Inner-shell multiple ionization of polyatomic molecules with an intense x-ray free-electron laser studied by coincident ion momentum imaging

As several previous publications studying both single atoms [3, 5–8] and molecular systems [9–15, 19] have shown, the ionization process at the pulse intensities that can be reached at current XFEL facilities proceeds mostly by sequential inner-shell photoionizations and subsequent Auger decays, while direct ('non-sequential') two-photon absorption was found to be rather small [4, 47]. In methylselenol and ethylselenol molecules, the target systems chosen in this work, the photon energies of 1.7 and 2.0 keV mainly result in photoionization of the selenium L-shell with cross sections of 0.7 and 0.4 Mb, respectively. Since the cross sections for photoionization of the selenium M- and N-shells and of the carbon K-shell and valences are significantly smaller at these photon energies (≤0.01 Mb), this results in an initial photo-absorption almost fully localized at the selenium L-shell. For heavy atoms like Se or Kr a vacancy in the L-shell leads to several relaxation steps in the form of an Auger cascade. Kr, which has an electronic configuration resembling that of Se and a similar photoionization cross section, is therefore chosen in this work for comparison to the Se-containing molecules. The first relaxation most likely happens by intra-atomic LMM Auger (hole lifetime ∼500 as) on the Se site producing mainly 3d (and less likely 3p) vacancies. This is followed by the decay of these vacancies involving the molecular valence electrons (MNN Auger) which occurs on a ∼10 fs time-scale [48, 49]. The latter step causes a considerable portion of the total charge to be distributed over all molecular constituents [19] even though the initial inner-shell photo-absorption and the first Auger decay are very likely fully localized on the selenium atom.

As a result of the (multiple) inner-shell ionization at the Se L-edge and the subsequent Auger decays, the molecules become highly charged and consequently break up into multiple ionic fragments. For the simpler case of methylselenol molecules, this reaction schematically proceeds in the following way:

$$\begin{eqnarray*} &&{$\fl {\rm CH}_3 {\rm SeH} + n\hbar \omega \mathop \to \limits^{{\rm photoionization},{\rm Auger}} [{\rm CH}_3 {\rm SeH}]^{a + } \mathop \to \limits^{{\rm dissociation}} {\rm Se}^{b + } + {\rm C}^{c + } + 4{\rm H}^{d + }$} , \end{eqnarray*}$$

where the variables a, b, c, d are integer numbers fulfilling a = b + c + 4d. Note that b, c and d may include zero, meaning that also neutral fragments can be produced.

As shown previously for the cases of methylselenol [19] and nitrogen [13], the reaction does not proceed strictly sequentially and is governed by an intricate interplay between the time scales of the multiple photoionization events and Auger decay cascades and significant nuclear motion that already occurs on the same time scale. The following results and discussion are meant to provide further insight into the details of these complex reactions.

Figure 2(a) shows the ion time-of-flight spectra resulting from the ionization and fragmentation of methylselenol and ethylselenol molecules by LCLS pulses with a nominal pulse duration of 5 fs, a nominal pulse energy of 0.4 mJ, and a photon energy of 2.0 keV (methylselenol, red dashed line) and 1.7 keV (ethylselenol, blue solid line). Note that the actual pulse energy on target is lower since the beamline transmission on the order of 35% [6] is not included in the number given above.

Zoom In Zoom Out Reset image size

The two spectra are normalized on the Se¹⁺ peak such that differences in the other peak heights represent relative differences with respect to Se¹⁺. Here it should be noted that the shoulders appearing on the left side of Se¹⁺ and on the right side of Se²⁺ peaks result from the residual gas ionization (most likely contaminations by larger hydrocarbons) and not from the target molecules. This was verified considering the position offset characteristic to all fragments originating from the supersonic gas jet. Comparing the spectra for the two different molecules, a significantly higher abundance of Se²⁺, Se³⁺, Se⁴⁺ and C²⁺ relative to Se¹⁺ can be observed for methylselenol compared to ethylselenol, while the relative yield of C¹⁺ is slightly higher in ethylselenol. Apart from the fact that the ethylselenol data were taken at a lower photon energy for purely technical reasons, which increases the total ionization probability since the Se L-shell photoionization cross section at 1.7 keV is higher than at 2.0 keV, the only difference between the two molecules is the addition of one carbon atom and two hydrogen atoms in the case of ethylselenol as compared to methylselenol (see the inset of figure 1). From the inspection of the ion time-of-flight spectra, we can therefore conclude that fewer multiply charged fragments are produced from ethylselenol since the total charge in the molecule can be distributed over a larger number of constituents.

