Main

In contrast to gas-phase X-ray or electron diffraction1,2,3,4,5,6,7, Coulomb explosion imaging (CEI) is an experimental technique that is equally sensitive to light and heavy atoms, providing information in momentum space, typically in a molecular frame of reference. It is inherently tailored to study single molecules and has originally been performed by sending beams of ionized molecules through thin foils8, thus stripping off electrons. The key to the success of CEI is a rapid charge up of all the atoms, triggering an explosion of molecules due to Coulomb repulsion. The fast removal of sufficiently many electrons is important to ensure that the molecule fragments into atomic ions without undergoing structural rearrangement during the charge up. The formation of long-lived intermediate molecular fragment ions would complicate the mapping from asymptotic fragment momenta to the initial atomic positions9. CEI is ideally suited to separately address all the atoms in a molecule, thus providing site-specific information on the entire molecule. Moreover, it has the potential of imaging the complete (square of the) nuclear wavefunction8.

Nowadays, CEI is typically triggered through photoionization, which opens the door to time-resolved experiments. For example, intense, femtosecond laser pulses allowed retrieving the complete three-dimensional (3D) fragmentation pattern of a small molecule with five atoms10 or isolating a rare roaming reaction11. Inner-shell absorption of an X-ray photon can—depending on the photon energy and atomic species—also create multiple charges on a molecule due to Auger cascades. However, among the many studies on 3D momentum imaging using X-ray ionization, only a few of them have studied somewhat larger molecules up to now12,13.

With the development of X-ray free-electron lasers (XFELs) offering pulse duration of a few femtoseconds, the achievable intensity has increased by orders of magnitude. This facilitated, for the first time, multiphoton inner-shell absorption, removing many electrons from a single atom within one X-ray pulse14. Several XFEL experiments have obtained 3D momentum distributions of small molecules with four to five atoms15,16, and pioneering work touched the frontier of imaging larger molecules17,18. The first time-resolved experiments have investigated processes such as dissociation19, vibration20, isomerization reactions21,22 and charge transfer23 with CEI. However, CEI of complex molecules was considered unfeasible, because it was expected that recording all the molecular constituents in coincidence would be necessary—a requirement, up to now, impossible to fulfil for more than a few atoms with sufficient statistics, as the detection efficiency of each ion is typically only about 60%.

Here we demonstrate that intense, femtosecond soft X-ray pulses from a high-repetition-rate free-electron laser, the European XFEL, make it possible to image a complex molecule in its entirety, as well as to obtain detailed information on the ultrafast intramolecular electron rearrangement without measuring all the fragments in coincidence. The experiment was carried out using a cold-target recoil ion momentum spectroscopy (COLTRIMS) reaction microscope24 that is part of the Small Quantum Systems (SQS) scientific instrument at the European XFEL25. 2-Iodopyridine (C5H4IN) or 2-iodopyrazine (C4H3IN2) molecules were prepared in a dilute gas jet through supersonic expansion, such that each X-ray pulse typically interacted with only a single molecule. The X-ray focus size was ~1.4 μm and the photon energy was set to 2 keV; the average pulse energy was 1 mJ. The 3D momenta of the ionized fragments were measured in coincidence. More details are given in Methods.

Figure 1 shows the ion momenta resulting from the fragmentation of molecules into I+, N+, C+ and H+. The molecular frame of reference is defined by the I+ and N+ momenta; the ion species, identified by their different mass-to-charge ratios, are plotted in different colours. The structural analogies between the equilibrium molecular geometries and momentum distributions are very clear. In particular, the hydrogen (H3–H6) signals are well localized in Fig. 1, but the momenta of the individual carbon atoms (C2–C6) can become similarly separated (Fig. 3). As far as we are aware, momentum images of this quality are unprecedented for such complex molecules. We attribute the clarity predominantly to the fast charging of all ten or eleven atoms within only a few femtoseconds (Fig. 2d), leading to a direct explosion without the rotation or formation of intermediate molecular fragments.

