Introduction

Capturing the transient position of nuclei with sub-Angstrom and femtosecond spatiotemporal resolution for a specific electronic state can visualise the ultrafast structural dynamics of polyatomic molecules, which is a key step towards a better understanding and controlling of the chemical reaction. Many ultrafast structural imaging techniques have been developed to achieve this goal, such as diffraction imaging techniques with X-ray1,2 and ultrafast electron bunch3,4,5,6, laser-induced electron diffraction (LIED)7,8,9,10 and Coulomb explosion imaging (CEI)11,12. Using LIED, Blaga et al. and Wolter et al. established that the extension of carbon–hydrogen bond occurs at a time scale of a few femtoseconds, suggesting that femtosecond to sub-femtosecond time resolutions are critical for capturing the motion of hydrogen in electronic excited states8,9. The CEI was developed decades ago to study the molecular structure by ionising the target to a highly charged state upon various radiation sources, such as X-ray, electron beams and intense femtosecond laser pulses. The molecular structure prior to Coulomb explosion (CE) can be reconstructed from the momentum information of all the fragments in the molecular frame of reference11. Benefited from the ion momentum imaging technique, CEI has equal sensitivity for the probing of light and heavy atoms13, and has been used to trace the roaming dynamics of hydrogen within the molecules14 and the conformation of the chiral molecule and complex organic molecule11,13. However, retrieval of the accurate electronic-state resolved structure of molecules with CEI is still elusive, since the complex nuclear dynamics during the multiple ionisation can distort the mapping between the initial structure to the observed momentum information15. For the sequential ionisation of valence electrons driven by the femtosecond laser pulse, the bond length of molecules retrieved from the CEI is usually larger than the equilibrium value, which can be explained by a concerted enhanced ionisation model that the ionisation yields reach maximum as the bond length extends to a critical value in the cation or dication states16. To capture the accurate transient position of the atom including hydrogen with CEI, one needs to freeze the nuclear motion during the multiple ionisation by projecting the molecule to the higher charge state within the few-femtoseconds regime. For the CEI of polyatomic molecules induced by electron impact, ultrafast nuclear relaxation dynamics can occur after inner-shell ionisation, and its structure evolution closely relates to the time scale of Auger decay. Moreover, a direct comparison study of the CEI induced by the ionisation of intense laser pulses and electron impact can provide solid experimental evidence to reveal the electronic state-resolved ultrafast nuclear relaxation dynamics of polyatomic molecules.

The structural deformation of water triggered by ionising radiation is essential for many research areas, ranging from radiation damage of biological tissue to the complex water-related reactions in interstellar space and the production of H3O+ and OH radicals17,18,19. Significant efforts have been devoted to image the transient structure of the water molecule20,21,22. Légaré presented a symmetrically stretched and straightened geometry of water with a few-cycle intense laser pulse based on CEI23. Liu et al. applied LIED to image the water molecule and observed the most probable structure of ionic states with a stretched bond length24. Interestingly, the electron can be tunnelled from both the highest occupied molecular orbital (HOMO) and HOMO-1 of water, which can initiate dramatically different vibrational wave-packet evolutions and lead to the population of the ionic ground (X) and excited states (A)25. By ionising inner-shell electron with X-ray free electron laser followed by Auger decay, the bond stretching at different instants along dication is probed with CEI, where the structure relaxation during the Auger decay (assumed to be 3 fs) is ignored20. Thus far, direct imaging of the excited-state resolved nuclear motions of water and comparing the structure deformation induced by inner-shell and valence ionisation remains largely unexplored.

In this work, by developing the laser-induced electron recollision-assisted Coulomb explosion imaging approach, we reveal the ultrafast nuclear relaxation along the ground and excited electronic states of cation and dication, and retrieved the accurate geometry of neutral D2O. With the help of the simulations, the snapshots of the vibrational wave-packets of the excited (A) and ground states (X) of D2O+ are captured simultaneously with sub-10 picometre and few-femtosecond spatiotemporal precision. We show the ROD can stretch more than 50 pm within approximately 5 fs after double inner-shell ionisation induced by electron impact. The accuracies of those results are limited by the simulations.