The photoion–photoion coincidence (PIPICO) spectrum of methylselenol fragmentation is displayed in figure 2(b). The diagonal lines observed in the PIPICO spectrum reflect the momentum conservation between the carbon and selenium ions of different charge states. Since the momenta of the protons/hydrogen atoms are considerably smaller, they only result in a broadening of the lines (compared, e.g., to the case of diatomic molecule fragmentation [46]). For strong channels, contributions due to a few (up to five) main isotopes of selenium can be clearly identified in the spectrum as distinct parallel lines.

From this coincidence spectrum and the corresponding triple coincidence (PIPIPICO) spectrum for ethylselenol (not shown here), it is possible to determine the relative yields of the different selenium–carbon coincidence pairs or selenium–carbon–carbon coincidence triplets, respectively, which are presented in figures 3(a) and (b) and the total charge state distributions shown in figures 3(c) and (d). In the latter two, the sum of Se and C charges measured in coincidence is denoted as 'heavy ion charge', while the total charge of the molecule assuming that four or six H⁺ ions were produced is denoted as CH₃SeH and C₂H₅SeH charge, respectively. While this assumption is well justified for the fragmentation of the most highly charged molecules [50], deviations are expected for the channels with lower heavy ion charge, especially for the ethylselenol molecule.

Zoom In Zoom Out Reset image size

Nevertheless, clear trends can still be derived from the comparison of the molecular charge state distributions to the charge state distribution of isolated krypton atoms at 2.0 keV, which is also shown in figures 3(b) and (d). Kr has a similar electronic configuration and absorption cross section (0.5 Mb at 2.0 keV) to Se, and therefore serves as a model to estimate ionization without the molecular environment. As noted earlier [19], the maximum total charge induced on the methylselenol molecule and the overall charge state distribution for this molecule is very similar to the atomic case while the individual charge of the Se atom is much lower than for Kr, which is a clear indication of charge redistribution in the molecular environment.

In contrast to this, figure 3(d) for ethylselenol shows a significantly higher total charge than both methylselenol and krypton, even though the relative yields of the individual higher charged ions (Se²⁺, Se³⁺, Se⁴⁺) compared to Se¹⁺ is reduced, as seen in the non-coincident ion time-of-flight spectrum discussed above. For ethylselenol, the 'heavy ion charge' distribution already shows a similar shape to the Kr charge state distribution, while the total charge of the molecule clearly exceeds the case of the isolated atom as well as that of methylselenol, even if one takes into account that, most likely, not all six hydrogen atoms are emitted as protons. Some of this effect can be attributed to the higher photoionization cross section for (neutral) selenium at 1.7 keV photon energy as opposed to methylselenol and Kr at 2.0 keV, but we suspect that an additional contribution comes from the fact that there are considerably more (valence) electrons in ethylselenol, which leads to more efficient Auger cascades that can reach more highly charged final states. Unfortunately, these two possible causes cannot be disentangled in the present study and their resolution will require further experimental and/or theoretical investigations.

In addition to measuring ion time-of-flight and PIPI(PI)CO spectra, our 3D-momentum resolving spectrometer allows for precise determination of the fragment ion kinetic energies for all combinations of coincident fragments, as already shown in a previous publication [19]. In figures 4 and 5, we present a selection of kinetic energy distributions (KED) of singly and doubly charged carbon ions resulting from methylselenol (figures 4(a) and (b), and figure 5(a)) and ethylselenol (figures 4(c) and (d), and figure 5(b)) fragmentation for different final charge states (defined from the coincident measurements). In order to understand how these results relate to the geometry of an unperturbed molecule, we performed a simple simulation of molecular Coulomb explosion.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To simplify the simulation, we do not include the photoionization step nor any subsequent relaxations or other electronic effects. Instead, we assume all ionization processes to happen instantaneously and start the simulation with a set of ions with charges corresponding to the final (measured) charge states, and place them at the positions of the atoms in the equilibrium geometry of the neutral molecule.

The forces on the individual ions are determined by purely Coulombic interaction, and time propagation is given by a set of differential equations which are solved by a fifth-order Runge–Kutta method using Dormand–Prince parameters [51]. All particles are treated purely classically, and an adaptive time-step size ensures small numerical errors of positions and particle velocities while propagated towards their asymptotic values at the particle detector.

