoretical curve for the classical structure fits excellently with the experimental data, whereas the curve for bridged structure fits poorly. This result unambiguously determines the structure of the C$ _2 $F$ _4 $I radical to be classical. However, the temporal resolution in the experiment is still insufficient to capture atomic motion in the first step which has recently been achieved using MeV UED with higher temporal resolution [34].

    Figure 4.  Comparison of experimental ∆f(∞, 5 ps, r) curve (blue) with theoretical curve (red) obtained using ab initio calculations of (a) the bridged and (b) the classical structure for C2F4I. Reprinted with permission from Ref.[14] ©2001 American Association for the Advancement of Science.

  • The temporal resolution $ \tau $ in a gas phase UED experiment is determined by four parameters: the duration of pump laser $ \tau_{ {\rm{pump}}} $, the duration of the electron pulse $ \tau_{ {\rm{electron}}} $, the time-of-arrival jitter between the laser and electron pulse $ \tau_{ {\rm{jitter}}} $, and the group velocity mismatch $ \tau_{ {\rm{VM}}} $ arising from the different velocity of the laser and electron beam during passage of the gas sample [35]. Considering these four parameters, the temporal resolution can then be written as,

    The duration of the pump laser pulse is typically not the limiting factor, since $ \sim $25 fs laser pulses are commercially available. The duration of the electron pulse is determined by the duration of the laser pulse that triggers the photoemission, the initial energy spread of the photoelectrons, the acceleration gradient, and the spreading during propagation due to Coulomb forces [36]. According to Coulomb's law, the magnitude of the electric force is directly proportional to the charge and inversely proportional to the square of the distance. So when millions of electrons are produced with a femtosecond laser pulse through photoemission, they tend to repel each other. The Coulomb force, in general, accelerates electrons in the front part of the bunch while it decelerates those in the back, leading to pulse broadening.

    The easiest way to reduce the electron pulse duration from space charge force is to reduce the number of electrons per pulse [37, 38]. However, to obtain the same scattering events one has to increase the repetition rate or data acquisition time which puts high stringency on laser parameters and machine long-term stability. A short propagation distance can also minimize the space charge induced pulse broadening [39] by reducing the time, and the Coulomb force acts to the beam. However, there is a tradeoff between the distance from the photocathode to the sample and the vacuum level in the electron gun, which limits the allowed density of gas when the distance is short.

    Currently, the most effective way to reduce electron pulse length is bunch compression. In this method, the electron beam is first sent through a radio-frequency buncher cavity or a THz buncher, where the bunch head is decelerated to a lower energy while the bunch tail is accelerated to higher energy; after passing through a drift, the bunch tail catches up with the bunch head, leading to pulse compression. With this method, keV beam with tens of femtoseconds duration [40] and MeV beam with 6 fs pulse width [41] have been produced.

    The time-of-arrival jitter between the laser and electron pulses arises from the amplitude and phase stability of the radio-frequency cavity either used for accelerating the electron beam or compressing the beam [41]. Such a jitter is measured to be on the order of 100 fs and is the main limiting factor for solid sample UED when bunch compression technique is used. The solution to mitigate such a jitter is to replace the radio-frequency buncher cavity with a THz buncher cavity [42, 43], or using a recently demonstrated DBA compressor scheme [24, 44]. Also one may measure the arrival jitter on a shot-to-shot basis with THz streaking method and then correct the timing jitter to improve the resolution [41, 45, 46]. However, this time-stamping method is best suited for single-shot measurement and is not very useful for gas phase UED where each diffraction pattern is obtained by integrating over many pulses.