Results

Imaging of the excited states-resolved structures triggered by the valence ionisation

Experimentally, D2O is irradiated by linearly and circularly polarised intense laser pulses leading to the removal of three outer-valence electrons of the molecule, which is followed by the three-body CE process D2O3+ ⟶ D+ + O+ + D+. Measurement of the three-dimensional momenta of the fragment ions that are dissociated from D2O3+ enables the kinetic energy release (KER, sum energy of three fragments) and the angle between the two momentum vectors of D+ (θcm) in the centre-of-mass frame to be derived. The measured density plots of θcm versus KER are compared between linear and circular polarisations, which are shown in Fig. 1a and b, respectively. The plots exhibit distinctive features including the low- and high-KER region (labelled region I and II, respectively). The region I (centred at ~20 eV) contains three components with different θcm. In the case of an circularly polarised laser field (Fig. 1b), the distributions are nearly identical, which shows weak polarisation dependence. Those events originate from the sequential triple ionisation via the well-known strong field enhanced ionisation (EI) mechanism, where ultrafast bond extension within a few fs along the potential energy surface (PES) of the dication leads to the decrease of the KER16,22. We proposed a three-body electron recollision-assisted Coulomb explosion (TERCE) approach, where the sub-cycle laser-induced electron recollision process is used to freeze the nuclear motion in the EI process, leading the production of high-KER region (II). The tunnelling electron from the cation can be driven back to the vicinity of the dication by the oscillating electric field and then further ionise or excite the parent ion before prominent nuclear motion which can occur within one optical cycle (~2 fs in the present case)26. This idea has been demonstrated to be available for the proton wave-packet dynamics of H2 molecule27,28. TERCE thus can achieve the few-fs temporal resolution. Since the circularly polarised light suppresses the electron recollision dynamics, and region II is expected to be absent in the case of circularly polarised light, which can be seen in Fig. 1b. Moreover, the region II exhibits different maxima of the (θcm-KER) distributions relative to that originating from the enhanced ionisation process (region I). Furthermore, a comparison between Fig. 1a, b exhibits strong laser polarisation dependence in the region (labelled III) with KER around 23 eV and small θcm (less than 70∘), which indicates that TERCE plays a key role in its formation.

Fig. 1: Experimental results and simulations of TERCE.
figure 1

a, b present the θcm-KER distributions of the three-body CE channel induced by linearly and circularly polarised 40 fs laser pulses, KER and θcm stand for the total kinetic energy release and the bond angle. Here, I labels the enhanced ionisation with weak polarisation independence, and II and III label the distributions with strong polarisation dependence, indicating that these events are correlated with electron recollision processes. c θcm-KER distribution mainly originates from TERCE for linearly polarised laser pulses. The events with larger energy differences (>12 eV) between D+ and O+ are selected for region I and II. The events from asymmetric CE are added for region III. d θcm-KER distribution for circularly polarised laser pulses. The same conditions as c are used. The two-dimensional global fit of (c) with seven dominant (θcm-KER) components are shown in (f). The four components in region II are marked by the dashed and solid circles in (c) and (f). The intensity is plotted on a logarithmic scale. e Simulated θcm-KER distributions based on TERCE. For region II, the θcm-KER distributions dissociated along the doublet and quartet states of the trication are shown and marked with the dashed and solid circles, respectively. For region III, the θcm-KER distribution dissociated along the quartet state of trication is shown.

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To further reveal the dissociation dynamics of TERCE, we present the energy-correlations map between two D+ and Dalitz diagrams in Supplementary Fig. 1. Three regions can be well resolved in the energy-correlation maps, where regions II and III appear only in the results of the linearly polarised light. Region II has larger energy than I, and for both regions, two D+ ions have a similar energy, and thus a concerted three-body CE with symmetric geometry can be inferred. However, for region III, the two correlated D+ have large energy differences, suggesting the asymmetric concerted three-body CE process is dominant. These arguments can be further validated by the Dalitz diagram shown in Supplementary Figs. 1e, f, region II appears at the central zone, which stands for the symmetric CE process, and region III shows two arm-like distributions, indicating the asymmetric three-body CE process. By clarifying the concerted three-body CE mechanism for regions II and III, we can further retrieve the transient structure before the three-body CE.

