**3. Results**

#### *3.1. Photoionization of C60 with High-Fluence X-ray FEL Pulses*

One of the scientific motivations to study C60 with fs X-ray FELs is because these sources target atomic orbitals instead of molecular orbitals, and they allow simple measurements of the response of inner-shell electrons (localized with each atom forming the molecule) compared to the complex response of the molecular orbitals composed of all valence electrons. Probing inner-shell electrons with short wavelengths allows an efficient probing of physical and chemical phenomena from within, since it is an inside-out ionization. Inner-shell photoionization was carried out with synchrotron radiation [17], but the difference between these two light sources is that FELs have a fs time structure and are super intense [18] compared to synchrotrons. A synchrotron pulse on average has about 10<sup>4</sup> photons while FELs have about 1012, allowing the investigation of non-linear processes as well as time-resolved photoionization and fragmentation of the molecules [19].

Another motivation to choose to carry out the photoionization of C60 with intense FELs was to understand the radiation damage of large systems because this finding could contribute to the understanding of biomolecular imaging using X-ray scattering techniques, which do not provide detailed spectroscopic information. C60 is considered a benchmark molecule because it consists of chemically bonded carbon atoms with representative bond lengths and damage processes to bio-molecules [20]. Although FELs provide the incident brightness needed to achieve diffraction-limited atomic resolution experiments, they, nevertheless, induce possible electronic and structural damage, altering the sample despite the use of short pulse durations [21].

We carried out an experimental and theoretical investigation of C60 dynamics with intense fs X-rays to provide a spectroscopic study that offers either a quantitative or qualitative understanding of molecular dynamics. To understand the effects of increased per-atom fluence dose in the photon–molecule interaction, we used the large photoabsorption cross-section of carbon 1 s electrons. We ionized C60 with 485 eV photon energy to reach conditions in which each atom in a C60 molecule in the X-ray focus absorbs multiple photons. The study was performed with three pulse durations (4 fs, 60 fs, 90 fs) to ascertain the effect of the pulse duration. The core ionization induces the Auger–Meitner process, resulting in many photo- and Auger–Meitner electrons due to the cyclic multiphoton ionization. This process leads to secondary ionization of C60, and it fragments ions by the photoand Auger–Meitner electrons, which are found to be weak in isolated small molecules and absent in atoms. These effects were found, however, to be very significant for the ionization and fragmentation of C60 under high photon dose rate conditions and had to be incorporated in the model calculation to account for the experimental data. The C60 molecule charges up to C608+, based on our observation, and because of the short C–C bond lengths, it fragments via Coulomb repulsion into molecular and C ion charge states distribution from C+ to C6+ at 90 fs pulse duration. At a shorter pulse duration, 4 fs, the higher charge state obtained is only C5+, since the pulse is shorter, giving less multi-cyclic photoionization and Auger–Meitner decay. Our investigation focused on the production of charged atomic C states and not on the molecular fragments.

We show in Figure 1 some of the multi-ionized parent C60 as well as its fragmentation products, such as the molecular charged carbon chains, compared with the model [22]. Not all fragments are shown or taken into consideration in the calculation here; thus, the sum over all fractional fragmentation ion yields is not unity. Furthermore, we do not measure

the formation of neutral fragments in our experiment. As can be seen, there is not an agreemen<sup>t</sup> between the experimental molecular data and the model, which was tailored for the formation of charged atomic C states. The calculation is based on a model that follows both electronic and ionic dynamics in space and time, where the atoms/ions are treated as classical particles using Newtonian mechanics, but the rate equations and the cross sections are introduced quantum mechanically. The charges interact via Coulomb forces, and a non-relativistic equation of motion is used [22]. However, the molecular effects were not included, which is the reason for the discrepancy between the measurements and the calculation for the molecular fragment shown in Figure 1. Nonetheless, in the case of atomic carbon charge states, this model, which describes the charged particles behaving as if they were classical particles, agrees well with the experimental data, as shown in Figure 2.