    Velocity mismatch is caused by the relative difference in speed between the pump laser pulse and the electron probe bunch, leading to variations in delay time between the laser and electron beam at various depth of the sample. For co-propagating beams, the effect due to velocity mismatch can be expressed as: $ \tau_{ {\rm{VM}}} $ = $ W/v $-$ W/c $, where $ W $ is the width of the molecular beam, $ v $ is the speed of electron and $ c $ is the speed of light [35]. Typical molecular beam in a gas phase experiment has thickness in the order of $ W $$ \approx $300 μm. For 30 keV electrons with $ v $ = 0.33$ c $, the temporal broadening caused by velocity mismatch is about 2 ps which becomes the limiting factor for keV gas phase UED. It should be mentioned that for solid sample where the thickness is typically below 100 nm, $ \tau_{ {\rm{VM}}} $ is negligibly small and is not the limiting factor. It is also worth mentioning that by tilting the wave front of the laser and illuminating the gas sample with proper angle, $ \tau_{ {\rm{VM}}} $ may be significantly reduced for keV UED. However, this also adds complexity to the experiment [47].

    After considering all these factors, increasing electron beam energy to a few MeV and further compressing the beam seems to be the best approach to further increase temporal resolution of gas phase UED. First, the space charge effects are largely suppressed due to the relativistic effects in both the longitudinal and transverse directions [48], essential for obtaining a short bunch with small transverse size at the sample. Second, the high electron kinetic energy makes the effect of velocity mismatch negligible. For example, the velocity for an electron with 3.7 MeV kinetic energy is $ v $ = 0.993$ c $, corresponding to $ \tau_{ {\rm{VM}}} $$ < $10 fs. Third, benefiting from the development of free-electron lasers, high brightness MeV electron beam can be readily produced with photocathode radio-frequency guns [49].

  • To this end, we have witnessed a rapid development in MeV UED and many facilities have been constructed in US, Europe and Asia [19, 41, 50]. In the last five years, pioneering gas phase MeV UED experiments [20-23, 34, 51] have been carried out at SLAC and the temporal resolution of about 150 fs (FWHM) has been achieved, demonstrating the full potential of MeV UED in studies of gas phase molecular dynamics. Here we briefly review some of the representative results at SLAC.

    First, we discuss the photoexcited coherent motion of a vibrational wave packet for iodine molecules (I$ _2 $) in the gas phase, which has been recorded with a spatial precision of 0.07 Å and temporal resolution of 230 fs (FWHM) [21]. FIG. 5(a) shows the potential energy surfaces (dashed lines) and the wave packets (solid line) of the ground state (blue) and the excited B state (red) of I$ _2 $. In this experiment, the molecules are excited by a 530 nm laser, after which a vibrational wave packet at B state is created. On the excited state, the interatomic distance of excited iodine molecules began to oscillate in the range from 2.7 Å to 3.9 Å, and this bond length oscillation can be directly imaged with UED. FIG. 5(b) shows the experimental difference diffraction pattern $ \Delta I(t, -T, s) $ averaged over $ t $ = 50 fs to $ t $ = 550 fs, in which the ripple is from the expansion of average interatomic distance after excitation. The $ s $$ \cdot $$ M $ and $ f_ {\rm{r}} $ of excited molecules as a function of time can also be extracted from these diffraction patterns. Intuitively, this measurement may be understood as Young's double-slit interference experiment with the slits replaced by two iodine atoms. By tracking the separation of the peaks and dips in the diffraction pattern at various delay time following the laser excitation, the oscillation of bond length was clearly recorded [21].

    Figure 5.  (a) Potential energy surfaces (dash lines) and the wave packets (solid lines) of the ground state (blue) and the excited state (red) of I2. (b) Experimental difference diffraction pattern. Reprinted with permission from Ref.[21] © 2016 American Physical Society.

    In addition, it is also demonstrated that the diffraction pattern is sensitive to both the position and shape of the nuclear wave packet. For a diatomic molecule which has only one interatomic distance, the radial distribution $ f_ {\rm{r}}(r) $ in Eq.(7) becomes the probability density in the nuclear wave function. The shape and width of the measured probability density function is the real probability density function convolved with both spatial resolution and temporal resolution. The width of $ f_ {\rm{r}}(r) $ before time zero is predicted to be 0.1 Å and measured to be 0.7 Å in this experiment, limited by the spatial resolution. The change of the width of the wave packet after time zero is further blurred by the limited temporal resolution. As a result, fine details of the wave packet evolution are still massing in this experiment and may be resolved in future work with higher temporal and spatial resolution.

