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Simultaneous observation of nuclear and electronic dynamics by ultrafast electron diffraction

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Science  22 May 2020:
Vol. 368, Issue 6493, pp. 885-889
DOI: 10.1126/science.abb2235

Electronic and nuclear dynamics in one

Because of the complex, ultrafast interplay between nuclear and electronic degrees of freedom, probing both nuclear and electronic dynamics in excited electronic states within a single time-resolved experiment is a great challenge. Yang et al. used ultrafast electron diffraction in combination with ab initio nonadiabatic molecular dynamics and diffraction simulations to study the relaxation dynamics of isolated pyridine molecules after photoexcitation to the S1 state (see the Perspective by Domcke and Sobolewski). They showed that electronic state evolution and molecular structural changes can be recorded simultaneously and independently by tracing a transient signal in small-angle inelastic scattering and large-angle elastic diffraction, respectively.

Science, this issue p. 885; see also p. 820

Abstract

Simultaneous observation of nuclear and electronic motion is crucial for a complete understanding of molecular dynamics in excited electronic states. It is challenging for a single experiment to independently follow both electronic and nuclear dynamics at the same time. Here we show that ultrafast electron diffraction can be used to simultaneously record both electronic and nuclear dynamics in isolated pyridine molecules, naturally disentangling the two components. Electronic state changes (S1→S0 internal conversion) were reflected by a strong transient signal in small-angle inelastic scattering, and nuclear structural changes (ring puckering) were monitored by large-angle elastic diffraction. Supported by ab initio nonadiabatic molecular dynamics and diffraction simulations, our experiment provides a clear view of the interplay between electronic and nuclear dynamics of the photoexcited pyridine molecule.

Nonadiabatic processes exhibit a complex interplay between the electronic and nuclear degrees of freedom. For electronically excited polyatomic molecules, the vibronic or nonadiabatic couplings become so strong that the Born-Oppenheimer approximation often fails (1). This mixing between electronic and nuclear degrees of freedom presents great challenges to common experimental and theoretical approaches. Specifically, it is experimentally challenging to measure both electronic and nuclear dynamics independently within a single experiment. For time-resolved measurement of photoexcited molecules, most pump-probe spectroscopy focuses on the population dynamics between electronic states. Valence electron spectroscopy could be sensitive to both electron and nuclear dynamics, but the two contributions are often difficult to disentangle (2). Core electron spectroscopy, such as extended x-ray absorption fine structure, can resolve the structural dynamics around a local site but typically requires the presence of one or more heavy atoms (3). Time-resolved diffraction (TRD) techniques, including ultrafast electron diffraction (UED) pioneered by Zewail and colleagues in the 1990s (4) and time-resolved x-ray diffraction (TRXD) enabled recently by x-ray free-electron lasers, are able to resolve motion of atomic nuclei during photochemical reactions with femtosecond temporal resolution and sub-angstrom spatial resolution (57) but have so far been insensitive to electronic dynamics. In most TRD experiments, the independent atom model (IAM), in which the electron redistribution due to bond formation is completely ignored, is invoked to interpret the diffraction patterns. A recent TRXD study by Stankus et al. included the valence electron contribution to the elastic scattering signal in a Rydberg excitation, where the diffraction signature of electronic and nuclear dynamics is intertwined (7). As suggested from theory (8, 9), the inelastic scattering signal is expected to reflect electronic dynamics but, to the best of our knowledge, has yet to be used in a TRD experiment. In this work, we used UED to study the photophysics of pyridine excited to the S1(nπ*) state. We show that the inelastic electron scattering modulates the scattering pattern exclusively at small angles and thus is a sensitive observable related directly to the excited state population. By contrast, elastic scattering signals at higher angles encode geometric information. The clean separation of elastic and inelastic scattering signals enables a single UED experiment to simultaneously resolve both electronic [S1→S0 internal conversion (IC)] and nuclear (ring-puckering) dynamics of the S1(nπ*) state in pyridine.