**Figure 1.** Sequential multi-photon ionization of C60 displaying molecular ion fragments. The photon energy was 485 eV, the pulse duration was 90 fs, and the pulse energy was 0.61 mJ.

**Figure 2.** Charged atomic C state distribution measured with pulse duration of 90 fs and 900 μJ.

Figure 2 depicts the comparison between the experimental data and the model of the atomic Cn+ (n = 1–6) ion charge states generated after the Coulomb explosion of C608+. As can be seen, the pulse intensity allowed the formation of fully stripped C ions with 90 fs pulse duration. The model initially predicted more abundant charge states; however, the strong recombination of electrons with the C ions after the pulse ends led to the observed ion yield results [22].

In summary, the static experimental and theoretical investigation of C60 with intense pulses resulted in demonstrating that an intense X-ray FEL multiply ionizes the parent molecules before breaking into molecular ions as well as into highly charged atomic C states. We learned that, in the case of charged atomic C, secondary ionization (collisional ionization by trapped electrons) and recombination of electrons with C ion fragments were extremely important to the interaction of C60 with intense photons because the interaction created a microplasma that allowed high kinetic energy electrons to also ionize the C60 atomic fragments. The calculation for the charged atomic C states will not have agreed with the measurement if it did not include these effects. These effects were not sufficient for the case of the molecular fragment ions, which was not the focus of our investigation. Our work with intense X-ray pulses also contributed a detailed understanding of electronic damage (photoelectron, Auger–Meitner electrons) due to X-ray radiation, which is essential for the progress of bio-molecular imaging [22].

#### *3.2. Time-Resolved Photoionization of C60 with Mid-Fluence X-ray FEL Pulses*

The instrumental advances that provided the generation of pairs of synchronized femtosecond X-ray FEL pulses [23] has made it possible to carry out time-resolved studies enabling tracking, probing and ultimately understanding the time evolution of X-rayinduced photo processes. We thus extended our static investigation of C60 by carrying out a time-resolved experimental and theoretical investigation of its dynamics with mid-fluence fs X-rays. Specifically, we examined the role of chemical effects, such as chemical bonds and charge transfer, on the fragmentation following multiple ionization of the molecules. The X-ray pump-probe investigations enabled probing charge and nuclear dynamics after inner-shell photoabsorption. In this mid-fluence X-ray multiphoton regime, like in the previous intense case, there is a high degree of ionization, challenging the time-resolved theoretical work because of the response of a large number of degrees of freedom and the formation of highly excited states.

We performed X-ray pump/X-ray probe measurements [23] in which the X-ray pump pulse with 640 eV photons from the LCLS enabled K-shell ionization of the carbon atoms and induced a substantial degree of ionization. We then used an X-ray probe pulse to observe the dynamics initiated by the pump pulse, by detecting molecular and atomic fragment ions. The time evolution of the observed fragment ions was interpreted by numerical simulations. The ion fragments were detected with an ion time-of-flight spectrometer [22], which recorded the evolution of C60 into fragment ions. The time delays between the pump and probe pulses were between 25 and 925 fs [23]. The pulse duration of the first and second pulses was 20 fs and 10 fs, respectively. The measured total energy was 0.77 +/ − 0.01 mJ, while the estimated energy of the two pulses was 45% for the pump (peak intensity of 4 × 10<sup>15</sup> W/cm2) and 55% for the probe pulse. The theoretical modeling employed a molecular-dynamics-based simulation tool with recent additions to include the treatment of chemical bonds via classical force fields [22] and valence-electron charge transfer [24]. Under the current experimental conditions, multiphoton ionization and Auger–Meitner decay lead to multiply charged C60 molecules, stable up to C6013+, which break up into atomic and molecular fragments.

The examination of the charged atomic C fragments demonstrated a time-delay dependence to characterize the molecular time evolution. Figure 3 compares the experimental and theoretical atomic ion yields for C1+ to C4+ as a function of pulse delay, showing a qualitative good agreemen<sup>t</sup> between the experiment and modeling regarding only the dynamical behavior, not the absolute values of the yield of the charged atomic C states. As

can be seen, for both the measurements and the calculations, the behavior of the C+ ion yield changes little as a function of time delay between 25 and 925 fs. However, the ion yield behavior for C2+ - C4+ increases steadily over a time-delay range of approximately 600 fs; then, a plateau is observed at a longer time delay.