    The second example is dynamics in photodissociation of C$ _2 $F$ _4 $I$ _2 $. As discussed in Section III, keV UED has been used to successfully determine the structure of the transient intermediate in photodissociation of C$ _2 $F$ _4 $I$ _2 $. However, due to picosecond resolution, the time scale for formation of the intermediate radical is only determined to be less than 5 ps. Later on, the dynamics of this reaction has been studied by picosecond X-ray [52], velocity map ion imaging technique [53] and ab initio methods [54], adding more information into this fast process. Limited by the insufficient spatiotemporal resolution, however, some of the important information in this fast process is still missing. Recently, MeV UED has been used to revisit this process and the motion of the nuclear wave packet of the dissociating iodine atom followed by coherent vibrations of the C$ _2 $F$ _4 $I radical has been recorded with sub-Ångström spatial resolution and 150 fs temporal resolution [34].

    FIG. 6(a) shows the measured distribution of $ \Delta f_ {\rm{r}} $ at various time delay. Negative peaks at C-I, F-I, and I-I distances are immediately seen after laser excitation, which is due to the removal of an iodine atom. Positive peaks between 3.5 and 4.0 Å, and between 5.5 and 6.0 Å before 200 fs are produced from departing iodine nuclear wave packet. FIG. 6 (b) and (c) show the lineouts of $ \Delta f_ {\rm{r}} $, extracted from FIG. 6(a), at 3.1 and 3.9 Å, respectively. The bleaching signal at 3.1 Å, corresponding to ground-state distances of I-F atoms as well as the long C-I distance, reflects the departure of iodine atom and drops slower than that in the simulation due to finite time resolution of the experiment. The large positive signal at 50 fs and 3.9 Å, which is isolated from all of the ground-state distances, corresponds to the dissociating iodine wave packet as it passes through this position.

    Figure 6.  (a) Measured temporal evolution of $ \Delta f_ {\rm{r}} $. (b) and (c) Lineouts of $ \Delta f_ {\rm{r}} $ at 3.1 and 3.9 Å, respectively. (d) and (e) Calculated density maps of the remaining C-I atomic distances and long F-I atomic distances after dissociation. Reprinted with permission from Ref.[34] © 2019 American Physical Society.

    After dissociation, the modulation in the amplitude of $ \Delta f_ {\rm{r}} $ is caused by coherent oscillations in the C$ _2 $F$ _4 $I radical and is out-of-phase at the two distances. FIG. 6 (d) and (e) show the calculated density plots of the two C-I distances and the long F-I distance in the C$ _2 $F$ _4 $I radical, respectively. The dashed lines at 3.9 Å (red) and 3.1 Å (black) indicate that the oscillations in FIG. 6 (b) and (c) are related to the coherent large amplitude vibrations in FIG. 6 (d) and (e). This experiment with improved resolution not only determined the time for the formation of the transient C$ _2 $F$ _4 $I radical, but also successfully recorded the coherent dynamics in this radical.

    The third example to be discussed is direct imaging of the photodissociation and conical intersection dynamics of CF$ _3 $I along both the single and two photon channels [22]. As is well-known, conical intersection plays a critical role in excited-state dynamics of polyatomic molecules. Yet, it is still quite a challenge to observe the nonadiabatic dynamics through these intersections in real space and real time. MeV UED appears to be a very effective method for studying intersection dynamics. For CF$ _3 $I, a one-photon transition to the dissociative A band and a two-photon transition to the 7s Rydberg state can be initiated by a UV pump laser at around 265 nm. The one-photon channel preferentially excites species with the C-I axis parallel to the polarization of the laser, while the two-photon channel corresponds to a perpendicular excitation for which case C-I and F-I pairs preferentially appear in perpendicular direction. This allows one to separate the dynamics from the two different channels.