Pyridine is one of the simplest heterocyclic compounds with rich nonadiabatic dynamics. The investigation of its photophysics is central to the understanding of interplay between ππ* and nπ* states in heterocyclic compounds, which is critical for the photoprotection mechanism of nucleobases (10). It has been shown that the radiationless transition of the pyridine S1(nπ*) state is extremely sensitive to excess vibrational energy: Higher excess vibrational energy increases IC and decreases intersystem crossing quantum yield (11). This behavior is reminiscent of the “channel-three” decay in benzene and has drawn considerable interest in past decades (12, 13). Despite being extensively studied, the photophysics of such a simple molecule is still under heated debate. Lim (14) proposed a proximity effect mechanism, in which a pseudo–Jahn-Teller effect between the close-lying nπ* and ππ* states promotes an out-of-plane torsional motion, which then greatly enhances the Franck-Condon factor for S1→S0 IC. The strong dependence of the (S1→S0)/(S1→T1) branching ratio on the excess vibrational energy is explained by a higher energy barrier for the IC pathway. This model is supported by experimental absorption, fluorescence, and time-resolved photofragment spectroscopy (13, 15, 16). Sobolewski and Domcke (17) and Chachisvilis and Zewail (18) proposed that a crossing of the S2(ππ*) and S1(nπ*) states leads to the formation of a prefulvenic structure. Zhong et al. (19) proposed an isomerization to Dewar and Hückel structures after passing through a conical intersection (CI). Lobastov et al. (20) and Srinivasan et al. (21) reported ring opening of pyridine as the dominant pathway after excitation with 267-nm light. These conflicting models, each with its own experimental evidence, persist in part because none of the previous experiments directly measured the electronic and structural dynamics independently and simultaneously.

In most UED experiments, data are analyzed with the IAM, which ignores all electronic redistribution due to chemical bonding or electronic excitation. Specifically, this model neglects two effects: the binding effect that comes from the redistribution of average electron density due to bond formation (one-electron effect) and the correlation effect that comes from electrons avoiding each other because of Coulomb repulsion and Pauli exclusion (two-electron effect) (2227). Iijima et al. (22) and Bartell and Gavin (23) showed that the binding and correlation effects exclusively contribute to elastic and inelastic scattering, respectively (see supplementary materials). Typically, UED experiments use detectors without energy selectivity, and thus elastic and inelastic scattering are recorded together without distinction.

Our experimental setup has been introduced previously (5, 6, 28) and is schematically shown in Fig. 1A. Briefly, the 265-nm pump laser and the 3.7-MeV probe electrons intersected the target gas jet almost colinearly, and the overall instrumental response function (IRF) had a full width at half maximum of ~150 fs (28). To access inelastic scattering at small angles, we intentionally set the main electron beam off-center from the hole of the detector phosphor screen (Fig. 1B). This setup provided access down to s = 0.3 Å−1 in one quadrant, where s is the momentum transfer of the scattered electrons. Small-angle electron scattering is dominated by the inelastic component. For 0.3 < s < 1 Å−1, previous gas electron diffraction experiments have suggested that the inelastic scattering intensity is typically 5 to 10 times as large as the elastic scattering intensity (29). The pump laser launches a wave packet on the S1(nπ*) surface with ~3000-cm−1 excess energy, and the molecule relaxes through a CI along a ring-puckering coordinate (14, 15). Figure 1C shows the S0 and S1 potential energy surfaces at the floating occupation molecular orbital–complete active space configuration interaction (FOMO-CASCI) level of theory (supplementary materials).

Fig. 1 Experiment overview.

(A) Conceptual drawing of the experiment. The inelastic scattering (red scattered wave) concentrates at small angles and encodes information about electron correlation [represented graphically by the two electrons (yellow) in the lone-pair orbital (purple)]. The elastic scattering (orange scattered wave) dominates at high angles and encodes the molecular structure. (B) Diffraction pattern with low-s access. The two red rings near the center represent 0.25 Å−1 (inner ring) and 0.5 Å−1 (outer ring), respectively. (C) Pyridine potential energy surfaces (S1 and S0) along the bond length alternation and ring-puckering coordinates (fig. S6). Critical points (FC, Franck-Condon point) and the minimum energy reaction pathway are marked. Time scales were obtained from simulation.