Fig. 1: CEI of 2-iodopyridine and 2-iodopyrazine.
figure 1

a, Newton plots of N+ and H+ (b and g) and N+ and C+ (d and i) show the measured absolute momenta following Coulomb explosion of 2-iodopyridine (C5H4IN) (a) and 2-iodopyrazine (C4H3IN2) (f) molecules. For all the shots in which I+, N+, and at least one H+ and one C+ were detected, the coordinate frame is rotated such that the I+ momentum points along the z axis (\({p}_{{\mathrm{I}}_{x}}\) = \({p}_{{\mathrm{I}}_{y}}\) = 0) and the N+ momentum spans the y–z plane together with the I+ momentum (\({p}_{{\mathrm{N}}_{x}}\,\) = 0, \({p}_{{\mathrm{N}}_{y}}\) > 0). The momentum of the third particle is plotted in this coordinate frame. No background was subtracted. The corresponding modelling results from XMDYN are shown in c, e, h and j. The diamond-shaped markers depict the asymptotic momenta when a single positive charge is instantaneously applied to each atom.

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Fig. 2: Time-dependent geometry and charge evolution of 2-iodopyridine molecules, created from calculated XMDYN trajectories yielding I+ + N+.
figure 2

a,b, Snapshots of the distributions of ion momenta (a) and ion positions (b) at different times (red, I+; blue, N+; black, C+; grey, H+). The origin of the coordinate frame is the molecular centre of mass, the horizontal axis points along the equilibrium position of I, and the plane of the figure is spanned by the I and N equilibrium positions such that N points upwards. The grey gridlines indicate px = pz = 0. c,d, Average interatomic distances (c) and average charges (d). The yellow area in c indicates the assumed X-ray pulse shape, namely, a Gaussian with a full-width at half-maximum of 10 fs (Extended Data Fig. 2 shows the results for the 20 fs case). In d, the average number of absorbed photons per molecule and per femtosecond are shown in green.

Source data

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We emphasize that the Newton plots in Fig. 1 display coincidences between only three ions (out of sets of four measured ions; Methods). If only a fraction of the generated ion fragments is detected in coincidence, this usually implies a reduction of information. Due to the high repetition rate of the European XFEL (here up to 570 X-ray pulses per second), we could also record up to eightfold ion coincidences, which produce identical-looking images in this case (Extended Data Fig. 1). This reveals that for the studied planar molecules, the reduced set of information from partial coincidences captures the essence of the asymptotic momentum density distribution of the fully fragmented molecule. The sharp momentum distributions (Fig. 1) indicate that the entire fragmentation pathway is determined by the final charges of only very few atomic fragments. Therefore, we obtain molecular fingerprints in the momentum distributions that provide a direct insight into the fragmentation dynamics.

The carbon atom located closest to the iodine atom (C2; Fig. 1d) receives only little overall momentum, because it is repelled by the heavy iodine ion, as well as the other ions in the ring. The C2 ion, therefore, remains almost at rest after fragmentation (Supplementary Videos 1 and 2). Furthermore, the proton momenta (Fig. 1b,g) are unexpectedly small (∣pH∣ ≈ 55 a.u.). A simple point-charge Coulomb explosion that instantaneously assigns a charge of +1 to each atom at its equilibrium position results in proton momenta of ∣pH∣ ≈ 110 a.u. (Fig. 1c,h, black markers). The lower observed momenta, therefore, imply rapid proton ejection before the full charge up of the molecule. More advanced theoretical modelling is clearly essential for extracting all the information from the measured momenta.

We employed the XMDYN theoretical toolkit26, which combines atomic ab initio X-ray physics with molecular dynamics in a Monte Carlo scheme. It includes charge transfer between the atom pairs based on a classical over-the-barrier model. The resulting Newton plots are shown in Fig. 1c,e,h,j, and further computational details can be found in Methods. The overall agreement with the experimental data is surprisingly good considering that for computational efficiency, no molecular orbitals or chemical bonds are included in the modelling. The demonstrated ability to reproduce experimental ion momenta by inserting a known equilibrium molecular geometry into our model represents the first important step towards future structural inversions of experimental XFEL CEI data. The comparison with the experiment also helped to improve our model (Methods). We mainly ascribe the remaining discrepancies between experiment and theory (Fig. 1) to residual chemical bonding. This can probably be overcome in the future by adding a force field in the model. An iterative optimization scheme would compare the calculated and experimentally measured momenta, thus identifying the start geometry that leads to the best match. Although not a high-precision method, such a procedure could be used, for example, to reconstruct the D2O molecule from CEI data with an accuracy of 0.3 Å for the bond length and 15° for the bond angle27.

