Astrochemical relevance of VUV ionization of large PAH cations

As a part of interstellar dust, polycyclic aromatic hydrocarbons (PAHs) are processed by the interaction with vacuum ultraviolet (VUV) photons that are emitted by hot young stars. This interaction leads to the emission of the well-known aromatic infrared bands but also of electrons, which can significantly contribute to the heating of the interstellar gas.Our aim is to investigate the impact of molecular size on the photoionization properties of cationic PAHs.Trapped PAH cations of sizes between 30 and 48 carbon atoms were submitted to VUV photons in the range of 9 to 20 eV from the DESIRS beamline at the synchrotron SOLEIL. All resulting photoproducts including dications and fragment cations were mass-analyzed and recorded as a function of photon energy.Photoionization is found to be predominant over dissociation at all energies, which differs from an earlier study on smaller PAHs. The photoionization branching ratio reaches 0.98 at 20 eV for the largest studied PAH. The photoionization threshold is observed to be between 9.1 and 10.2 eV, in agreement with the evolution of the ionization potential with size. Ionization cross sections were indirectly obtained and photoionization yields extracted from their ratio with theoretical photoabsorption cross sections, which were calculated using time-dependent density functional theory. An analytical function was derived to calculate this yield for a given molecular size.Large PAH cations could be efficiently ionized in H I regions and provide a contribution to the heating of the gas by photoelectric effect. Our work provides recipes to be used in astronomical models to quantify these points.


Introduction
Polycyclic aromatic hydrocarbons (PAHs) play a major role in the physics and chemistry of photodissociation regions (PDRs). They strongly absorb vacuum ultraviolet (VUV) photons that are emitted by hot young stars and relax by emission in the aromatic infrared bands (AIBs). The interaction with VUV photons can lead to other relaxation processes including ionization and dissociation. All these processes together with reactive processes involving in particular electrons and hydrogen (H, H 2 ) govern the evolution of the PAH population in the diffuse interstellar medium (Le Page et al. 2003), in circumstellar disks (Visser et al. 2007), and in reflection nebulae (Montillaud et al. 2013). The results of these chemical models suggest that large PAHs with a typical carbon number, N C , of 50 or more dominate the AIB emission which led to the grandPAH hypothesis that large and possibly compact PAHs dominate the emission in bright PDRs Corresponding author. (Andrews et al. 2015). In some regions associated with these PDRs, large PAHs are expected to be ionized reaching even the dicationic stage (Tielens 2005;Andrews et al. 2016).
In a previous study we have investigated the branching ratio between ionization and fragmentation upon VUV irradiation for medium-sized PAH cations (Zhen et al. 2016) with a number of carbon atoms, N C , between 16 and 24. For all of these cations, fragmentation was observed to be the dominant channel at least up to a photon energy of 13.6 eV which is relevant for H i regions. In the case of larger PAH cations, ionization is expected to be by far the dominant channel as suggested by the study of the hexa-peri-hexabenzocoronene (HBC) cation, C 42 H + 18 , by Zhen et al. (2015). Here, our objective is to quantify the growing importance of ionization as the molecular size increases. Following Zhen et al. (2016), we have studied the photoprocessing of PAH cations with an N C between 30 and 48 atoms over the 9.5 − 20.0 eV VUV range. In addition to the branching ratio between ionization and dissociation, we aim to derive the photoion-Article number, page 1 of 10 arXiv:2005.02103v1 [astro-ph.GA] 5 May 2020 A&A proofs: manuscript no. VUVPAH_ion ization yield, which is important to model the charge balance of PAHs and its impact on the AIB spectrum (Bakes et al. 2001), but also to evaluate the contribution of these species to the photoelectric heating rate (Bakes & Tielens 1994;Weingartner & Draine 2001b). The experimental method is described in Sect. 2 and the results are presented in Sect. 3. In Sect. 4, we discuss the astrophysical implications and propose recipes to be used in astrophysical models. We conclude in Sect. 5.