The experimental and simulated UED data are given in Fig. 2. Figure 2A shows the experimental percentage difference (PD) signal, PDexp, defined as PD(s;t)=I(s;t)I(s;t<0)I(s;t<0)×100(1)where I(s;t) is the radially averaged diffraction intensity at any pump-probe delay time t, and I(s;t < 0) is a reference pattern taken before the arrival of the pump laser. In PDexp, the signal at s > 1.1 Å−1 appeared around t = 0 and persisted throughout our observation window, which reflects structural change of the molecule and will be discussed later. The signal at s < 1.1 Å−1, however, contained a sharp rise (IRF-limited) and a slower decay (1.1 ± 0.2 ps); see Fig. 2F. To understand this signal, we performed dynamics, quantum chemistry and diffraction simulations. The nonadiabatic dynamics of the lowest three singlet and four triplet states, including spin-orbit interactions, was simulated using the generalized ab initio multiple spawning (GAIMS) (30) method (supplementary materials). Diffraction patterns and PD were first calculated using the IAM (hereafter PDIAMsim); see Fig. 2B. PDIAMsim captured most of the large-angle features in PDexp but did not capture the strong increase at small angles (s < 1 Å−1; 0 < t < ~1.5 ps), indicating that the small-angle signal originated from electron dynamics through either binding (elastic) or correlation (inelastic) effects.

Fig. 2 Experimental and simulated UED signal for pyridine.

(A) Experimental PD signal, normalized by the 9% excitation ratio. (B) Simulated PD signal from the IAM (elastic component only), using all 24 initial and 2040 spawned trajectories. (C) Simulated PD total (elastic and inelastic) signal using AIED. (D) Elastic part of simulated PD using AIED. (E) Inelastic part of simulated PD using AIED. In (A) to (E), the red dotted line denotes s = 1.1 Å−1. (F to H) Lineout plots of the three strongest features from the experiment, plotted together with IAM and AIED simulations. Uncertainties in (F) to (H) are represented by shaded regions, calculated with one SD of a bootstrapped dataset (experiment) or one SEM of all trajectories (simulation). Simulation results are convolved with a 150-fs Gaussian kernel to account for the experimental IRF.

To properly account for scattering signal from both binding and correlation effects, we performed ab initio electron diffraction (AIED) simulations on GAIMS trajectories, similar to the method developed by Breitenstein et al. (31) and implemented in TeraChem (32) (supplementary materials). The resulting total, elastic, and inelastic PD (PDTotalsim, PDElasticsim, and PDInelasticsim) are shown in Fig. 2, C to E. PDElasticsimand PDInelasticsim are defined asPDElasticsim=IElastic(s;t)IElastic(s;t<0)I(s;t<0)×100(2)PDInelasticsim=IInelastic(s;t)IInelastic(s;t<0)I(s;t<0)×100(3)The PDTotalsim nicely captured all the major features in PDexp, with PDElasticsim and PDInelasticsim separately located in the s > ~1.1 Å−1 and s < ~1.1 Å−1 regions. Lineout plots of the three strongest features—the peak at 0.3 < s < 0.7 Å−1, the peak at 3.9 < s < 4.9 Å−1, and the trough at 5.5 < s < 6.5 Å−1—are shown in Fig. 2, F to H. Figure 2F shows that the IAM simulation fails to reproduce the experimental data at small s and that the AIED simulation and experiment agree reasonably well—both show fast-rising (IRF-limited) and slow-decaying (experiment: 1.1 ± 0.2 ps, simulation: 1.3 ± 0.1 ps) features. In addition, Fig. 2, D and E, shows that this signal exclusively came from the inelastic component.