Our modelling provides access to the structural dynamics occurring on femtosecond timescales. Figure 2a,b shows snapshots of the distributions of ion momenta and positions during and after the X-ray pulse. Figure 2c,d displays the average interatomic distances and average atomic charges as a function of time. Hydrogens exhibit the earliest onset of evolving dynamics, already starting during the X-ray pulse. The average C–H distance increases by almost a factor of two within the first 5 fs after the pulse centre, confirming the rapid proton ejection. Such a behaviour was also predicted for hydride clusters28. The heavier fragments only start moving notably after the X-ray pulse is over. Although the distances of the C–C and C–N bonds elongate as expected, the I–C2 distance first decreases drastically by almost a factor of two, reaching a minimum after 30 fs. It only starts to become larger than the equilibrium distance after about 50 fs. This intriguing behaviour is caused by the force acting on C2 that is initially directed towards iodine, until the ring has undergone Coulomb explosion and the repulsion by iodine dominates. The minimum of the I–C2 distance is also present for channels with a higher total charge, for example, in the I4+ + N2+ coincidence, where it is reached after 13 fs (Extended Data Fig. 3). In Fig. 2d, all the average charges first rise simultaneously. Although the I, C and N charges reach a plateau after 20 fs, the hydrogen charges exhibit a maximum after 10 fs, because from 10 to 14 fs, electron transfer is only possible from C to H+ but not from H to C+ due to the respective barriers in the model (Extended Data Fig. 4). The final charge states are determined by the late-time charge evolution (Extended Data Fig. 5), and the calculated average total molecular charge is +9 for fragmentation into I+ and N+.

At 2 keV photon energy, 91% of all the photoionization events take place at the iodine site (Extended Data Table 1), and the experimental data contain iodine ions with charges up to I25+. However, we also detect H+, C+–C4+ and N+–N3+, indicating that ultrafast electron rearrangement occurs within the molecule—a key process governing the structural dynamics and an active topic of investigation in several fields. To trace the result of the intramolecular electron transfer, that is, the final charges of the individual atoms, we can obtain site-specific charge-state distributions. The blurred carbon distributions (Fig. 1d) make such an assignment difficult, however, normalizing the carbon and nitrogen momenta by the magnitude of the corresponding iodine momentum (pnorm = p/|pI|) separates the distributions (Fig. 3a). We also note that the Newton plots for higher molecular charges provide clearly distinct carbon-ion distributions even without normalization, as shown in Fig. 3b for the I4+, N2+ and C2+ channel (see also Extended Data Fig. 6 for other charge states). A higher final charge implies a quicker charge up, thus approximating an instantaneous Coulomb explosion better.

Fig. 3: Momentum-space normalization and extraction of site-specific charge abundances.
figure 3

a, Normalized Newton plot for I+, N+ and C+ coincidences (compare with Fig. 1d). b, Absolute molecular-frame momenta for I4+, N2+ and C2+ coincidences. c, Visualization of the procedure for extracting site-specific charge abundances.

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For extracting site-specific charge-state distributions, we employ a multiple two-dimensional (2D) Gaussian fit to the normalized Newton plots (Fig. 3, bottom row, and Methods). Figure 4a–c displays the resulting experimental carbon charge-state distributions for each position in the ring and for different coincidence channels. The average carbon charge shifts to higher values for higher iodine charges. Moreover, although the abundances of carbon charge states are uniformly distributed over the ring for the I+ + N+ case (Fig. 4a), the C2 atom (red bar) is more often singly charged and less often triply charged than the other atoms for higher molecular charges (Fig. 4b,c). This may seem counterintuitive, because the C2 atom is located closest to the source of the charge (iodine) and in contrast to the other atoms, it stays within close vicinity of the iodine for several tens of femtoseconds (Fig. 2c). A shorter internuclear distance strongly increases the electron-transfer probability23. However, the trend in the charge-state distribution shows that these effects are overcompensated by the rapid rearrangement of electrons on timescales much faster than nuclear motion, adapting to the momentary geometry. Coulomb repulsion causes the positive partial charge to preferentially locate furthest away from the highly charged iodine atom, thus pulling the electron density towards the attractive potential of the iodine ion, as suggested previously29,30. The average charge is reproduced well in the calculations (Fig. 4d–f). However, the lower charge on the C2 atom for the higher charge coincidences is not captured by the current model and the overall distribution matches only for the I+ + N+ coincidence channel.

