Ultrafast dynamics of adenine following XUV ionization

An overview of the mass spectra obtained when adenine (135 u, 8.20 eV ionization energy [63]) is photoionized by an XUV attosecond pulse, and probed by a NIR pulse is shown in figure 1. The ionic fragment with the lowest appearance energy is 108 u (11.3 to 12.3 eV [54, 63, 64]), via the loss of neutral 27 u as depicted in figure 2(a) [61–63, 65]. Adenine furthermore exhibits sequential ejection of neutral 27 u CHN-groups, indicated by solid arrows in figure 1. This gives rise to the fragments C_n H_n N$_n^{+}$ (n = 5 is the parent cation) with appearance energies increasing gradually to 14 ± 0.6 eV [54] for n = 1 (a charged 27 u CHN$^{+}$ fragment). CHN should be seen as a sum formula, referring to either of the HCN or HNC isomers, which are usually not distinguished. As exemplified in figures 2(a) and (b), some hydrogen migration is necessary for 81 u and 27 u ions, while (d) shows a shortcut to 54 u by ejecting C₂H₂N₂ in one step.

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Dashed arrows in figure 1 indicate a sequence where also the neutral—NH₂ group is lost, explained in figure 2(e). This sequence ends with the 38 u C₂N⁺ fragment whose relative yield varies considerably in the literature [6, 54, 64–66], most likely related to its higher appearance energy of 20–23 eV [54]. Simulations of 70 eV electron-impact-ionization [61] failed to reproduce both 38 u and 27 u ions, while they were stronger than the 39 u in an experiment using 14 keV projectiles [66]. While 38 u was seen for 3 keV Cl⁺ projectiles, it was not for 6 keV F²⁺ [67] (and 27 u is not seen in any of their mass spectra next to the strong 28 u). In figures 2(b) and (e), the 27 and 38 u ions are assigned as the end products of long dissociation sequences, where small perturbations along the way might lead to other outcomes instead. In summary, the production of C₂N⁺ can be significant under the right conditions (see e.g. [54, figure 7]) but difficult to reproduce in simulations, making it interesting to try to better understand the relevant kinetics by examining the ionization of adenine also with higher photon energies (above 22 eV [63]).

As is evident from figure 1, XUV-photoionization leads to a high level of fragmentation (81% of the total yield) regardless of when (and if) probed by the NIR-pulse, indicating the moderate photostability of adenine in the 17–35 eV energy range [54]. The dashed blue curve with the NIR pulse before the XUV has the same fragment distribution as the XUV gives on its own [6, supplementary information] but when the NIR pulse is sent after the XUV (solid red curve) it deposits further energy to the molecules ionized or highly excited by the XUV and helps to fragment them into smaller pieces. This is seen more clearly in the difference mass spectrum, as strong enhancements of many small ionic fragments and reduced yields of the larger fragments. The net change is positive, indicating that the NIR not only dissociates but also photoionizes. On its own, the NIR-pulse can produce parent cations through multi-photon ionization, but essentially without fragmentation (1% of the total yield was 108 u).

To extract physical information from a pump–probe experiment, we will use a curve model based on a differential equation system where the probed state is being populated via transitions with a total rate of $1/\tau_1$ and simultaneously decaying with a total rate of $1/\tau_2$ to non-observable states. Under the assumption that $0 \leqslant \tau_1 \lt \tau_2$, the solution has two exponential terms and can be analytically convoluted with a Gaussian to represent the finite pulse durations [6, supplementary information]. In the limiting case of $\tau_1 \approx 0$, the model simplifies to a step function that decays with lifetime τ₂, and represents probing from a state immediately populated by the short XUV-pulse. In the opposite case of probing a slowly populated final-state, which does not decay within the scan range ($\tau_2 \rightarrow \infty$), the model can instead reduce to $(1-\textrm{e}^{-t/\tau_1}) h$. The step height h may be either positive or negative. Further details can be found in appendix A.