The simulation is thus designed to be fast and simple and to provide a rough idea of the ion kinetic energies (and ion emission directions) that are to be expected from an ultra-fast charge-up by intense FEL light-pulses followed by ultra-fast Auger decay. In particular, it does not include any geometric changes of the molecule during the multiple ionization process. Any deviations from the modelled kinetic energies and/or ion emission directions can therefore be interpreted as evidence for nuclear motion during the multiple ionization process.

Additional details of the model can be found in [52]. The results of the simulation are shown as vertical lines in figures 4 and 5.

In general, the KEDs for both molecules show a similar overall trend as discussed in [19] for methylselenol. As can be seen from figures 4(a) and (c) for the lowest charge states, the maximum of the KED fits well to the prediction of the Coulomb explosion model, indicating that there is no significant motion during the time needed to reach these final states. Since they are most likely produced by a single-photon absorption followed by one or two ultra-fast (sub-fs) Auger decay steps, this behaviour can be readily understood. However, considering higher charge states for both molecules, one can clearly see that the simulation starts to increasingly overestimate the measured kinetic energies, indicating that the final charges are reached at internuclear distances considerably larger than the equilibrium one. As we have shown for the case of methylselenol [19] considering intensity-dependent yields of different charge state combinations, the channels where more than two or three electrons are removed from Se and C fragments are typically produced by two- or multi-photon absorption. Thus, the deviations of the measured ion kinetic energies from the Coulomb explosion model for these higher charge states reflect the nuclear motion within the time defined by the delays in the sequential photo-absorption steps (inverse of photo-absorption rate) and Auger decay processes involving the valence electrons. Since the x-ray pulses used here are of the order of ∼5 fs long, these time scales are comparable for the charge states with a few electrons removed, whereas the Auger time scale starts to dominate for the higher charge states reaching tens of femtoseconds or more ([48], see also [7, 49] for Kr).

Although this behaviour is observed for both, methyl- and ethylselenol, the deviation from the Coulomb explosion model is more apparent for the smaller molecule, where the simulated kinetic energies for the highest charge state combinations even start to run out of the high energy flank of the KED (see figure 4(b)). In ethylselenol, this is less pronounced because of the contribution from the third heavy particle into the total momentum balance which causes the Coulomb explosion energy for a given total charge of the system to be distributed along two reaction coordinates instead of one (Se–C) for the case of methylselenol. The contribution of the third heavy fragment also explains the overall broader KEDs for ethylselenol fragments. As was shown in [19], the protons typically leave the system in the early ionization stage and do not influence the energies of heavier particles significantly.

In [19] we have also shown that for channels where the carbon fragment in the final state is charged higher than the selenium, very broad KEDs and extremely high fragment energies can be observed, which considerably exceed the predictions of the Coulomb explosion model for methylselenol. This is illustrated in figure 5(a), where the KEDs for Se²⁺ + C¹⁺ and Se¹⁺ + C²⁺ channels are compared. Although the simulation predicts similar explosion energies for both final states (note that according to the simulation, this is true independently of the proton charge), the measured distribution for the Se¹⁺ + C²⁺ channel extends to much higher energies. In fact, most of the events have energies well beyond the Coulomb explosion limit. We attribute this behaviour to the creation of a transient highly charged Se–C complex and subsequent charge transfer to the hydrogen atoms. Although this hypothesis cannot be strictly proven by the present experimental data, it provides the most plausible explanation for the anomalously high fragment energies observed. Recent experiments on heavy diatomic molecules which do not contain hydrogen atoms further confirm this explanation [53].

Under the above assumption, the charge transfer to the hydrogen atoms needs to occur after the (initially highly charged) heavy fragments have acquired their final kinetic energies. On the other hand, the measured energies of the protons detected in coincidence with the 'anomalous' channels where q_C > q_Se are considerably lower than the simulated Coulomb explosion values [19, 51] suggesting that they have moved significantly before the final charge state of the system has been reached. Therefore, one of the central questions that remains open concerns the time and length scales of the observed charge redistribution, i.e. how much the hydrogen fragments moved by the time when the charge transfer occurs.