We then inspected the connection between the simulated small-angles scattering signal and the electronic state population. The GAIMS calculation predicted that the S1(nπ*) state was exclusively populated and that >90% of the population returned to the ground state S0 within the 2.4-ps simulation window. The small-angle signal PDTotalsim(0.3<s<0.7 Å1;t) correlates well with the S1 population in the GAIMS simulation, as illustrated in Fig. 3A. To further show this correlation, we simulated the PDTotalsim signal for S0 and S1 states over all trajectories (Fig. 3B). We found that the S1 signal was about three times as strong as the S0 signal at 0.3 < s < 1 Å−1. This simulation therefore confirms that the small-angle signal could be used to trace the excited state population, and the experimentally observed positive signal (s < 1 Å−1; 0 < t < ~1.5 ps) shows both the S0→S1 photoexcitation and the S1→S0 IC.

Fig. 3 Small s scattering and excited state population.

(A) Simulated PD signal using AIED (blue, left y axis) and S1 population (red, right y axis). (B) The PDTotalsim signal on S0 and S1 integrated over the time course of the simulation (0 to 2.4 ps), calculated using all accessed geometries by each state. Uncertainty is represented by shaded regions, calculated with one SEM of all trajectories (A) or one SD of all visited geometries (B).

Here we provide a simple physical picture for the observed inelastic signal. The diffraction signature of the correlation effect is a negative contribution to small-angle inelastic scattering, and most (80 to 90%) of this effect comes from dynamic correlation due to Coulomb repulsion (26, 27, 31). In the ground state, the two electrons in the lone-pair orbital are spatially close and the dynamic correlation is strong. In the photoexcited (nπ*) state, however, the two electrons no longer occupy the same molecular orbital, leading to a marked reduction of the dynamic correlation. According to the above-mentioned arguments, small-angle inelastic scattering is therefore substantially increased by photoexcitation and decreased upon relaxation to the electronic ground state. We have also simulated the expected AIED signal for the S2, T1, and T2 states (fig. S2), which confirms that all of these open-shell excited states give rise to a strong increase in small-angle inelastic scattering. Although we believe this picture provides an intuitive explanation of the observed inelastic signal, the concrete details and generality are subject to future studies.

To extract the nuclear structural dynamics, we used 1.1 < s < 10.5 Å−1 data to apply a genetic χ2 structural fitting algorithm (supplementary materials) (33). Three fitted structural parameters—dihedral angle α, interior angle β, and average bond length of the ring Δr—are shown in Fig. 4A (circles with error bars), together with the value extracted from the GAIMS simulation (lines with shaded regions). Because the contrast between a nitrogen atom and a CH group is small in electron diffraction, it is difficult to experimentally distinguish which atom puckers out of the plane. Therefore, the dihedral angle α and interior angle β are both referring to the heavy atom with the largest out-of-plane torsion (Fig. 4A, inset). Both experiment and simulation show a large (~30°) change in dihedral angle and a ~0.04-Å expansion of the ring bond lengths, with a small change in angle β. The most-accessed S1/S0 CI geometry from the GAIMS simulation is shown in Fig. 4B. It is described by ~60° out-of-plane torsion on a carbon atom adjacent to the nitrogen atom. Because the molecule spent relatively little time at the CI and the torsion angle was smaller both before and after the CI (Fig. 1B), the averaged out-of-plane torsion at any time appeared to be only ~30°.

Fig. 4 Combined structural and electronic dynamics.

(A) Experimental structural evolution (circles with error bars) retrieved from a genetic χ2 fitting algorithm. Vertical error bars represent one SD of 86 individual fitting results; horizontal error bars represent the time window used for each fitting. Simulated values (lines with shaded regions) were obtained from weighted averages of all spawned trajectories from GAIMS simulation. The two dashed lines show the position of 120° and 180°. (B) Geometry of the most-accessed S1/S0 CI from GAIMS simulation. Blue, nitrogen atom. (C and D). Experimental (C) and simulated (D) temporal evolution of small-angle PD signal (blue, normalized to the maximum value) and dihedral angle (red). Uncertainty is represented by shaded regions, calculated by one SD of a bootstrapped dataset (experiment) or one SEM of all trajectories (simulation). Simulation results are convolved with a 150-fs Gaussian kernel to account for experimental IRF.