Experimental method and data analysis
We have used the Thermo Scientific TM LTQ XL TM linear ion trap (LTQ ion trap) as described in Milosavljević et al. (2012), which is available at the VUV beamline DESIRS at the synchrotron SOLEIL (Nahon et al. 2012). The production of PAH cations in the LTQ ion trap was performed using an atmospheric pressure photoionization (APPI) source which required the species of interest to be in solution before their injection with a syringe. This part was a major limitation on the size range of PAHs we could study due to the nonsolubility of large PAHs. Four large PAH cations with number of carbon atoms, N C , ranging from 30 to 48 could be investigated in this study, namely (a) benzobisanthene, C 30 H + 14 , (b) ovalene, C 32 H + 14 , (c) dibenzophenanthropentaphene (DBPP), C 36 H + 18 , and (d) dicoronylene, C 48 H + 20 . Sample (b) originated from Janssen Chimica (Belgium), samples (a) and (c) from the PAH Research Institute in Greifenberg (Dr. Werner Schmidt). The synthesis of compound (d) is briefly reported in Appendix A. The molecular structures of the studied species are depicted in Fig. 1. Emptying the syringe was performed at a flow rate which was kept constant for each experiment. Values of 4, 6 and 10 µl min −1 were used for compounds (a) and (b), (c) and (d), respectively. The presence of UV irradiation from a Kr discharge lamp ensured a soft creation of PAH cations without fragmentation (Giuliani et al. 2012). The formed cations were then guided through ion optics into the LTQ ion trap in which a constant He pressure of p ≈ 10 −3 mbar was held. The ions were cooled by the collisions with He atoms and the PAH cations of interest, the socalled parent ions, were isolated through specific mass selection and ejection of other species from the ion trap including the 13 C isotopomers.
The parent ions were then submitted to the VUV synchrotron radiation which was tuned from 9.5 to 20.0 eV in steps of 0.1, 0.2, 0.3 or 0.5 eV depending on the photon energy range, with the exception of C 30 H + 14 , for which we were able to scan only at low energies up to 16.0 eV. Higher harmonics of the VUV undulator synchrotron radiation with photon energies lower than 16.0 eV were filtered out by a gas filter filled with Ar gas to a pressure of 0.23 mbar. Above 16.0 eV no such gas filtering is necessary. The photon flux was measured with a IRD AXUV100 calibrated Si photodiode for a monochromator exit slit width of 200 µm and was between 0.8 and 2.8 10 12 photons s −1 over the studied photon energy range. A typical photon flux can be derived using a previous calibration of the beam size as a function of photon energy (Douix et al. 2017), yielding values of 1.5 − 5.2 10 14 photons cm −2 s −1 . In order to limit possible two photon consecutive absorption processes, we tuned the photon flux by changing (i) the irradiation time from 0.8 to 0.2 s for the lower and higher photon energy ranges, respectively, and (ii) the monochromator exit slit width from 200 µm at low energies to 70 µm at high energies, except for dicoronylene for which values of 400 and 100 µm at low and high energies, respectively, were used to improve the S/N ratio. The photon flux was assumed to be linearly proportional to both the irradiation time and the monochromator exit slit width. The probability of two photon absorption processes could be estimated on the formation of triply charged parent ions, yielding only very small relative intensities below 2 % of the total number of photoproducts.
Depending on the acquisition time, a few hundred mass spectra were recorded at each photon energy and averaged to yield one mass spectrum per photon energy step. Following the same procedure, we also recorded blank mass spectra at each photon energy by selecting a mass close to but different enough from each parent ion. This allowed us to perform background subtraction which eliminates contamination peaks from the mass spectra. The averaging procedure provides us with a statistical standard error (see Appendix D). As an example, the background subtracted mass spectra for ovalene, m/z = 398, recorded at two different photon energies of 9.5 eV and 15.5 eV are depicted in Fig. 2. The parent ion, C 32 H + 14 , is well isolated, the 13 C isotopic parent ion has a residual contribution of less than 1 % remaining in the ion trap. By increasing the photon energy, three different secondary ions can be observed and unambiguously separated, namely the H and 2H/H 2 loss, and the main doubly ionized parent ion channels. For the presented example of the ovalene cation, C 32 H + 14 , these species are C 32 H + 13 , C 32 H + 12 , and C 32 H 2+ 14 , respectively (see Fig. 2). When extracting the peak intensities as will be done in the following, one has to consider the detector gain efficiency that varies with the charge and the mass of the ions of interest. Recommended scaling factors were therefore applied (see Appendix B).