As can be seen from figure 5(b), a similar effect is observed for the ethylselenol molecule. Here, the C²⁺ fragment energy for the Se¹⁺ + C²⁺ + C²⁺ final state considerably exceeds the one for the Se²⁺ + C²⁺ + C¹⁺ final state, even though the total charge of the system is the same and the Coulomb explosion model yields almost identical values. As a matter of fact, the KED for the Se¹⁺ + C²⁺ + C²⁺ channel is very similar to the one of the Se³⁺ + C²⁺ + C²⁺ state which has a considerably higher total charge. This again corroborates our hypothesis of a transient highly charged Se–C complex and subsequent charge transfer to the hydrogen atoms.

Such a delayed charge transfer from the Se–C complex to the hydrogen atoms is expected to occur, with certain probability, for essentially all channels and is most likely responsible for the rather large widths of the KED spectra, in particular, for the high-energy tails of the KEDs. However, the final state channels where the weakly absorbing carbon atoms are charged higher than the strongly absorbing selenium have, statistically, undergone the most charge redistribution within the molecule and the signature of the delayed charge transfer to the hydrogen atoms is thus most pronounced here.

By measuring the 3D momentum vectors of multiple fragments in coincidence, we are also able to investigate vector correlations, i.e. correlations between the emission directions of the various fragments relative to each other. This yields information about the fragmentation mechanisms and fragmentation time scales (see e.g. [54–57]). It also provides data that could allow one to determine the orientation of certain molecular axes in space [31–37]. Here, we explore to what extent this technique, when applied to multiple inner-shell photoionization by intense XFEL pulses, is able to provide information on the molecular orientation on a shot-to-shot basis.

3.4.1. Methylselenol

Figure 6(a) shows the angular correlation between carbon and selenium ion momentum vectors, i.e. the measured distribution of angles between C and Se ions detected in coincidence. For all combinations of C and Se ion charge states, the distributions are peaked around cos(α_Se,C) = −1 corresponding to an angle α_Se,C of 180° between the momentum vectors of the C and Se ions. In other words, the two heavy ions are almost always emitted 'back-to-back', similar to the fragmentation of a diatomic molecule. This back-to-back emission is more pronounced the higher the C and Se ions are charged, while the distribution is rather broad for coincidences of Se¹⁺ with C¹⁺. Qualitatively, this behaviour can be easily rationalized since the contribution of the relatively light protons to the total momentum is rather small.

Zoom In Zoom Out Reset image size

Given the rather strict back-to-back emission of all but the lowest charge combinations of heavy fragments, the emission direction of these fragments is a good marker for the orientation of the Se–C axis at the time of fragmentation (since the pulse duration as well as the Auger lifetimes are short compared to the rotational period). In figure 6(b), the emission angle of the protons is thus plotted relative to the momentum vectors of the carbon ions stemming from Se²⁺–C²⁺ and Se⁵⁺–C²⁺ coincidences. The resulting distribution shows two clear maxima at cos(α_C,H) = −0.4 and cos(α_C,H) = + 0.4 (corresponding to angles of 114° and 66°) that can be attributed to the hydrogen atoms bound to the selenium and carbon (left and right peak), respectively. The integrals of the two peaks also show a 3:1 ratio corresponding to the numbers of hydrogen atoms bound to these species. This also supports the assumption made earlier that all hydrogen atoms are emitted as protons during the fragmentation. The width of the peaks reflects the width of the Se–C angle distribution plus any additional angular motion of the proton during the multiple ionization.

Compared to the bond angles of the hydrogen atoms in methylselenol in the equilibrium geometry given in the literature [58], which are 70.0° for the hydrogen atoms next to carbon and 95.5° for the hydrogen atom next to selenium, the measured angles for the carbon-site protons are in good agreement with the equilibrium geometry, whereas the measured angles for the protons from the selenium-site are larger than expected. This is due to the nature of the Coulomb explosion, where each charged particle interacts with all its charged neighbours. Because of the geometry of the molecule, with a close to 90° bond angle of the C–Se–H site and bond lengths d(H–Se) = 1.53 Å and d(C–Se) = 1.97 Å, the distance between the Se proton and the carbon is only 2.49 Å. This leads to a significant repulsion between the 'selenium' proton and the carbon charge, thus producing a larger angle between the emission direction of this 'selenium' proton and the carbon. A similar effect is also discussed in a study of UV-photo dissociation of H₂S [59].