Taking into account all of the analysis discussed above, we were finally able to plot electronic and nuclear dynamics together in Fig. 4, C and D. The small-angle PD signal at 0.3 < s < 0.7 Å−1 represents excited state population (blue curves), whereas the dihedral angle represents the structural change along the main reaction coordinate (red curves). The torsion started ~100 fs after the S0→S1 photoexcitation, agreeing well with the model that a small barrier is present in the out-of-plane ring-puckering coordinate. The S1→S0 IC started only after the dihedral angle reached a certain point (~150° for experiment and ~160° for simulation), consistent with the prediction that the S1→S0 IC requires a relatively large out-of-plane torsion. This plot, along with the lack of structural changes in other degrees of freedom, confirms that the out-of-plane torsion was the major motion that drove the S1→S0 IC. Even though our data are consistent with the UED data reported by Srinivasan et al. (21), we have a different interpretation of the dynamics that does not include ring opening. A detailed comparison between the two experiments is given in the supplementary materials.

In summary, through the correlation of a specific nuclear degree of freedom to electronic structure change, we have demonstrated that structural and electronic dynamics can be retrieved simultaneously and independently from a single UED dataset. This method allows us to identify the relaxation mechanism in the nπ* state of pyridine. Owing to the universality of the diffraction signature from correlation effects (2427, 31), we expect that this method will be widely applicable in ultrafast photochemistry. Moreover, the inelastic electron scattering is a Fourier transform of the change of the two-electron density caused by electron correlation. In contrast to spectroscopic probes, it measures spatial rather than energetic aspects of electron correlation (23). Because electron correlation is at the heart of modern quantum chemistry simulations, inelastic electron scattering provides a benchmark for state-of-the-art and future theoretical and computational methods.

Supplementary Materials

science.sciencemag.org/content/368/6493/885/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S14

Tables S1 and S2

References (3553)

Movie S1

References and Notes

Acknowledgments: We thank G. M. Stewart from SLAC National Accelerator Laboratory for assistance in making Fig. 1A. M.G. serves on the Science Advisory Committee of LCLS, which manages the SLAC UED facility. Funding: The experimental part of this research was performed at SLAC MeV-UED, which is supported in part by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (DOE BES) SUF Division Accelerator & Detector R&D program, the LCLS facility, and SLAC under contract nos. DE-AC02-05-CH11231 and DE-AC02-76SF00515. T.J.M., T.J.A.W., X.Z., J.K.Y., and R.M.P. were supported by the AMOS program within the Chemical Sciences, Geosciences, and Biosciences Division of the DOE BES. M.G. and M.N. are funded via a Lichtenberg Professorship of the Volkswagen Foundation. J.P.F.N., B.M., and M.C. were supported by the DOE BES under award no. DE-SC0014170. Y.L. and T.W. were supported by the DOE under award no. DE-FG02-08ER15984. Author contributions: J.Y., J.P.F.N, T.J.A.W., Y.L., R.L., S.P., X.S., S.W., T.W., and X.W. carried out the experiments. J.P.F.N., M.N., M.C., and M.G. improved the experimental system. J.P.F.N., B.M., and M.C. tested the sample delivery system. J.Y. analyzed the experimental data and performed the genetic structural retrieval algorithm. X.Z. and T.J.M. performed the GAIMS simulation. X.Z., R.M.P., and T.J.M. developed the computational method for AIED simulation. X.Z., J.K.Y., and T.J.M. carried out the AIED simulation. J.Y., X.Z., M.G, T.J.M., and X.W. prepared the manuscript, with discussion and improvements from all authors. Competing interests: None declared. Data and materials availability: All data underlying the figures are deposited at Zenodo (34). The raw experimental data are archived at the SLAC MeV-UED facility, and the raw simulated data are stored at the Martinez laboratory at Stanford University and SLAC. All data needed to evaluate the conclusions in the paper are present in the paper or the supplementary materials.

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