Region II in Fig. 1a contains several components with different peak positions of the (θcm-KER) distribution, indicating that multiple dissociative pathways are involved. To isolate those pathways, the detailed information of each component needs to be extracted. We first zoom in on the distributions from TERCE by selecting events in high-KER region. In the concerted symmetric CE, the events with the higher KER will have larger energy difference between D+ and O+, which is shown in Supplementary Fig. 2. By selecting the events with energy differences larger than 12 eV, we can keep the events from symmetric CE in region II and remove most of the events from regions I and III. The results are shown in Fig. 1c. Moreover, the events from the asymmetric TERCE channel (region III) have larger energy differences between two D+ (see Supplementary Figs. 1a, c), based on this feature, the events from region III can be selected and added to Fig. 1c. With the same conditions for the circularly polarised light, we show those events in Fig. 1d, and only a small fraction of region I can be observable. With the custom-developed two-dimensional fitting program, we conducted a global fit for Fig. 1c and the fitting output is shown in Fig. 1f. In this fit, only the number of components was assumed, and the peak positions of (θcm-KER) for each component were not fixed (see Supplementary Fig. 3). The fit is in good agreement with the raw results. For region II, four dominant components can be obtained from the fit, and the peak values of (θcm-KER) are listed in Table 1. Region III contains one dominant component, which will be discussed in the following section. A custom-developed molecular dynamic method is used to simulate the TERCE channels, and the results are presented in Fig. 1e, which can quantitatively reproduce the experimental patterns shown in Fig. 1c.

Table 1 Comparison of peak positions between experimental fit and simulations
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The detailed triple ionisation mechanism mediated by the laser-assisted electron-recollision is sketched in Fig. 2a for region II. Here, electron-recollision-induced double ionisation from the cation to the trication is expected, as indicated by the black arrow in Fig. 2a, because the high-KER events can only be produced when the ultrafast nuclear motions along the PES of the dication are nearly frozen29. In the rising edge of the laser pulses, the X and A states are firstly populated by the direct tunnelling ionisation of HOMO and HOMO-1 of neutral water. Interestingly, low vibrational states are activated for the X state and highly excited vibrational states are activated for the A state after the vertical ionisation; thus, the evolutions of the vibrational wave-packet are expected to differ markedly25,30. We calculated the time-dependent quantum wave-packet evolutions ionised from the X and A states to the trication as shown in the Fig. 2b, respectively31. For the X state, the wave-packets oscillate in a small range, while for the A state the large amplitude vibrations proceed rapidly along both θDOD and ROD, and the wave-packet distributions at 1, 3, and 5 optical cycles after initial ionisation are shown in P13, P14 and P15, respectively (see Supplementary Figs. 7, 8). The coupling of the X and A state via dipole transition can play a minor role in the TERCE, which will be discussed in the future. We further calculate the most probable instant of the tunnelling ionisation for both X and A states based on the molecular Ammosov–Delone–Krainov (MO-ADK) model32. The double ionisation yield via sub-cycle tunnelling depends on both the amplitude of the electric field within the laser pulse and the ionisation potential of the water cation at the ionisation instant. The ionisation potential between the water cation and dication decreases dramatically as the bond length and bond angle increase. As sketched in Fig. 2a, the ionisation energy of dication and trication is lower for larger θDOD (150∘) than the equilibrium bond angle (105∘). Given our experimental conditions, the calculated results reveal that the most probable instant of double ionisation for the X and A states occur approximately 2 and 3 optical cycles after single tunnelling ionisation, respectively (see Supplementary Figs. 9, 12). The distributions of the transient wave-packets at these instants are presented in P12 to P14 of Fig. 2b, and 150∘ is the θDOD of A state at the most probable double ionisation instant.