Action spectra and branching ratio
The action spectra are determined following the procedure described in Appendix B yielding relative intensities of the photoproducts as used in previous work (Zhen et al. 2016). The resulting spectra for the photoionization (dication, denoted I) and photodissociation (fragments, denoted F) channels of the four studied PAH cations are shown in Fig. 3 as a function of the photon energy. The F channel remains small for all investigated PAH cations at all photon energies and is barely notable for the dicoronylene cation in Fig. 3. More specifically, Fig. 4 shows that the branching ratio (BR) for photoionization relative to photodissociation increases significantly with increasing N C and reaches a minimal value of 0.98 for the largest studied cation. This trend  of large PAHs differs from what was observed in our earlier study of medium-sized PAH cations for which a larger fraction of fragments was observed (Zhen et al. 2016). It is in line with the ionization BR of about 0.97 at 20 eV which was derived by Zhen et al. (2015) for the HBC cation, C 42 H + 18 , by operating their home-made ion trap setup at the DESIRS beamline. The authors also reported a value of 0.70 ± 0.10 for the ionization BR of the ovalene cation at 20 eV, which can be compared to a value of 9 10 11 12 13 14 15 16 17 18   0.87 ± 0.02 in our experiment. This difference can be interpreted by the low mass resolution achieved in the former experiments which impacted both the isolation of the 12 C parent isotopomer before irradiation and the quantification of the abundance of -H fragments in the photoproducts. From Figure 3, we derived appearance energies for the formation of PAH 2+ , AE 2+ . The values are listed in Table 1 and compared to the theoretically computed adiabatic ionization potentials, IP 2+ , which are extracted from the Theoretical Spectral Database of PAHs 1 (Malloci et al. 2007a) or calculated at the same level of theory for the missing IP 2+ of the DBPP cation according to Malloci et al. (2007b). Experimental and theoretical 1 http://astrochemistry.oa-cagliari.inaf.it/database/ values are found to be consistent and the trend of a slow decrease of IP 2+ with N C 30 carbon atoms reported by Malloci et al. (2007b) is confirmed.

Photoionization cross sections
Experimental total action cross sections per carbon atom, σ C I+F , were obtained following the procedure described in Appendix C. The photoionization cross sections, σ C I , were then derived by using the branching ratio depicted in Fig. 4. The σ C I+F curves are expected to provide a lower value for the absolute photoabsorption cross sections, σ C abs (see Eq. (C.1)). Since σ C abs of the studied cations could not be extracted from the performed experiment and have not been reported so far in the literature,  we compare these curves with the theoretical photoabsorption cross sections, σ C abs, theo , which have been computed using Time-Dependent Density Functional Theory in line with our previous work (Malloci et al. 2004(Malloci et al. , 2007a and as described in Appendix E. All obtained cross sections, experimental and theoretical, are displayed in Fig. 5 and compared to each other in the following at high (> 14 eV) and low (< 14 eV) energies.
Above 14 eV, the cross sections are globally consistent (see Fig. 5). Still, the values of σ C I+F are found to be systematically larger than those of σ C abs, theo around the peak at 17 eV. In addition, there is a trend of increasing σ C I+F at the peak with molecular size. The case of C 48 H + 20 has to be considered with caution though due to a less accurate calibration procedure (see Appendix C). On the contrary to the experimental cross sections, the values of σ C abs, theo stay close to each other, which is expected from the proportionality of the photoabsorption cross sections with N C . Still, it is not yet possible to access how precise the calculated cross sections are. The comparison with an experimental photoabsorption cross section at high energies (up to 30 eV) has been done so far only for neutral anthracene, C 14 H 10 (Malloci et al. 2004). It is interesting to mention that this comparison reveals an overall good agreement between the calculated and measured cross sections but with differences on the band positions and widths (in the theoretical spectra the band width is artificial). Also around the high energy peak observed at 18 eV, the discrepancy appears similar to the one illustrated in Fig. 5 in the case of C 32 H + 14 and C 36 H + 18 . Below 14 eV, we can see the presence of a plateau from 11.3 to 12.9 eV, for both σ C I+F and σ C I , whereas σ C abs, theo (see Fig. 5) exhibits strong bands. This indicates that, in this range, direct ionization is not the dominant process and there is a strong coupling between electronic states and with nuclear states. This implies that a large fraction of the absorbed photons lead to vibrational excitation of the parent ion, which will subsequently relax by radiative cooling since no fragmentation is observed, the so-called σ * given in Eq. C.1. Such a relaxation scheme could be, at least partially, promoted by long-lived Rydberg states for which radiative cooling can be an efficient relaxation channel (Jochims et al. 1996). Such states could involve autoionization (AI) resonances as was clearly observed in the photoelectron spectroscopy of neutral coronene (Bréchignac et al. 2014). In our data, only the peak at 13.4 eV observed in σ C I of the dicoronylene cation provides evidence for AI resonances. The energy steps used in our scans were however too large to catch efficiently these possibly narrow AI resonances and determine how frequently they occur. Although we can discuss qualitatively the contribution of σ * at energies below 14 eV, this is not the case at higher energies. This implies that the maximum values that can be achieved for the photoionization yield as presented in Sect. 4.2 are unknown.