In addition to the enhanced dissociation described in the previous section, we find that a delayed NIR-pulse also leads to the production of adenine²⁺, the parent dication where no bond is broken but an extra electron is removed. Energetically, this outcome should be allowed already by the 17–35 eV XUV-pulse on its own, since, a dication appearance energy of $23.5 \pm 1.0$ eV is known from electron impact ionization [54]. However, we are not aware of any reports of adenine dications produced by photons, prior to our own [6].

The difference-spectrum in figure 1 shows that the dication with a mass/charge ratio of $135~\mathrm{u}/2 \mathrm{e} = 67.5$ u/e has the fourth strongest dependence on NIR-delay, and is much stronger than any other ion between 65 and 70 u/e. The existence of a 67 u ion from the XUV-photon alone, however, makes it difficult to determine the exact baseline level of adenine dications. An estimate, after adjusting for the partly overlapping peak shapes, is that the NIR-enhancement step height parameter, h, is $182 \pm 99$% of the baseline, which is more than twice as large as the relative enhancement for any fragment ion.

Even more interesting is that the dication enhancement starts, as seen in figure 3, with a small but certain delay compared to the changes in most of the cationic fragment yields, when fitting the pump–probe scans data as described in the Methods section. The zeroing of the delay-axis was described in the supplement of our previous publication [6]—briefly it is given by the simultaneous increase of many cationic fragments as well as atomic krypton (the Kr²⁺ yield). The onset-time for the dication is $\tau_1 = 2.32 \pm 0.45$ fs in the previously reported experiment (one fit to the average of seven successive delay-scans) [6]. Here we present the results obtained by including additional data from three other experiments performed on different days under similar conditions. With this procedure, we can now extract a new onset time of $\tau_1 = 2.42 \pm 0.80$ fs (median and sample standard deviation of fits to four experiments). τ₁ does not appear to depend on the NIR-intensity, although the enhancement most likely requires the absorption of two NIR photons (based on NIR-intensity scaling and the fitted Gaussian pulse widths) [6].

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To investigate what mechanism can be responsible for the 2.4 fs delay between XUV-photoionization and the NIR-enhanced production of dications, we explored nuclear as well as electronic dynamics in different theoretical frameworks (see appendix B). First of all, we verified that even if an electron is only removed from any of the four highest occupied orbitals (lowest-energy holes), the instability of the adenine cation manifests itself as a substantial bond-elongation. The result with a hole in HOMO−3, as an example, is shown in figure 4, and several bonds oscillate and tend to elongate on a timescale of 15–85 fs (potentially proceeding toward dissociation). These calculations were made using time-dependent density functional theory (TDDFT) and Ehrenfest dynamics. We stress, however, that in the very beginning, it takes almost 4 fs before any bond has changed by 1%, so pure nuclear dynamics is not likely to be important for the observed phenomenon.

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Considering instead the electronic dynamics, we identified that a multi-electronic process can fill the initial XUV-created inner-valence hole, while exciting at least one other electron to a normally unoccupied bound state. We refer to this as a shake-up state (although not requiring a shift in the kinetic energy of the primary photoelectron), but one can also refer to it as a frustrated Auger–Meitner-state (although no secondary electron has been emitted yet) [68, 69]. The cross-section for further photoionization by the NIR-pulse would then vary depending on the shake-up state, favoring those with one highly excited electron whose ejection is allowed in a single-active-electron picture.