Fig. 2: Scheme of TERCE and the time-dependent wave-packet motions.
figure 2

a Detailed scheme of the TERCE. The electron is firstly ionised to the cation state via tunnelling of the HOMO and HOMO-1 of neutral water, which directly populates the X and A states. With time intervals of a few femtoseconds, the second electron is released via further tunnelling ionisation of the X and A states, and then recollides with the dication and kicks out the third electron, which can be called non-sequential double ionisation (NSDI, indicated as black arrow). Then the trication can dissociate along both the doublet and quartet trication states. The wave-packet evolutions in different states are illustrated as Gaussian distributions. The PESs for 150∘ are offset for the clarity of presentation, and 150∘ is the most probable bond angle for the tunnelling ionisation of A state. b Simulated time-dependent vibrational wave-packets dynamics during TERCE. The X axis stands for the time-delay between single ionisation and double ionisation. T stands for the optical cycle (2.7 fs in our case). The panels P11 to P15 present the vibrational wave-packet (WP) distributions along the X and A states of cation at different time intervals, and are initiated by the tunnelling ionisation of HOMO and HOMO-1. For typical time intervals, the projected wave-packets on dication states are also presented after 2 fs evolutions along the dication (panels P21 to P25). The panels P31 to P35 and P41 to P45 present their corresponding wave-packets before the CE along the doublet and quartet states of the trication, respectively. The electron collision-induced ionisation yields of wave-packets are considered.

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The wave-packets at different instants are projected to the dication, and these projected wave-packets further evolve along the PES of the dication within 2 fs (3/4 of one optical cycle) during the electron recollision process26, and the wave-packet distributions after evolvement are presented in P21 to P25 of Fig. 2b. The wave-packets are further projected to the dissociative trication state via the electron recollision process, and the final wave-packets distributions are calculated with multicenter three-distorted-wave (MCTDW) method33. In those calculations, two assumptions are used as follows: first, the ionisations via strong field tunnelling and electron recollision satisfy the Franck-Condon principle, namely the nuclear vibrational wave-packets stay the same during the ionisation; second, the laser field can be considered as a perturbation interaction, which only affects the orientational distribution and has no influence to the evolutions of vibrational wave-packet along the PESs. Here, the high-precision three-dimensional PESs of the trication state of water were calculated using the multireference configuration interaction (MRCI) method34,35, and we found that the two lowest-lying states of D2O3+ (\({}^{2}{{{{{{{{\rm{A}}}}}}}}}^{{\prime} }\) and 4A″) have similar potential energies in the 100–130 pm region. Hence, their contributions to TERCE should both be considered here. Based on the calculated wave-packets distributions on the doublet and quartet states, we simulated the dissociation dynamics along the accurate PESs, and the results are shown in Fig. 1e. All the details about the calculation method are documented in the Supplementary information (see Supplementary Notes 3–5).

The simulated θcm-KER distributions of the four CE channels ionised from X and A states are presented in region II in Fig. 1e (marked by dashed and solid curves), which well reproduced the θcm-KER distributions from TERCE in Fig. 1c. The peak values of these four channels are compared quantitatively with the fitted values in Table 1. The quantitative agreement between the simulations and experimental fit verifies that the four components in region II correspond to the four channels starting from the X or A states and ending with the doublet and quartet states of the trication. The simulated peak positions of KER and θcm were in good agreement with the two channels from the A state and the channel from the X state (quartet dissociative channel). The deviation is relatively larger for the doublet channel from the X state because its lower-energy distribution in the measurement overlaps with the enhanced ionisation region. Our simulations considered the time-dependent vibrational wave-packet propagation in different ionisation stages, the dependence of the molecular tunnelling ionisation yields on the transient structure including orientation effect, and the electron-recollision induced ionisation yields, and thus enabled the direct comparison and interpretation of experimental results from TERCE.