Fig. 4: Charge-state distributions of carbon atoms for different coincidence channels of 2-iodopyridine.
figure 4

a–c, Experimental ion yields are obtained by fitting a 2D Gaussian to each peak in the respective Newton plots (Fig. 3). The experimental error bars represent an estimate of the systematic error introduced in the fitting (Methods). The experiment is insensitive to neutral fragments. d–f, Corresponding theory results are shown with the statistical error derived from the finite number of trajectories. The fluences used in the calculations are 0.75 × 1011 (d), 1.80 × 1011 (e) and 2.30 × 1011 (f) photons μm–2.

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Our results demonstrate that Coulomb explosion induced by intense, femtosecond X-ray pulses can, under certain conditions, image complex molecules in their entirety, particularly including all the hydrogen atoms. Its scalability to non-planar and more complex molecules, such as samples without marker atoms, remains to be tested in future experiments. The key advantage of using an XFEL to trigger the explosion lies in the ease of creating very high charge states within a few femtoseconds, which is very difficult to achieve with femtosecond optical lasers. The ability to identify all the atoms in the momentum maps allowed us to retrieve the result of the intramolecular electron rearrangement at each atomic site. Advanced theoretical modelling added an insight into the ionization dynamics and geometry evolution of the fragments. In addition, the comparison with experimental data initiated theory developments necessary on the route towards structural inversion. We could show that partial ion coincidences of complex molecules with a well-defined structure can offer an unexpected degree of information. The method will further benefit from even shorter pulse durations and steadily increasing repetition rates of XFELs, which will enable the detection of even higher many-fold ion coincidences. The capability to reveal higher-order correlations renders the combination of XFEL and CEI a promising atomic-resolution imaging tool. In diffraction-based methodologies, typically, only second-order correlations are accessible. Although both ultrafast X-ray and electron diffraction hold the prospect to measure hydrogen atoms according to simulations31, a direct experimental demonstration in the gas phase is still pending and will require future improvements in the data quality31. Possible future advances of XFEL-induced CEI include its application as a probe step in the monitoring of atomic motion in time-resolved pump–probe experiments, as well as employing multiple FEL pulses of different colors, targeted to ionize specific atoms or the entire molecule. The unprecedentedly clear experimental momentum distributions, in combination with a powerful theoretical toolkit, are thus very encouraging with regard to recording videos of photochemical reactions.

Methods

The experiment was performed using a cold-target recoil ion momentum spectroscopy (COLTRIMS) reaction microscope24 that is available for users as part of the SQS scientific instrument at the European XFEL. The simulations were carried out with an extended version32,33 of the XMDYN26 toolkit that models the dynamics of matter exposed to high-intensity X-rays.

X-ray pulse properties

The European XFEL, operated at a base repetition rate of 10 Hz, provides bursts of electron pulses with a spacing of 1.1 MHz, out of which we used every sixth pulse for generating X-ray pulses for our experiment, that is, the photon pulses had a spacing of 5.5 μs, limited by the flight times of the heaviest fragments. Depending on other operating constraints of the facility, we received 250–570 X-ray pulses per second. The photon energy was 2 keV. The single-shot X-ray pulse energy (1 mJ on average) was measured upstream of the beamline mirrors by a gas monitor detector. The transmission was measured to be 80% at 2 keV for the beamline configuration during user run 3, resulting in 0.8 mJ on the target. The X-ray pulses were focused by a pair of Kirkpatrick–Baez mirrors, and the calculated focus size was 1.4 μm. The calculated upper limit of the X-ray pulse duration was 25 fs based on the electron bunch charge of 250 pC in the accelerator. To date, no direct measurement of the X-ray pulse duration has been carried out at the European XFEL, but recent indirect measurements suggested that the pulse duration can be as short as 10 fs34. Simulations in the manuscript were carried out with 10 fs (full-width at half-maximum) pulses. The calculated Newton plots for 20 fs pulse duration (Extended Data Fig. 2) look very similar. The average total molecular charge is +9.2 for 10 fs and +9.1 for 20 fs; the fraction of I+ + N+ trajectories decreases from 30% (10 fs) to 24% (20 fs).