**Figure 3.** Comparison between experiment and modeling of the time-resolved ionization and fragmentation dynamics of C60 displaying charged atomic C fragments. The top panels show the measurements while the bottom panels show the calculations. Panels (**<sup>a</sup>**,**<sup>e</sup>**) show the C1+; (**b**,**f**) show the C2+; (**<sup>c</sup>**,**g**) show the C3+; and (**d**,**h**) show the C4+ fragment ions. See text for details.

Our analysis of the data guided by the calculation allowed us to understand the real-time evolution of the parent fragments after the pump pulse. Specifically, we found out that a substantial fraction of the ejected fragments, subsequent to the ionization of C60**,** are neutral carbon atoms. We calculated that beyond about 300 fs, there is an even larger number of C neutral than C+ ions. This modeling allowed us to deduce that the probe pulse generates C2+ predominantly through the ionization of neutral C by a photoionization and Auger–Meitner decay (P-A) sequence, while C3+ is created similarly after ionization of C1+ by a P-A sequence. C4+ is formed from neutral C via two P-A sequences or from C1+ by a P-A sequence and a valence ionization or secondary ionization. Based on the measurement and modeling, we concluded that the production of C2+, C3+ and C4+ is primarily due to the ionization of C/C1+ fragments by the probe pulse.

Our modeling demonstrated that chemical bonds and valence charge transfer are important in the photoionization of C60, since we found no time-delay dependence in the yield of the C2+, C3+ and C4+ ions without inclusion of such chemical effects. We found that the parent ion C6013+ does not undergo instantaneous fragmentation because it is delayed, as shown in Figure 3. The fragmentation is delayed relative to the pump pulse due to the still existing chemical bonds because it takes time for the 60-atom system to break up into smaller fragments, most of which exist only transiently for several tens of femtoseconds. In addition, during this structural transformation, it takes additional time for those fragments to eject neutral and singly charged atomic ion fragments. We show the impact of the chemical effects in Figure 4 (top panel) by plotting the maximum atomic displacement for the parent ion C6013+ based on MD simulations, for two situations: (1) chemical phenomena, such as bonding and charge transfer, are removed; (2) the full model that includes both chemical bonding and charge transfer.

It is clear that chemical effects minimize significantly the maximum displacement of C atoms, demonstrating evidently that C60 is structurally resistant, on time scales of tens of femtoseconds, against the impact of X-ray multiphoton ionization. Figure 4 (bottom panel) shows the simulation snapshots of the real-time evolution of C6013+ for the full model, illustrating the ionization and fragmentation dynamics of C60 irradiated by femtosecond X-rays.

**Figure 4.** Movie snapshots of the real-space and real-time simulation dynamics of C60 13+ induced by XFEL pulse.

The implications of this work for the field of femtosecond molecular imaging is that charge transfer, nuclear arrangement, chemical bonds, and thus, the chemical structure are resistant to the intense electromagnetic environment created by XFEL irradiation. The impact of this work is that delayed fragmentation will play a critical role in most other intense X-ray multiphoton ionizations of molecules. With the advent of several new FELs all over the world, our results, which lay the foundation for a deeper understanding and quantitative modeling of XFEL-induced radiation damage, will impact biomolecular imaging.

In summary, this time-resolved investigation gave new insight into the dynamics of the C60 fragmentation subsequent to mid-fluence absorption of the X-ray photon. It revealed the importance of chemical effects, such as covalent bonding and charge transfer, in stabilizing the molecule against fragmentation over several hundred femtoseconds after the X-ray pump pulse. Such detailed understanding of X-ray-induced ionization dynamics and atomic motions in molecules is crucial for the applications of high-intensity X-ray beams [25].