We attempted to determine the transient geometrical structure based on TERCE. Initially, we assumed that the PES of the trication to be purely Coulomb repulsive36,37, and the reconstructed O-D bond length (ROD) corresponding to the four components are listed in Table 2. Overall, the extracted values are much larger than that of the equilibrium values of the neutral ground state (105∘-97 pm, θNeq-RNeq). Under this assumption, the two observed CE channels from the same cation state (X or A state) are thought to originate from different initial structures, which is not the case here. To overcome this problem, the calculated high-precision three-dimensional PESs of the trication states were adopted to determine the initial structure before CE. We first searched for geometries that can produce the observed KER based on nuclear dynamics simulation along the calculated PESs; then, starting with these geometries, the three-body CE was simulated along the PESs using the semiclassical trajectory approach. Finally, a comparison of the momentum angle θcm between the simulated and experimental results enabled us to derive the transient structures of the X and A states of D2O3+ before CE. The geometries obtained from different channels are listed in Table 2. Importantly, the two channels from the doublet and quartet states of the trication provide an in situ self-reference for the accuracy of structural retrieval. For the two channels starting from the X state and ending to the doublet and quartet trication states, the retrieved geometries of (θDOD-ROD) before CE are (113∘-113 pm) and (97∘-108 pm), respectively. The excellent agreement between them indicates that the sub-10 pm and few-degree accuracy are attainable with the present TERCE approach. Moreover, the most probable geometry before CE from the simulation is (106∘-110 pm), which confirms the accuracy of our structural retrieval. Compared with the equilibrium structure of the neutral ground state, the retrieved ROD before CE extends approximately 11–16 pm during the ionisation process from the neutral to the trication state, and the θDOD stays similar to θNeq within the error bars. Using accurate transient structural imaging, we can directly establish that, by removing one electron from the HOMO, only large amplitude symmetric bond stretching motion is initiated and the bending motion is rarely activated. In the simulation, the corresponding most probable instant for projecting the wave-packets from the X state to the dication is approximately 2 optical cycles (5 fs) after tunnelling ionisation of the HOMO. The time-dependent wave-packet dynamics are presented in Fig. 2b. More specifically, the wave-packets simulations further show that ROD extends approximately 7 pm within 5 fs in the X state, and further extends 5 pm along the dication within 2 fs during the electron recollison process (see Supplementary Fig. 9). We succeeded in capturing the transient structure of X state for water cation with an unprecedented accuracy (sub-10 pm and few-degree).

Table 2 Summary of the retrieved structures of X and A states
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For the A state, the extracted transient θDOD before CE are 159∘ and 148∘ from the doublet and quartet dissociation channels with TERCE, respectively, which are approximately 50∘ larger than the θNeq. This indicates that highly excited bending motions are initiated by the direct tunnelling ionisation of HOMO-1. The retrieved ROD before CE for two channels is both 116 pm, which is approximately 20 pm larger than RNeq. In our simulation, the most probable structure before CE is (149∘-115 pm), which is in quantitative agreement with the measurement within the error bars for both channels. Moreover, the most probable instant for the double ionisation is 3 optical cycles (8 fs) after the first tunnelling ionisation, and this transient wave-packet distribution has a maximum with the geometry of (146∘-107 pm), as shown in Fig. 2b. The value of θDOD increases approximately 40∘ and ROD stretches approximately 10 pm after evolution in the A state within 8 fs. The ROD further extends 7 pm along the PES of the dication within 2 fs, while the variation of θDOD is minor during the electron recollision process (see Supplementary Fig. 9). Here, the captured nuclear motion can serve as a dynamical fingerprint to resolve the ionic ground and excited states.

In contrast to the symmetrical three-body CE of the X and A states, the asymmetrical CE channel is also observed as shown in Fig. 1a (region III). This distribution can be well reproduced with the two-dimensional fit in Fig. 1f. These events are selected by setting the kinetic energy difference of two D+ larger than 6 eV according to their characteristic distribution in region III of Supplementary Figure 1. The one-dimensional distributions of KER and θcm for the asymmetric channel are presented in Fig. 3a and b, respectively. The measured KER is fitted with a peak of 22.4 ± 0.3 eV, and θcm is centred at 76 ± 4∘. Compared to region II, the dramatically different θcm-KER distribution indicates the involvement of an additional ionic excited state. The ab initio calculations of the electronic states of the water cation have a higher excited state (C) with a highly asymmetrical structure, where the two O-D bonds are asymmetrically stretched and the two deuterium atoms are located on the same side of the molecule38. Based on the calculated PESs of the cation, dication and trication, we simulated the three-body CE process; that is, (O-D-D)+ → (O-D2)2+ → (O+ + D+ +D+), where the equilibrium geometry of the C state was the initial geometry with ROD ~ 227 pm and 122 pm, and θDOD ~ 0∘. In the simulation, the elongation of the O-D bond along the dication state during the ionisation from dication to trication is dominated by the strong field-enhanced ionisation at a critical distance, where the distance between the two D atoms is assumed to be similar to that of the enhanced ionisation of D\({}_{2}^{+}\) molecule39. The simulated KER and θcm distributions are presented in Fig. 3a and b (also shown in Fig. 1c, region III), and are in quantitative agreement with the experimental results. Thus, region III can reflect the geometrical structure of the C state. However, the ionisation potential of the C state is more than 10 eV higher than that of the X state, suggesting the direct population of the C state via tunnelling ionisation of the neutral ground state is unlikely. Moreover, considering the strong polarisation-dependent yields of region III, we propose that the electron recollision-induced excitation leads to the population of the C state. The details are sketched in Fig. 3c. The tunnelling electron from the neutral ground state can return to the vicinity of the parent ion and excite the parent ion to the C state via recollision process. After the initial population, the vibrational wave-packet evolves along the PES to the global minimum with an asymmetric O-D-D geometry, where the triple ionisation occurs via further strong field-induced double ionisation. For this state, only one channel from the quartet state is dominant because the ionisation potential of the quartet state is much less than that of the doublet state of the trication for the larger bond lengths. According to the measured KER and θcm, we determined the initial geometry before the CE by adopting the accurate PES of the trication. The retrieved ROD was \(27{7}_{-4}^{+5}\) pm and \(12{2}_{-2}^{+2}\) pm for the two O-D bonds with a bond angle of \({6}_{-1}^{+1}\)∘. Compared to the equilibrium geometry of the C state, the shorter ROD is identical and the larger ROD is extended by a further 50 pm along the PES of the dication. Ultrafast structural imaging enabled the population of the higher excited state C with an asymmetric structure to be experimentally established. Our studies indicate that the large amplitude bending motion and asymmetric stretching motion of molecular dynamics can be efficiently triggered by an electron collision process.