    In the experiment, it is shown that as the dissociation wave packet formed in the single-photon channel moves to large internuclear separations and rotationally dephases, the two-photon channel became dominating after 200 fs. To analyze the behavior of nuclear wave packet near the conical intersection, an experimental real-space reaction trajectory of the nuclear wave packet was produced by a ridge-detection algorithm. The experimental results are in good agreement with the simulated trajectory of the wave-packet along the C-I coordinates using ab initio multiple spawning molecular dynamics simulations, as shown in FIG. 7. The trajectory bifurcates at around 300 fs and 450 fs as the wave packet passes through the conical intersection.

    Figure 7.  Simulated nuclear wave packet along the C-I coordinate for various time delay. Reprinted with permission from Ref.[22] © 2018 American Association for the Advancement of Science.

    In addition to the conical dynamics, the results also show that in the single-photon channel, there was a 30 fs delay between the bleaching of F-I pair signal and C-I pair signal, as shown in FIG. 8. This is because the cleavage of the C-I bond is directly initiated by the pump laser, but F and I atoms do not form a bond. Because iodine atom is much heavier than carbon, the recoil effect makes the carbon bounce back after the breaking of C-I bond while F and I atoms remain essentially unchanged. Then the three fluorine atoms move together with the carbon, leading to a delay in the signal for loss of F-I pair.

    Figure 8.  Measured evolution of C-I and F-I internuclear distances. Reprinted with permission from Ref.[22] © 2018 American Association for the Advancement of Science.

    The fourth example which shows that MeV UED can be used to record electronic dynamics is quite a surprise. It is shown recently that UED can be used to simultaneously and independently record both electronic and nuclear dynamics, which is challenging but important for a complete understanding of molecular dynamics in excited electronic states. In most UED experiments, data are interpreted with the independent atom model (IAM), neglecting the electron redistribution due to bond formation or electronic excitation. This analysis method was recently challenged in Ref.[51], it is shown that the elastic scattering signals at high angles contain geometric information of the nuclei and the inelastic scattering signals at small angles actually contain information about the excited state population.

    In this experiment, pyridine was used to show that a single UED experiment can simultaneously resolve both nuclear (ring-puckering) and electronic (S$ _1 $$ \rightarrow $S$ _0 $ internal conversion) dynamics of the S$ _1 $(n$ \pi^* $) state. The experimental percentage difference signal (PD$ ^{\exp} $) measured at various time delay is shown in FIG. 9(a). PD calculated using the IAM, called PD$ _{{\rm{IAM}}}^{{\rm{sim}}} $, is shown in FIG. 9(b). It can be seen that the IAM model captures most of the large-angle features in PD$ ^{\exp} $ but does not reproduce the strong increase at small angles, indicating that the small-angle signals originating from electron dynamics are not included in IAM. Further analysis shows that the small-angle signal is mainly from inelastic scatering and it correlates well with the S$ _1 $ population, showing both the S$ _0 $$ \rightarrow $S$ _1 $ photoexcitation and the S$ _1 $$ \rightarrow $S$ _0 $ internal conversion.

    Figure 9.  (a) Experimental PD signal and (b) simulated PD signal from the IAM. Reprinted with permission from Ref.[51] © 2018 American Association for the Advancement of Science.

    The physics behind this may be understood as follows: in the electronic ground state, the localized $ n $ orbital is doubly occupied, resulting in strong dynamic electron correlation due to Coulomb repulsion, while in the S$ _1 $($ n\pi^* $) excited state, the two electrons occupy spatially separated orbitals, reducing the dynamic correlation [51]. This method, capable of retrieving structural and electronic dynamics simultaneously and independently from a single UED data, may provide a benchmark for future theoretical and computational methods of which electron correlation is extremely important.