Experimental setup

Vapour of the target substances (C5H4IN or C4H3IN2) was generated by heating an out-of-vacuum reservoir to 60 °C. A supersonic gas jet was formed using 500 mbar of helium as the carrier gas, expanding the mixture into a vacuum through a nozzle of 200 μm diameter, and collimating it by three skimmers and a set of adjustable slits. Gas line, nozzle and the first section of the jet vacuum chamber were also heated to 60 °C to prevent condensation. The base pressure in the experimental chamber was retained at 1 × 10−11 mbar during operation. The jet was crossed with the X-ray beam at 90° in the centre of the reaction microscope. The spectrometer had a total length of 250 mm, separated in two sections. At the interaction point, a high extraction field of E = 423 V cm–1 was applied (length, 86 mm), whereas the remaining part was set to the same voltage as the end of the high-field region. This combination yielded a sufficient mass-over-charge resolution, and provided decent momentum resolution and keeping the total applied voltage to <4,000 V. The fragment ions created by the X-ray ionization were extracted towards a time- and position-sensitive large-area microchannel plate detector (diameter, 120 mm) with hexagonal delay-line position readout. The ions originating from each X-ray pulse were measured in coincidence. The analogue detector signals were recorded at 10 Hz with fast analogue-to-digital converters.

Reconstruction of ion momenta

The ion trajectories inside the spectrometer were reconstructed from the recorded impact times and positions, yielding the initial momentum vectors of the ions. The ion flight times depend on the mass-over-charge ratio (m/q) and thus can be used to identify the ionic species. However, the statistical distribution of a given m/q value has a spread in time due to the ion’s kinetic energy. This can cause ions with similar m/q ratios to partially overlap. In the present experiment, this was the case for N+ and C+ in particular. In the coincidence analysis, we, therefore, omitted N+ with a high initial laboratory-frame momentum directed towards the detector, that is, ∣plab,z∣ > 175 a.u. Moreover, 3D momentum gates were applied to H+, C+, N+ and I+ to suppress random coincidences, restricting the laboratory-frame momentum distributions to ∣pH∣ < 100 a.u., ∣pC∣ < 230 a.u., ∣pN∣ < 300 a.u. and ∣pI∣ < 480 a.u., respectively (covering the entire momentum distributions). An additional momentum gate was applied to the sum momentum of all the measured particles, requiring ∣psum∣ < 500 a.u.

Creation of Newton plots

Molecules in the gas phase are randomly oriented in space. In a coincidence measurement, transformation from the laboratory frame to the molecular frame can be made by selecting the emission directions of certain ions as a reference. To obtain the momentum distributions in Fig. 1, the z axis of the coordinate frame was defined along the momentum of the iodine ion. The momentum of the nitrogen ion fixes the y–z plane (the plane spanned by iodine and nitrogen momenta). For 2-iodopyridine, the direction of the y axis was defined such that the y component of the nitrogen momentum is positive. For 2-iodopyrazine, the two nitrogen atoms were distinguished by the relative emission angle α between the measured nitrogen and iodine ions. Nitrogen ions with cos(α) > −0.125 were labelled N1 (Fig. 1), and if an N2 nitrogen was identified, the y axis was mirrored. To obtain the representation shown in Fig. 3a, all the ion momenta were further normalized to the magnitude of the iodine momentum, that is, scaled by a factor of 1/∣pI∣ for each event. Fourfold coincidence events, where at least one hydrogen, one carbon, one nitrogen and one iodine ion were detected in coincidence, were used (Fig. 1), even though only three ions are depicted in each panel. Threefold as well as higher-order coincidences yield identical-looking Newton plots (Extended Data Fig. 1). Coincidence detection of up to eight ions was feasible, although with low statistics.