Fig. 3: Details of the asymmetric CE channel induced by the electron recollision induced excitation.
figure 3

a, b Measured θcm and KER distributions (Exp.) for region III. The dotted red and solid blue lines represent the fit and simulated results (sim.), respectively. c Detailed mechanism of the TERCE from the C state. The tunnelling electron is promoted to the ground state of the cation via tunnelling ionisation, and this ionised electron can recollide with the cation and excite a second electron to a higher excited state (C), which is also known as recollision induced excitation (RIE) (indicated as black arrow). This excitation initiates the large amplitude bending and asymmetric stretching motions. This enables the molecule to relax to the minimum of the PES of the C state, where further tunnelling ionisation to the dication state occurs instantly because of the much lower ionisation potential at larger bond lengths. The wave-packets evolve along the dication for certain time interval and are projected to the trication via enhanced ionisation. Finally, the wave-packet dissociates along the quartet state of the trication.

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Imaging of structure and dynamics triggered by the inner-shell ionisation

The rich nuclei dynamics along the cationic states limit the possibility to retrieve the accurate equilibrium geometry of neutral D2O experimentally with TERCE, and directly imaging the accurate neutral structure with CEI can serve as a benchmark for the study of water dynamics, which has not been achieved so far. To address this issue, a 200 eV pulsed electron beam is used to induce vertical triple ionisation of D2O, and the three-body CE occurs following the triple ionisation process and the momenta of the produced two D+ and O+ fragments are measured in coincidence. Three electrons from the valence bands can be directly kicked out by the electron impact, and the duration of the electron impact ionisation process is in attosecond regime, which can fully freeze the nuclear motions before CE and enable the accurate imaging of the equilibrium geometry of neutral water with CEI. The measured (θcm-KER) distribution is shown in Fig. 4a, and three components with highest KER are marked with grey circles. Compared to Fig. 1c, their KERs are larger and θcm are all below 150 ∘, indicating the nuclear motions along cationic states in TERCE are frozen by the ultrafast electron impact ionisation. To explore the underlying dynamics of those three components, we implemented a similar molecular dynamics simulation with semi-classical trajectory method as the TERCE, but ignoring all the nuclei motions during the ionisation, i.e., directly projecting the neutral wave-packet to the electronic states of trication, as shown by the black wave-packet in Fig. 4d. Here, three electronic states with the lowest ionisation energy are considered including the doublet and quartet states used in TERCE, and the simulated (θcm-KER) distributions dissociated along them are shown in Fig. 4b (marked by grey circles). The simulated and measured θcm and KER show good agreements, the obtained peak values are presented in Table 3. The consistency confirms that the direct vertical triple ionisation and following CE lead to the production of the three high-energy components, which also verified the validity of our simulation approach. Based on the measured values of (θcm-KER) for three pathways, we retrieved the equilibrium geometry with the same procedure used in TERCE, and the obtained (θDOD-ROD) are (102∘-94 pm), (100∘-99 pm) and (102∘-95 pm), respectively. These values are in very good agreement with the theoretical equilibrium (105∘-97 pm) for all three independent pathways. These results provide so far the most accurate neutral structure retrieved with the CEI technique experimentally, to the best of our knowledge.