Charge state of astro-PAHs
A couple of modeling studies on the charge state of astro-PAHs have considered that these species could reach the dication and marginally the trication states (Bakes et al. 2001;Weingartner & Draine 2001b;Andrews et al. 2016). In Figure 7, we compiled the ionization potentials from cation to dication and dication to trication, which have been obtained from calculations (Malloci et al. 2007b) or from experiments (this work and Zhen et al. (2016)). This data set can be described following the formalism given by Weingartner & Draine (2001a), who adopted an empirical approach to estimate the first and second ionization potentials of PAHs as a function of their charge, Z, and effective radius, a, with where ε 0 is the vacuum permittivity in F nm , e is the elementary charge in C, W is the work function of bulk graphite, W = 4.4 eV, and a is proportional to N C via the relation Adjusting Eq. (1) (see Weingartner & Draine 2001a, Eq. (2)) for Z = 1 and Z = 2 to the IP (Z+1)+ and AE (Z+1)+ values reported in Fig. 7, we find that a value of W = 3.9 eV fits our data better than the value of bulk graphite. This is in line with W values of about 4.0 eV as calculated for similarly sized PAHs by Kvashnin et al. (2013). We can see from Fig. 7 and Eq. (1) that a fraction of the photons absorbed in H i regions can induce ionization of PAH cations. Taking the absorption and ionization cross sections shown in Fig. 5 and considering the radiation field of the prototypical NGC 7023 NW PDR (Joblin et al. 2018), we can estimate that typically one photon over three absorbed in the [10 − 13.6] eV range by PAH cations with N C = 30 − 36 will lead to ionization. The fraction of ionizing events will increase with increasing molecular size as the ionization potential shifts to lower energies. It reaches 0.5 for C 48 H + 20 . We also note that the formation of C 2+ 60 will be more difficult to achieve than that of a PAH 2+ of similar size, since the corresponding cations have relatively similar absorption cross sections but the value of AE 2+ for C + 60 is significantly higher, (10.5±0.1) eV (Douix et al. 2017), compared to 8.7 eV for a PAH + with N C = 60 (see Fig. 7

Photoionization yield
Photoionization yields of PAH cations were derived for all studied species by dividing the experimental photoionization cross section, σ C I , by the theoretical photoabsorption cross section, σ C abs, theo . In Sect. 3.2, we discussed the precision of both the experimental and theoretical cross sections. This can impact the photoionization yields. At energies below 14 eV, the presence of bands in σ C abs, theo , which are not present in σ C I , can induce spectral features in the photoionization yields (e.g. the 12 eV peak obtained for C 32 H + 14 ), which are as precise as the calculated spectrum. Still, Fig. 8 shows that the photoionization yields display comparable features for the studied molecules, with a rise starting at the ionization thresholds, AE 2+ , the plateau in the 11.3 to 12.9 eV range followed by another rise to reach the maximum value. There is some uncertainty on this maximum value because of the unknown contribution from σ * (cf. Sect. 3.2). In the following, we made the hypothesis that the contribution of σ * at high energies (20 eV) is minor and that the photoionization yields are limited by the photoionization BR, which never reaches unity as shown in Fig. 4. The mean values at high energies of the photoionization yields were thus scaled using the ionization BR at 20 eV. The resulting curves are presented in Fig. 8. Data on the photoionization yields of neutral PAHs have been previously derived from experimental studies performed by Verstraete et al. (1990) and Jochims et al. (1996). The latter authors have proposed a rule of thumb to facilitate the implementation of this yield into models. This consists of a linear function of the photon energy with dependence on the ionization potential. On the basis of our results, we propose to use a similar approach to describe the evolution of the photoionization yield of PAH cations with molecular size. The resulting function, Y + ion , is based on the above described ionization regimes which occur in different energy ranges (values in eV) as (hν − 12.9) + α β(N C ) for hν < IP 2+ IP 2+ ≤ hν < 11.3 11.3 ≤ hν < 12.9 12.9 ≤ hν < 15.0 hν ≥ 15.0, where α = 0.3 is the value of the plateau and β depends on N C with The reported β values represent the values at 20 eV of the ionization BR (Fig. 4). They can be considered as maximum values since they neglect a possible contribution of σ * to the photoabsorption cross section as discussed above. These values were found to increase linearly with size for the studied size range with the dependence given by Eq. (4). Extrapolation to larger sizes leads to a β value of 1 for N C ≥ 50. This trend differs from the case of neutral PAHs for which Jochims et al. (1996) concluded that β = 1 is independent of size, in agreement with previous measurements by Verstraete et al. (1990). Figure 9 displays examples of Y + ion [N C ](hν) which were calculated from Eqs. (3) and (4), illustrating the variability of Y + ion [N C ](hν) with molecular size. No significant variation of this yield is expected for PAH cations with N C ≥ 50. In their PAH evolution model, Andrews et al. (2016) 4) and (5) from Jochims et al. (1996) adapted for neutral PAHs but taking into account the shift of the ionization potential to IP 2+ , which is relevant for cations. The dashed vertical line marks the 13.6 eV photon energy cut-off for H i regions.