We examined this proposed mechanism using two complementary theoretical frameworks while keeping the nuclei fixed. A rate-based approach, consistent with the experimental curve model, used Fermi's golden rule and first-order perturbation theory to obtain exponential time-constants for each final-state of the highly excited electron. More sophisticated many-body time-dependent simulations were made using a method [6, 70, 71] based on the non-equilibrium Green's function that can handle both the shake-up electron dynamics triggered by the XUV photoionization and the subsequent absorption of a delayed NIR pulse. Both these methods singled out LUMO+6 as a unique shake-up state due to rising relatively slowly but surely, while being in the energy range favored by two-photon NIR-photoionization. The rate-equation approach gives a time-constant of about 3 fs for shake-up to LUMO+6 [6, figure 2]. The many-body-simulated XUV + NIR signal in figure 3 shows that the LUMO+6 contribution remains at zero when the pulses fully overlap (in contrast to an instantaneous transition which would have reached half of its peak-value) and then starts to grow nearly linearly with delay. After 4 fs it surpasses other states whose contributions stayed at a plateau reached within the first femtosecond [6, figure S18]. Even without discussing individual states of a particular basis set, the Green's function method allows visualization of the overall net change in electron density caused by intrinsic electronic relaxation: figure 5(b) shows snapshots with the change in electron density as function of time, with respect to just after XUV-ionization, visualized as red (increased) or blue (decreased). The electron density more than 3 Å from the plane of the molecule is integrated and shown as a curve in figure 5(c). It clearly grows with time. We label the vertical axis simply as 'inflation' to summarize that what this observable represents is a charge migration from the plane of the molecule to more than 3 Å outside. Although multiple states contribute, the importance of LUMO+6 is hinted by the fact that its orbital in panel (d) has large π-like lobes on either side of the molecular plane, like the net charge migration and intuitively a large electric-dipole transition matrix element for photoionization by the NIR-pulse.

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To summarize, we deduced that a specific electronic rearrangement in inner-valence-ionized adenine opens up the possibility for the NIR-pulse to create stable dications of the intact molecule. Compared with any rapidly dissociating dications [72] that might be created by the XUV-pulse directly, the route involving shake-up and NIR-photoionization must be creating dications with less excitation energy, perhaps helped by ejecting the second photoelectron. While the NIR-pulse can immediately contribute to further dissociation of adenine cations, the stabilization-enabling process takes a relatively long time (τ₁ of a few femtoseconds) compared with other inner-valence electronic transitions, which makes this channel stand out in the experiment. The NIR-pulse then has to be sent before other processes, like the motion of the nuclei, close the window of opportunity—the dication signal decays with $\tau_2 = 22 \pm 4$ fs. However, if this sequence is completed, the resulting dication remains stable for at least the 3 µs it takes to traverse the mass spectrometer.

This combined theoretical and experimental work constitutes, to our knowledge, the first demonstration of correlation-driven charge migration. Conceptually, it is also more of a one-way charge migration than the back-and-forth oscillation so far observed in isolated amino acids [7, 39–41] and smaller systems [8, 9]. The mere ability to resolve a transition time of a few femtoseconds as non-instantaneous is testament to the usefulness of isolated attosecond pulses to investigate even molecules with as many as 15 atoms.

While some fragment ion signals were already used as a time reference for accurate measurement of the intact dication's delay in [6], we here report a careful analysis of the time-constants extracted from the dissociative photoreactions, including data from many more ions. The delay-dependent yields of several fragments are shown in figure 6 and it is clear that they vary in different ways as a function of the XUV–NIR delay.

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Starting with the τ₁-parameter that tells whether the probe's effect starts like a step function or gradually via a transition (defined on page 6), table 1 shows a clearly nonzero τ₁ for the 70 u cation C₂H₄N$_3^{+}$, in addition to the previously described 2.4 fs electronic dynamics leading to the dication. The 70 u ion yield is hardly influenced by the NIR-probe at zero delay in figure 6 but is then gradually depleted, with the time constant $\tau_1 = 9.1 \pm 5.1$ fs. The uncertainty mainly represents the possibility of a continued slope outside the scan range and an even longer τ₁ (the four experiments summarized in table 1 gave τ₁ from 8.7 to 19.2 fs), while a shorter τ₁ would fail to fit the data. The 70 u fragment is one of the few that require a concerted two-hydrogen migration [63], which turns the 108 u precursor ion into its lowest-energy isomer [62] and enables the dissociation path shown in figure 2(c). We can therefore speculate that the XUV-ionized molecule evolves in a way that eventually allows the NIR-absorption to suppress fragmentation into 70 u by preventing the initial hydrogen migration.