By selecting those protons whose momentum vectors have angles relative to the Se–C axis with negative or positive cosine value, we distinguish protons neighbouring the selenium or carbon site, respectively. The KED of these site-selected protons for two sets of Se–C charge states, Se²⁺ C²⁺, and Se⁵⁺ C²⁺, are plotted in figures 6(c) and (d). Surprisingly, no difference is observed in the high-energy part of the spectra, indicating that protons are emitted long before the final state charge is reached. In the low-energy part of the spectra, considerable enhancement of the low-energy feature (between 10 and 20 eV in figure 6(c) and centred at 20 eV in figure 6(d)) is found for protons emitted at the Se site. According to the simulation, this would correspond to a proton emitted from a singly or doubly charged Se and a neutral C atom, respectively [52]. This distinct feature, which can be observed for essentially all final charge state combinations, suggests that the low-energy part of the proton KED reflects the initial step in the sequential build-up of the total charge of the molecule, whereas the high-energy tail is due to the channels where the whole molecule is charged fast before significant nuclei displacement occurs.

3.4.2. Ethylselenol

Investigating the fragmentation of the larger ethylselenol molecule, we now have to consider a breakup into three heavy fragments, one selenium and two carbon ions. For such a nonlinear polyatomic molecule, the angular correlations of the fragment momentum vectors no longer reflect the molecular geometry directly but rather the sum of the Coulomb forces produced by all charges situated on the individual ions. In principle, these can be compared to predictions from a Coulomb explosion model, although the angular correlations, even more so than the fragment ion KEDs, are very sensitive to changes of the molecular geometry that occur during the multiple ionization process.

Maps of the angular correlations between the selenium and the two carbon ions for four representative channels (Se¹⁺ + C¹⁺ + C¹⁺, Se²⁺ + C¹⁺ + C¹⁺, Se¹⁺ + C²⁺ + C¹⁺ and Se⁵⁺ + C²⁺ + C¹⁺), which are obtained by measuring in coincidence the 3D momentum vectors of the three heavy ions that are created from an ethylselenol molecule, and are shown in figure 7 together with the respective simulated angles.

Zoom In Zoom Out Reset image size

The simulated angular correlations for a given final charge state from our Coulomb explosion model gives two values for each channel (indicted by dots in figure 7). These two values correspond to two scenarios of molecular dissociation that cannot be distinguished by our experimental method. For channels with symmetric carbon charges, e.g. Se²⁺ + C¹⁺ + C¹⁺, the dots correspond to the angles of the Se momentum vector with either of the two carbon ions. For asymmetric channels, e.g. Se⁵⁺ + C²⁺ + C¹⁺, where the two carbons have different charge, they correspond to the angle between the Se and C¹⁺ ion for the two cases where the C¹⁺ starts from the position closer to the Se or from the position further away, respectively.

Overall, a significant change of the predicted angular correlations occurs for the different channels, while the change in experimental data is much less dramatic. The experimental correlation maps display broad features whose maxima only shift slightly as a function of the final charge distribution.

A possible explanation for this observation could be that the fragmentation process starts already at an early stage in the ionization sequence and although ionization continues towards the detected final charge state, the angular distribution of ions is governed mainly by the initial phase of the dissociation that occurs at relatively low total charge states. This hypothesis is consistent with our observation described in section 3.3 that the ion kinetic energies for high final charge states are also significantly lower than expected.

Qualitatively, we note that the angular distributions for the Se²⁺ + C¹⁺ + C¹⁺ and Se⁵⁺ + C²⁺ + C¹⁺ channels show somewhat sharper peaks than the Se¹⁺ + C¹⁺ + C¹⁺ and Se¹⁺ + C²⁺ + C¹⁺ channels, where the combined charge of the two carbon ions is higher than the selenium ion charge. As noted in section 3.3, these latter channels also show broad KEDs with energies far above the Coulomb limit that we attribute to delayed charge redistribution during the fragmentation process.

A more quantitative interpretation of the observed angular correlations will not be attempted here as we conclude that our simplified simulations that do not include motion of the nuclei during the multiple ionization process are not suited to adequately describe the angular correlations of complex fragmentation channels, especially considering the ultra-fast charge exchange processes that may be involved.

Considering the small difference between the simulated angles for the two cases of carbon charge distribution, for example in the Se⁵⁺ C²⁺ C¹⁺ channel, and the given broad experimental distributions, an unambiguous assignment of the original positions of the two carbon ions is very challenging and, with the statistics of the present measurements, not feasible. Angular-resolved analysis of ion yields as well as studies of bending motion in the molecule upon multiple ionization is, thus, not further pursued in this work.