Extraction of charge-state distributions

The site-specific carbon charge-state distributions (Fig. 4) were obtained from the threefold coincidence dataset. For each carbon charge state, normalized Newton plots (analogous to Fig. 3a) were created. Fitting a sum of five 2D Gaussian functions (Fig. 3c) yields the relative abundances at each carbon site (C2–C6). Neutral fragments are not detected in the experiment, but we consider the carbon atoms to have a very low probability to stay neutral, particularly in coincidence with higher charge states of iodine. This is also consistent with the fact that extremely few neutral C atoms are found in the calculations.

Statistics and error bars

The 2-iodopyridine data shown in Fig. 1 were obtained within 15 h of data collection and those for 2-iodopyrazine in 6 h. The statistical validity of the data can be estimated from the number of recorded ions per figure. Figures 1b,d and 3a show a total of 491,986 recorded ions. Figure 1g,i shows 364,450 ions and Fig. 3b depicts 70,068 ions in total. On close inspection of Fig. 3c, it is clear that the carbon-ion momentum distributions are only approximately described by 2D Gaussian functions. We, therefore, consider the fitting errors alone to underestimate the real error present in the extracted ion yields (Fig. 4). We have instead reperformed the fitting after rotating the Newton plot by 45°, to account for the partially asymmetric distributions, and used the difference obtained from both fits as a systematic error. This error probably somewhat overestimates the experimental uncertainty. For higher iodine charge states, a small diffuse background feature partially overlaps with the distribution of singly charged C2. We accounted for this by adding an additional 2D Gaussian to the fitting function, which is subtracted before processing the ion yield. In this way, we verified that this background does not cause the increased yield of singly charged C2 (Fig. 4b,c).

Theoretical modelling

The XMDYN framework26 follows a hybrid quantum–classical approach: neutral atoms, atomic ions and free electrons are considered classical particles, and are propagated using classical molecular dynamics. Bound electrons are treated as quantum electrons assigned to atomic orbitals, disregarding molecular states. Orbital binding energies, photoionization cross sections, and Auger and fluorescence decays rates are supplied by the ab initio XATOM toolkit26. Ionization dynamics leading to changes in the occupation numbers of the atomic orbitals are tracked in time using a Monte Carlo algorithm. All the occupied atomic orbitals of the neutral ground state are taken into account. The initial neutral equilibrium molecular geometries were obtained using the general atomic and molecular electronic structure system (GAMESS)35 at the restricted Hartree–Fock level of theory with a 3-21G* basis set. The resulting structure of 2-iodopyridine is in reasonable agreement with the experimental parameters36. We applied the velocity Verlet algorithm with one million time steps of one attosecond, propagating the Monte Carlo trajectories up to 1 ps. Unless specified otherwise, a fluence of 7.5 × 1010 photons μm–2 was employed, optimized to yield a high portion of I+ + N+ coincidences. As a consequence of the highly selective nature of the presented reaction microscope data, many more Monte Carlo realizations had to be calculated than could be used in Fig. 4 (Extended Data Table 2).

Classical over-the-barrier model in XMDYN

In XMDYN, all the charged particles interact via Coulomb forces. Atoms can exchange electrons via charge transfer according to a classical over-the-barrier model37, which yields critical distances for charge transfer that agree well with experiments23,38. The model determines electron transfer for any diatomic pair of neighbouring atoms, from donor D to acceptor A. Electrons from any atom in the molecule can, thus, be transferred to the iodine atom. The potential experienced by the electron being transferred from D to A is given by

$$V({{{\bf{r}}}})=-\frac{{Q}_{D}+1}{| {{{\bf{r}}}}-{{{{\bf{r}}}}}_{D}| }-\frac{{Q}_{A}}{| {{{\bf{r}}}}-{{{{\bf{r}}}}}_{A}| },$$
(1)

where QD and rD (QA and rA) are the charge and position of the donor (acceptor), respectively. The top of the potential barrier along the straight line connecting D and A is given by

$${V}_{\mathrm{b}}=-\frac{{\left(\sqrt{{Q}_{D}+1}+\sqrt{{Q}_{A}}\right)}^{2}}{R},$$
(2)

where R = ∣rA − rD∣ is the donor–acceptor distance. Using first-order perturbation theory within the electrostatic monopole approximation, the energy level of the donor, ED, is determined by the atomic orbital energy, εD, influenced by the electrostatic interaction with atom A:

$${E}_{D}={\varepsilon }_{D}-\frac{{Q}_{A}}{R}.$$
(3)

We perform electron transfer if the electron energy at the donor is higher than the potential barrier, that is, when the condition

$${E}_{D} > {V}_{\mathrm{b}}$$
(4)

is satisfied.