Table 1. Summary of delay-dependence fitted for selected ions. The step height parameter expresses the enhancement (+) or suppression (−) with respect to the baseline signal at negative NIR-delay (approximately the XUV-only signal, but for 108 u and the parent cation the baseline also has a NIR-only contribution), before convolution with a Gaussian and not limited by the scan range. The table shows median values of fits to four experiments from different days with similar but not identical conditions, each containing 5, 6, 7 or 10 delay-scans. Uncertainties indicate the sample standard deviation between the four experiments and table cells with values smaller than their uncertainty are italicized. No time constants are shown for ions without clear delay-dependence (uncertain sign of the step height). For very long decay times, $\infty$ is shown rather than arbitrary values ($\geqslant$443 fs) influenced by the chosen fitting bounds.

Mass (u)	Sum formula	τ1 (fs)	τ2 (fs)	Step height (arb. u.)	Relative step height (%)
27	CHN+	$0.5 \pm 0.2$	$51 \pm 10$	$+1.8 \pm 0.8$	$+64 \pm 16$
38	C2N+	0.6 ± 0.7	$56 \pm 32$	$+1.4 \pm 0.6$	$+48 \pm 28$
43	CH3N$_2^{+}$	0.9 ± 19	$\mathit{\infty}$	$+0.7 \pm 0.2$	$+5 \pm 3$
53	C2HN$_2^{+}$	0.7 ± 0.8	$63 \pm 27$	$+5.2 \pm 1.5$	$+30 \pm 9$
54	C2H2N$_2^{+}$	—	—	−1.7 ± 2.4	−6 ± 9
65	C3HN$_2^{+}$	0.4 ± 0.7	$42 \pm 27$	$+0.8 \pm 0.2$	$+17 \pm 9$
66	C3H2N$_2^{+}$	$28 \pm 17$	$\mathit{\infty}$	$+0.3 \pm 0.2$	$+3 \pm 2$
70	C2H4N$_3^{+}$	$9.1 \pm 5.1$	117 ± 326	$-0.5 \pm 0.4$	$-10 \pm 6$
81	C3H3N$_3^{+}$	3.0 ± 7.4	$\mathit{\infty}$	$-0.7 \pm 0.4$	$-9 \pm 3$
92	C4H2N$_3^{+}$	$5.0 \pm 3.3$	$7.0 \pm 1.5$	$-0.5 \pm 0.2$	$-16 \pm 8$
108	C4H4N$_4^{+}$	0.4 ± 4.0	$47 \pm 21$	$-2.6 \pm 1.2$	$-13 \pm 4$
135	C5H5N$_5^{2+}$	$2.4 \pm 0.8$	$22 \pm 4$	$+2.2 \pm 1.2$	(${\approx}{+}182 \pm 99$)
135	C5H5N$_5^{+}$	—	—	−2.4 ± 3.4	−3 ± 4

The lifetime τ₂ tells how quickly the effect of the NIR-probe decays or recovers, and values between 40 and 70 fs are found for many of the fragment ions in table 1. Shorter lifetimes are found for the dication ($22 \pm 4$ fs) and for the weak dip in the 92 u yield ($7.0 \pm 1.5$ fs).

The fragment ions most strongly affected by the NIR-probe are 53 u, 108 u, 27 u and 38 u (all shown in [6]). We will here focus on 27 and 38 u, which have the largest relative step heights: 64% and 48% of their negative-delay (or XUV-only) baselines, and whose relative yield has varied between types of experiments in the literature (see section 3.1). In the following section we will also examine possible oscillations in their fragment yields.

Neutral 27 u HCN or HNC fragments appear in many dissociation paths of adenine (e.g. 40% of those in [64]), with several examples shown in figure 2 based on assignments for ionization by a single photon or projectile. It is, however, not clear which dissociation path is the most likely to yield charged 27 u fragments for one-photon ionization and whether the delayed NIR probe enhances the same or another path. Since the 38 u ion has been investigated less in the previous literature, we drew ellipses in figure 2 to mark where C₂N could be produced in other ways than via the known—NH₂-loss sequence in figure 2(e) [63]. We then included the suggested precursors or competing products in table 1 to look for similarities in delay-dependence. Seeing that the 54 u yield is not influenced by the probe-pulse allows us to exclude figures 2(b) and (d), and that the time constants for 70 u and 43 u are very different from those for 38 u speaks against figure 2(c). We thus conclude that 65 u is the most plausible precursor for 38 u, and it is remarkable that the complementary part of 65 u would be 27 u, i.e. 65 u could be a precursor for both of the fragments with the largest relative NIR-enhancement. Different isomers of 65 u appear in the (c) and (e) dissociation paths, in both cases with the breakage of a CN-bond as a final step.