Fig. 4: The experimental results induced by the electron impact ionisation.
figure 4

a Measured distribution of (θcm-KER) for three-body CE induced by the electron impact ionisation. Three components marked with grey solid circles with high-KER originate from the vertical triple ionisation process. One low-KER component marked with red solid circle stand for the three-body CE induced by the inner-shell ionisation process followed by Auger decay. b Simulated distributions of θcm vs KER for the four components marked in (a), which comes from three-body CE induced by the ionisation of both valence and inner-shell electrons. c Schematic plot for the relaxation mechanism for the inner-shell ionisation and Auger decay. Two 2a1 electrons are kicked out by the incident electrons, and after the ultrafast nuclear relaxation, two 1b1 electrons filled the double holes, and the third electron is ionised by absorbing the radiation. d The potential energy curves for the involved electronic states of trication and autoionisation state of dication. The instant of the Auger ionisation is indicated by the vertical blue arrow after ultrafast nuclear relaxation along the autoionisation state.

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Table 3 Strucutres retrieved from the electron impact ionisastion of valence and inner-shell electrons
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The inner-shell ionisation of polyatomic molecules can also lead to ultrafast nuclei relaxation, which can be different from that induced by the valence ionisation. Our 200 eV electron beam can provide enough energy to kick out two 2a1 electrons of D2O, and induce the triple ionisation via the Auger decay process40,41. In Fig. 4a, the low-KER component (27.5 eV, marked by red circle) can be observed. The dissociation limit of the lowest quartet state of trication is calculated to be 50.1 eV, and the KER for this pathway is 27.5 eV, thus according to the energy conservation law, the initial energy of autoionisation state should be higher than 77.6 eV, and only the 2a\({}_{1}^{-2}\) state is in this energy range according to the literature41. The most possible pathways to lead to the production of this component are schematically shown in Fig. 4c, two 2a1 electrons are firstly ionised by electron impaction and an autoionisation state of dication with the energy of 83.5 eV is populated, which is still lower than the vertical ionisation energy of ground state of trication (85.0 eV)41. This can be seen in Fig. 4d, the calculated potential energy curve of the autoionisation state locates below the ground state of trication in the Frank-Condon region. However, as the wave-packet propagates along the stretching motion of ROD, the ionisation energy of this state can decrease and cross with the quartet state of the trication, where the triple ionisation via Auger decay is energetically possible. After the crossing point, the Auger decay can occur at certain instant as indicated by the blue arrow, which leads to the low-KER components dissociated along the quartet states. Based on the measured KER and the energy of potential energy curve of the quartet state, we can infer the ROD = 163 pm at the instant of Auger ionisation for this pathway because of the energy conservation. Based on all these information, we simulated the θcm distributions dissociated along this pathway, and the peak value is shown in Table 3. The good agreement of the θcm between simulation and measurement confirms the above conclusion. Furthermore, we can infer the time scale of the Auger decay for this pathway based on the measured KER and simulations, which is determined as 3.2 fs. The CEI thus can serve as a clock for the complex Auger decay process in the polyatomic molecule.

Summary of the electronic state-resolved structural dynamics of water

In Fig. 5, we summarised the structural evolutions along different electronic states of D2O induced by the femtosecond laser pulse and electron beam. The equilibrium geometry of D2O is experimentally retrieved from the three-body CE induced by kicking out three valence electrons via electron impact. Ejecting one valence electron through strong field tunnelling leads to the population of X and A state of cation, and based on the simulations, the wave-packets evolve for approximately two and three optical cycles, and their ROD extend 7 pm and 10 pm, respectively. Moreover, the bond angle increases from 97∘ to 146∘ for A state. Ejecting the second valence electron at this instant from X and A states lead to the population of the ground state of dication, and according to the retrieved structures, the ROD extends 4 pm and 9 pm within 2 fs, respectively. A higher excited state of cation can be populated by the recollision-induced excitation within 2 fs, and then form an asymmetric geometry before double ionisation, the longer ROD can reach 277 pm before three-body CE. Ionising two inner-shell electrons by electron impact leads to the direct population of autoionisation state of dication, according to our simulations, after the relaxation of 5 fs, the ROD extends approximately 60 pm before CE, indicating the much faster stretching motions along autoionisation state than that for the ground state of dication.