XMDYN model improvements

Prior to this work, an electron-transfer methodology also used in surface hopping39 was employed in XMDYN32,33, ensuring energy conservation after electron transfer between the atomic orbitals with different energies via a small, sudden kinetic energy transfer to the ion cores. In those cases, all the atoms had the same atomic number and the system consisted of neutral or singly charged atoms, such that the electronic configurations of two atoms typically were simply exchanged in the charge transfer, yielding no overall energy change. In the present study, atomic numbers strongly differ and the system is highly ionized; therefore, large energy differences relative to the total energy of the system can emerge between the atomic orbitals involved in an electron transfer. Modifying the ion kinetic energies to enforce strict energy conservation, thus, leads to strong artifacts in the Newton plots (Extended Data Fig. 7A,B). We, therefore, disregarded the atomic orbital energy differences and changes in the potential energies in the current charge-transfer scheme, and did not perform any sudden change in ion kinetic energies. The obtained Newton plots in Fig. 1 and Extended Data Fig. 7C,D are in very good agreement with the experimental results.

A further modification introduced in XMDYN improved the agreement between the calculated charge-state distributions and the experimental data (Fig. 4), particularly the average total charges. Direct transfer of electrons from other atoms into the M and N shells of iodine needed to be excluded (Extended Data Fig. 8). Allowing such electron transfer neglected the Auger lifetimes (1.1 and 13.4 fs) of holes in the M and N shells of iodine, which predominantly absorb X-ray photons at 2 keV photon energy (Extended Data Table 1). Moreover, the transferred electron no longer occupies the outermost (highest quantum number) acceptor atomic orbital with a vacancy. Instead, the electron is put into the orbital with a vacancy at the acceptor atom that is the most similar in energy to the donor-atom orbital originally occupied by the electron. This approach is based on quantum mechanical principles. Extended Data Fig. 8 illustrates this improvement.

Ion momenta in experiment and theory

The calculated ion momenta (Fig. 1) are overestimated by about 60% for I+, 40% for C+, 30% for N+ and 20% for H+ with respect to the experimentally measured values. We consider this to be a consequence of the lack of chemical bonds in the simulation, which give rise to a force naturally working against the Coulomb explosion into atomic fragments. An earlier study found that after X-ray multiphoton ionization, C60 with ~13 positive charges does not undergo instantaneous explosion, but takes time to break up into smaller fragments with still-existing chemical bonds33. In that case, the XMDYN simulation included charge transfer as well as chemical bonds, which strongly reduced the maximum C-atom displacement compared with a simulation without chemical effects. We have recently implemented a generic reactive force field describing bond breaking and bond formation for molecules other than C60 in XMDYN, but although first-test calculations on light-atom systems were successful, the force field cannot yet describe heavy atoms such as iodine. In the present study, the average charge on each of the atoms is considerably higher than in the case of C60, and we do not have evidence for a significant formation of intermediate molecular fragments. Therefore, a large part of the total electrostatic energy is spent on breaking the chemical bonds, diminishing the Coulomb energy being turned into kinetic energy, and thus reducing the momenta of atomic ions. Based on tabulated bond dissociation energies, the sum of all the binding energies in 2-iodopyridine would be 54 eV. The highly ionized states in the present study are, however, expected to have smaller binding energies compared with the neutral ground state. For the coincidence channels involving higher charges, the overestimation of the iodine momentum becomes smaller (about 50% for I4+ + N2+ and 40% for I6+ + N2+ versus 60% for I+ + N+). This indicates that the missing chemical bonds become less important at higher total charges, for which the potential energy surfaces start to resemble a pure Coulomb repulsion without bound potentials. This is in line with another study9 in which a model covering only Coulombic forces and no chemical bonds overestimates the fragment-ion velocities for low charges, but achieves an increasingly adequate description for higher charges. Furthermore, another study40 suggested bound potentials as a reason for the experimental kinetic-energy release of CH3I fragmenting into CH3+ + Iq+ (q ≤ 3) being lower than the one calculated for pure Coulomb potentials.