To examine whether there is any oscillation in the ion yields on top of the time dependence fitted in the previous section, a single-frequency oscillation was fitted to the residual data points, using only the part of the scan at positive NIR delay to select oscillations excited by the XUV-ionization. Such oscillations are found for the 27 u HCN⁺/HNC⁺ and 38 u C₂N⁺ fragment yields, as shown by dashed lines in figure 7(a). The median and standard deviations for the periods in four experiments under similar conditions are $15.0 \pm 3.2$ fs and $17.2 \pm 3.8$ fs, respectively. Oscillation periods for the other ions were not consistent between experiments, with standard deviations of 6–7 fs for two of them and exceeding 11 fs for eight of them. The 27 u and 38 u oscillations have similar periods and are initiated with approximately the same phase, having the first cosine peak at NIR-delays of $5 \pm 4$ and $6 \pm 4$ fs. This suggests that the modulating NIR-transition occurs as a common precursor rather than as a delay-dependent competition between the two fragmentation outcomes.

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To investigate whether the oscillation frequency or amplitude vary during the scan, figure 7(b) shows spectrograms computed using a sliding Welch [73] window function. Its spectral properties lie between those of the Hann and the rectangular windows [74]. We find that the oscillations are stronger when the window is centered near the end of the scan (e.g., +25 fs) than when close to the start of the scan (e.g. −15 fs), which confirms that the oscillations occur in the XUV-ionized sample and are probed by the NIR-pulse (not excited by the NIR-pulse). The strongest signal/noise ratio is found at NIR-delays of 5–10 fs, near the peaks of the non-oscillating model curves in figure 7(a).

In the frequency range of the observed oscillation, neither coherent beating between electronic states nor coherently excited vibrational wavepackets can be excluded a priori. The onset of nuclear motion could change the spacing between electronic states and lead to decoherence [75, 76] but the oscillation amplitude remains roughly constant for at least as long as the τ₂ lifetime of the non-oscillating step. While a time-dependent localization of charge on the 27 u-side in the dissociation figure 2(a) could probably modulate the 27 u ion yield, there does not appear to be any such immediate path toward charged 38 u fragments. Considering these arguments and the difficulty of simulating coherent electronic dynamics while letting the nuclei move, we will in the following focus on a vibrational assignment.

The observed oscillation frequency is consistent with the general band for CN-stretching vibrations, possibly in the 65 u precursor and certainly in the neutral 27 u and 38 u fragments (16 fs for HN–C [77] and HC–N [78], 17 fs for C–C–N asymmetric stretch [79, 80]). Although NIR-photoionization of electronically excited fragments can have a cross-section dependent on their bond lengths, such an assignment is difficult to reconcile with the immediate onset of the oscillations. In particular, the 38 u fragment shown in figure 2 cannot be formed without substantial nuclear motion [61, 63], which must be expected to take time.

To get an idea of which bonds start to elongate quickly, and better support a vibrational explanation, we revisit figure 4 and our TDDFT Ehrenfest dynamics calculations for the adenine cation [6, supplementary figure S10]. Two CN-bonds in the backbone show rapid elongation: bond #9 relating to figure 2(a) and bond #11 which concerns the—NH₂-group which has already been highlighted in the dissociation path of figure 2(e). Figure 4 shows that the C–NH₂ bond #11 elongates dramatically by 6.5% in 15 fs after the sudden removal of an electron from HOMO−3. The simulation as well as vibronic spectroscopy on adenine [81, 82] give period times of 30–33 fs for this bond, so that its second overtone would match the ion yield oscillations perfectly. A coherent comb beating at twice the fundamental frequency could be excited if only the even-numbered vibrational levels have nonzero Franck–Condon factors [83] (or classically by a transition occurring only at the equilibrium geometry twice per oscillation period). Within the experimental uncertainty, a directly matching fundamental 20 fs oscillation period has also been reported for a mode that involves both the C–NH₂ stretch and NH₂ scissoring [84–86]. (An even better matching peak at 17 fs, 1909 cm⁻¹, in the calculations of Nowak et al [86] was weak and not assigned.)