  • In MeV UED, the electron beam is produced in a photocathode radio-frequency gun. Because of the fluctuation of gun amplitude and phase, the electron beam energy as well as the arrival time at the sample both varies on a shot-to-shot basis. Generally speaking, the temporal resolution of MeV UED is limited by the electron pulse width and timing jitter. In the past decade, many methods such as radio-frequency buncher, time-stamping, compression with a THz pulse, have been proposed and developed to improve the temporal resolution, albeit with limited success [41-43, 45, 46, 55]. Recently, a novel bunch compression scheme based on a double bend achromat (DBA) has been demonstrated by our group [24] and for the first time UED resolution beyond 50 fs FWHM has been achieved.

    The schematic layout of the DBA-based MeV UED beamline is shown in FIG. 10. The electron beam is produced in a photocathode radio-frequency gun by illuminating a femtosecond UV laser on the cathode. Affected by Coulomb force, the electron bunch head is accelerated and the bunch tail is decelerated, generating a positive energy chirp and increasing the electron bunch length as it propagates in the drift. The beam then passes through a DBA that mainly consists of two dipole magnets and three quadrupole magnets. Contrary to a drift, the DBA has positive longitudinal dispersion where electrons at the bunch head with higher energies follow longer paths and thus need longer time to pass through, leading to a negative energy chirp at the DBA exit. After another drift with again negative longitudinal dispersion, electrons with higher energies now at the bunch tail exactly catch up with the head, achieving full compression at the sample position.

    Figure 10.  Schematic of DBA based gas phase UED.

    The longitudinal dispersion from the cathode to the sample position is designed to be zero, thus the arrival time of the beam is independent of its energy. Meanwhile, to meet the compression condition at the sample, the energy chirp from space charge force at DBA entrance is controlled by varying the charge and transverse size of the beam. Thanks to this jitter-free compression technique, the arrival timing jitter for a beam containing about 10$ ^5 $ electrons are measured to be about 22 fs (FWHM) with the bunch length being about 29 fs (FWHM), as shown in FIG. 11(a). The beam temporal distribution measured over 1 h (including both the bunch temporal profile and timing jitter) is fitted to 40 fs (FWHM) shown in FIG. 11(b). Combined with commercially available ultrashort lasers ($ \sim $25 fs FWHM), the temporal resolution in this MeV UED can reach 50 fs FWHM [24], which is so far the highest temporal resolution achieved in MeV UED. The residual timing jitter comes from the different acceleration time in the radio-frequency gun because of the radio-frequency phase jitter. With a newly designed 2.33 cell electron gun, the timing jitter may be reduced to below one femtosecond. Together with few cycle lasers [56], sub-20 fs FWHM time resolution in MeV UED will be realized in the near future.

    Figure 11.  Statistical results of (a) the electron bunch length after compression and (b) integrated beam temporal distribution after a DBA compressor. Reprinted with permission from Ref.[24] © 2019 American Physical Society.

    FIG. 12 shows a top view of our gas phase sample chamber. The blue and red lines represent the electron and laser beam trajectory, respectively. The pulsed supersonic gas nozzle is above the interaction point installed on a 3D moving stage. The brown line represents a THz beam for measuring the electron bunch length and timing jitter. The THz beam is focused by an off axis parabolic mirror with a 2 mm diameter hole. The tubes in the left and right sides of the picture are used for achieving 100-fold pressure reduction between the sample chamber and the neighboring chamber. Another differential aperture is mounted before the DBA entrance to further improve the vacuum level in the electron gun. With this differential-pumping system, backing pressure up to 10 bar in the pulsed gas nozzle can be used under normal operation at 100 Hz.

    Figure 12.  Top view of the gas phase sample chamber.

    With this powerful tool of DBA, we have carried out a series of laser alignment experiments for testing the performance of gas phase UED in our lab. A molecule can be aligned by a non-resonant intense laser through the torque generated by the interaction between the laser field and the induced dipole moment of the molecule. When the laser pulse duration is much shorter than the rotational period of the molecule, the alignment is considered non-adiabatic. This rotational dynamics has been widely studied by optical birefringence [57], strong field ionization [58], high harmonic generation [59, 60], Auger electron spectroscopy [61], and by UED in SLAC [20].