of PAH cations based on the recipe given by Jochims et al. (1996) for neutrals but taking into account the appropriate photoionization potential for cations, i.e., values of IP 2+ . To illustrate the impact that this approximation may have on the model results, we report in Fig. 9 these estimated yields and compare them with our recommended yields by integrating from IP 2+ to 13.6 eV. We found that for the medium-sized PAHs, as represented by N C = 34, our integrated yield is larger by 19 % compared to the previously available one, whereas for large PAHs, as represented by N C = 60, it is smaller by 14 %. These simple estimates are however not conclusive and models have to be run to evaluate the impact on the ionization of the PAH population in specific environments.

Conclusion
We have studied the interaction of trapped PAH cations with VUV photons in the range of 9 to 20 eV. Our initial goal was to explore the properties of large species for N C up to about 80 atoms. However we could only achieve measurements on molecular sizes from 30 to 48 carbon atoms due to the very low solubility of large PAHs. Still, studies in this range allow us to access the major trends in the ionization properties of PAH cations due to a molecular size increase. We found that (i) below 13.6 eV, the formation of a hot ion with subsequent (radiative) cooling is the major relaxation channel, followed by ionization whose yield reaches about 0.5 at 13.6 eV. From a molecular physics point of view, the yield comprises an interesting plateau at a value of 0.3 that extends over the energy range from 11.3 to 12.9 eV. This plateau reveals a spectral range in which there is a strong competition between electronic and nuclear states. It would be interesting to investigate the dynamics of the relaxation of excited electronic states in this range using fs pump-probe experiments (Marciniak et al. 2015).
(ii) contrary to previous studies on neutrals, we could not observe that the photoionization yield reaches a value of 1 at high energies. At 20 eV, some dissociation is observed for all studied PAH cations, implying that the maximum of the yield cannot be larger than the branching ratio between ionization and dissociation, which increases with molecular size and reaches 0.98 for the largest studied ion, C 48 H + 20 . In addition, we have not included a possible contribution in the photoabsorption events of the formation of a hot ion that would subsequently relax by radiative cooling in isolated conditions. This contribution would further lower the values of the photoionization yield. We have no explanation for the difference observed between neutrals and cations. Whether this is due to a change in their respective properties or the fact that experiments like ours using ion trapping are more sensitive to quantify this effect than experiments carried out on neutrals with different techniques, is out of our reach and would be interesting to further investigate.
Concerning astrophysical applications, we provide recipes to determine both the ionization potential and the photoionization yield of PAH cations as a function of their molecular size, which can be extended to larger sizes (typically N C = 100). This yield can be combined with photoabsorption cross sections that are readily available from calculations using TD-DFT. All this molecular data can be used in models that describe the chemical evolution of PAHs in astrophysical environments. For example, the cavity around the star in NGC 7023 is expected to be an environment in which large PAH + and PAH 2+ are present (Andrews et al. 2016;Croiset et al. 2016). The presence of dications is expected to impact both the heating of the gas by photoelectric effect and the AIB emission. Some first IR action spectra of large PAH cations and dications have been recorded by Zhen et al. (2017Zhen et al. ( , 2018. They provide encouraging results about large ionized PAHs being good candidates for carrying the AIBs. It is still not clear though if the spectral differences between cations and dications will be sufficient to differentiate both charge states in the observations. Still, we can predict that a detailed modeling approach combined with the wealth of spectral and spatial information, which will be delivered soon by the James Webb Space Telescope, will be able to highlight the charge evolution of the PAH population and its impact on the physics and chemistry of PDRs.