TDDFT, the extension to the time-domain of the ordinary density functional theory is a formally exact quantum mechanical ab-initio method able to describe the dynamics of many-body systems [89, 90]. The TDDFT standpoint is the effective one-particle potential called exchange-correlation potential. While TDDFT within standard exchange-correlation functionals flavours is not able to capture the level of electronic correlation required to describe the correct correlated electronic dynamics in ionized adenine, it can still be used as an affordable solution to simulate the qualitative dynamical nuclear behavior following XUV ionization. Specifically, we follow the nuclear motion after a sudden single (or double) ionization by means of TDDFT + Ehrenfest dynamics within a self-interaction-corrected PBE exchange correlation functional [91, 92]. The TDDFT + Ehrenfest dynamics method is a non-adiabatic molecular dynamics approach which couples the time-dependent propagation of the Kohn–Sham orbitals with classical equations of motion for the nuclei determined on the base of the electronic potential energy surface (PES). In practice, the combined electronic–nuclear dynamics is carried out by a time stepping procedure where first the electronic evolution is obtained from TDDFT to calculate the time-evolved density and the latter is then used to calculate the PES from which the nuclear forces are evaluated and used to displace the nuclei within classical equations of motion. While this approach allows to treat non-adiabatic effects, it is formally justified only as long as the nuclear propagation is well described by single PESs and no quantum mixing of nuclear trajectories is expected to take place, like in the case of conical intersections which we neglect in this work. We utilize the Octopus code [93, 94] to perform TDDFT + Ehrenfest dynamics on adenine following the single (or double) removal of an electron from a given Kohn–Sham state. As discussed in the text we are able to demonstrate that ionization of adenine without any stabilization mechanism initiated by electronic correlation inevitably leads to bond elongation (figure 4) and eventual molecular dissociation on a time scale (${\gt}10$ fs) much longer than the one associated with the electronic charge migration.

As mentioned in the above section the available TDDFT exchange correlation potentials are not mature enough to capture the electronic correlation necessary to describe shake-up effects. For this reason we here employ a time-dependent density matrix propagation method based on non-equilibrium Green's function theory (NEGF) [95]. The NEGF formalism is based on a non-local non-hermitian self-energy operator comparable to the exchange-correlation potential in TDDFT, with the fundamental difference that one has a systematic perturbative approach to handle electron-electron and electron-photon interactions. The time-dependent equation for the density matrix reads:

$$\begin{equation*} \frac{d}{dt}\hat{\rho}(t)+\textrm{i} \left[\hat{h}_\text{HF}(t),\hat{\rho}(t)\right] = -\hat{I}_\text{c}(t)-\hat{I}_\text{c}^{\dagger}(t)-\hat{I}_\text{ion}(t)-\hat{I}_\text{ion}^{\dagger}(t), \end{equation*}$$

where $\,\hat{h}_\textrm{HF}(t)$ is the single particle Hartree–Fock Hamiltonian describing the system, and $\,\hat{I}_\textrm{c}(t)$ and $\,\hat{I}_\textrm{ion}(t)$ are the collision and ionization integrals respectively. The collision integral, which is expressed in terms of the correlation self-energy contains all the relevant electron-electron scattering processes. The ionization integral instead allows to include the laser induced ionization. Recent implementations of the density matrix propagation approach, such as the one in the CHEERS code [70], have made accurate simulations of realistic systems computationally accessible. Here we numerically solve the above equation for the charge dynamics of adenine induced by an experimental attosecond XUV pulse. Specifically, we construct the Hartree–Fock Hamiltonian starting from the Kohn–Sham wavefunctions and approximate the self-energy at the second-Born level; all details are provided in our recent report [6].