    In our experiment, a Ti: Sapphire laser with central wavelength of 800 nm is used to align the nitrogen and carbon dioxide gas introduced through an Even-Lavie pulsed nozzle. Typical diffraction pattern for carbon dioxide is shown in FIG. 13 (a). In this experiment, the degree of alignment in a diffraction pattern was calculated by the difference divided by the summation of the total counts in the horizontal rectangle and the vertical rectangle as shown in FIG. 13 (a). The anisotropy is defined as ($ V_1 $+$ V_2 $-$ H_1 $-$ H_2 $)/($ V_1 $+$ V_2 $+$ H_1 $+$ H_2 $)$ \times $100%, where $ V_1 $, $ V_2 $, $ H_1 $, and $ H_2 $ represent the total counts in the rectangle marked in FIG. 13(a). With laser excitation, the molecules will be aligned, resulting in anisotropic diffraction pattern, as shown in FIG. 13(b). This anisotropy was calculated using the measured diffraction pattern at each time step, and the temporal evolution of the rotational wave packet could be inferred from the anisotropy, as shown by the blue line in FIG. 13(c). The measurement is in excellent agreement with the theoretical value (red line in FIG. 13(c)) obtained by solving a time-dependent Schrödinger equation. The right axis of FIG. 13(c) shows the degree of alignment $ \cos^2\theta $ for the simulated curve, with $ \theta $ being the angle between molecular axis and laser polarization. When the gas is randomly orientated, we have $ \cos^2\theta $ = 0.33, while a value of $ \cos^2\theta $ = 1 corresponds to perfect alignment.

    Figure 13.  (a) Diffraction pattern before laser excitation, (b) the representative diffraction pattern for aligned molecules, (c) Temporal evolution of the rotational wave packet.

    In FIG. 13, each datum point is accumulated for about 60 s (6000 electron pulses at 100 Hz). The signal to noise ratio is sufficient to resolve changes as small as 1%. The data demonstrate several features of nonadiabatic alignment. First, we see a fast rise of the anisotropy followed by a fast decrease after laser excitation, which is from dephasing of the different rotational states in the wave packet. Second, it can be clearly seen that there are periodic revivals of the alignment at 21 ps and 42 ps, corresponding to half and a full rotational period. It should be noted that the distribution changes very rapidly from alignment state to anti-alignment state at the revivals. For example, at the half-revival (delay of 21 ps), the anisotropy changes from maximum to minimum in less than 600 fs, so high temporal resolution is crucial to capture the details of alignment.

    To highlight the change of excited molecules, FIG. 14(a) shows the diffraction-difference pattern at the maximum point in FIG. 13(c), and FIG. 14(b) shows the corresponding simulated results. The modified pair distribution function (MPDF) which contains the information on both the bond length and the angular distribution can be extracted from these patterns [62]. FIG. 14 (c) and (d) show the MPDF calculated from FIG. 14 (a) and (b), respectively. The inner and outer ring in these patterns represent the C-O and O-O atom pairs respectively. Because there are two C-O atom pairs but only one O-O atom pair in a carbon dioxide molecule, the inner ring is much brighter than the outer ring. The density distribution of the ring reflects the probability density of the nuclear wave packet. As can be seen, more molecules are distributed in the direction of the polarization of the laser (vertical) as a result of alignment.

    Figure 14.  (a) Measured and (b) simulated diffraction-difference pattern at the maximal alignment condition, and the corresponding modified pair distribution function for (c) the measurement and (d) the simulation.

  • In summary, gas-phase UED has been already proven a successful method to capture the trace of each atom and the evolution of nuclear wave packet during a reaction triggered by a laser. In addition, recent results show that inelastic electron scattering signal can be used to study electronic states. With the technique of DBA compressor, the temporal resolution in MeV UED has reached 50 fs FWHM and may be further improved to sub-20 fs in the future. These progresses make MeV UED truly complementary to X-ray free-electron lasers. We expect this technique to have a strong impact on studies of chemical dynamics in the coming years.

  • The work was supported by the National Natural Science Foundation of China (No.11925505).

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