Fig. 5: The summary of the structural evolutions for different electronic states of D2O.
figure 5

The transient structures at different time instants from the X, A and C states are firstly given based on the simulations in the current condition. For example, the ROD stretches from 97 pm to 107 pm along the A state within approximately three optical cycles, and further extended to 116 pm evolving along the ground state of the dication within 2 fs (electron recollision time). In the lower panels, the retrieved geometry of neutral water on average is 101∘-96 pm. The simulations indicate that after ultrafast relaxation within 5 fs along the autoionisation state of dication, the ROD stretched to 163 pm for the Auger decay pathway.

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In summary, we captured the remarkable transient geometrical structure for the ionic ground state and excited states of the D2O molecule at an unprecedented spatiotemporal resolution. We implemented the three-body CEI induced by strong field tunnelling ionisation and direct electron-impact ionisation, which have been well interpreted by our custom-developed ’ab initio’ nuclear dynamics simulation. Based on the same observable, the nuclei dynamics induced by the inner-shell and valence electron ionisation are compared. For the cation, we present the bond stretching of 7 pm for the X state within approximately two optical cycles, and significant bending motions (50∘) accompanying with 10 pm bond extension within approximately three optical cycles for A state, respectively, according to the comparison between measurements and simulations in the present condition. We established that the excited state (C) with O-D-D type structure can be effectively populated by the excitation induced by the recollision process, which may constitute a new possible pathway for the formation of the H3O+ in interstellar space or proton transfer in the liquid water. For the dication, we visualised the bond extension of 60 pm before Auger decay following the autoionisation state, and this value is much larger than the bond extension along ground state during 2 fs. The accuracies of those results are limited by the simulations. Our results present a comprehensive study of ultrafast transient structure imaging of neutral and ionic water, and the combination of TERCE and CEI induced by electron impact ionisation can provide deep insight into ultrafast nuclear relaxation after ionisation. We demonstrate a robust route for imaging excited-state resolved ultrafast molecular dynamics with sub-10 picometre and few-femtosecond spatiotemporal resolutions.

Methods

Experimental details

Laser pulses with a wavelength of 800 nm and pulse duration of 40 fs (full width at half maximum, FWHM) were produced using a Ti-sapphire laser system with a repetition rate of 1 kHz. The laser beam was focused on the molecular beam using a mirror with a focal length of 75 mm. D2O molecules were evaporated into a chamber using supersonic expansion. All ionic fragments induced by the laser pulses were collected in coincidence using cold target recoil ion momentum spectroscopy (COLTRIMS) (see Supplementary Figure 18), and their three-dimensional momentum vector can be determined by combining the time information of the time-of-flight spectrometer and position information recorded by a position-sensitive detector42. The length of the time-of-flight was 7 cm with the homogenous voltage of 45 Volt/cm. Linearly and circularly polarised laser pulses with the same amplitude of electric field were used for comparison in the experiment, and their peak laser intensities were estimated to be 3.0 × 1014 W/cm2 and 6.0 × 1014 W/cm2, respectively, and the corresponding maximum recollision energy of returning electron is approximately 70 eV. The same setup is used for the CEI measurement driven by pulsed electron beam with the energy of 200 eV, and the details have been introduced previously43,44,45.

Theoretical calculations

In this work, a custom-developed molecular dynamic method is used to simulate the three-body breakups of D2O3+. The present simulations consider the complete nuclear wave-packets dynamics for the sequential triple ionisation from D2O to D2O3+, which enables the direct quantitative comparison with the measurement. Both the changes of vibrational wave-packet and molecular orientation distribution are performed in full quantum time-dependent wave-packet evolution method31. The tunnelling ionisations induced by intense laser pulses and the ionisation from dication to trication induced by the electron recollision are considered properly by the semi-classical MO-ADK32 and Multicenter three-distorted-wave (MCTDW) methods33, respectively. Detailed theoretical calculation details, calculation steps and all the used approximations can be found in Supplementary Information.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.