Appendix B: Action spectra scaling procedure
From the recorded mass spectra, peak intensities of parent ions and their photoproducts can be deduced. The secondary ions produced upon VUV irradiation consist of the dication with peak intensity S I , and the photofragments with summed peak intensity S F , including the H and 2H/H 2 loss channels. Due to detector characteristics, doubly ionized molecules are detected more efficiently than singly ionized molecules. Therefore, the peak intensities derived from the mass spectra have to be scaled by the detector gain efficiency, ε, to retrieve values that scale with abundances. Thermo Scientific TM provides ε + = 0.29 for parent ions and fragments, ε 2+ = 0.42 for dications and a value of 0.54 for trications. There is some gain change with mass but this is a minor correction for the range of studied masses.
The total number of ions in the trap, P 0 (in uncalibrated values), can then be calculated with where P t ε + is the number of parent ions after irradiation time, t. Building the action spectra requires to derive normalized photoproduct intensities for S I and S F , which can be obtained by first dividing them by P 0 and then correcting for the variation of the photon flux, Φ(ν). Indeed the latter evolved in energy due to spectral shape variations and changes made in the irradiation time, t, and monochromator exit slit width, s, so that the total photoproduct intensity remains smaller than ca. 12 % of P t , as seen in the mass spectra. This led to where Φ norm (ν) is normalized to be 1 at its maximum at 9.5 eV. Note that the obtained intensities are in arbitrary units (see Fig. 3) and not in percentage of the total number of ions because of the scaling by the relative photon flux.

Appendix C: Photoproduct cross sections scaling procedure
The absorption of a photon by the parent ion leads to different relaxation channels. Considering monochromatic radiation, the photoabsorption cross section, σ abs , can therefore be decomposed into the sum of the cross sections for each relaxation channel as σ abs = σ I+F + σ * , (C.1) where σ I+F is the cross section leading to the production of the secondary products with intensities S I and S F (see Appendix B), and σ * is the cross section for the creation of a hot ion that will relax its internal energy by radiative cooling and/or collisions with buffer gas (He) in our experiment. These processes cannot be traced in our experiment and only σ I+F can be estimated following with the photon flux, Φ, in photons cm −2 s −1 , a form factor, γ, describing the overlap of the photon beam and the ion cloud, the total number of ions, P 0 , and the number of parent ions, P t ε + , after irradiation time, t. Plugging P 0 from Eq. (B.1) in Eq. (C.2), we get In order to determine cross sections in absolute units, the photon flux, Φ, and the form factor, γ, have to be well-known. Douix et al. (2017) managed to record the absolute photoionization cross section, σ C + 60 I , for the buckminsterfullerene cation, C + 60 , by carefully measuring these parameters and applying Eq. (C.3), where the term S F P t was zero due to the non-dissociation of C + 60 2 . In our experiment, we trapped C + 60 and recorded its dication peak under the same irradiation conditions used for our studied PAHs except dicoronylene as explained below. We could therefore derive the value of γ Φt and use this factor to obtain experimental values for σ I+F from the photoproduct evolutions of our PAHs according to Eq. (C.3). This used scaling procedure yields reasonable cross section values only above the AE 2+ of C + 60 . We bypassed this limitation by scaling the action spectra (see Sect. 3.1 and Appendix B) to the cross sections and replacing the values below the AE 2+ of C + 60 with the values from the scaled action spectra. Finally, to simplify the comparison between species, we divide σ I+F of each PAH cation by its respective N C , yielding σ C I+F . We note that in this calibration procedure, dicoronylene required a specific treatment. Indeed this ion was studied in different conditions since both the syringe flow rate and the monochromator exit slit width, s, were increased in order to get a sufficient signal. In order to correct at best for these changes, we applied corrections to the γ Φt factor in Eq. (C.2) by assuming that not only the photon flux but also the beam overlap with the ion cloud scales linearly with s, the later is likely disputable but this is the best we could do.