# Gas-phase hydrogenation of large, astronomically relevant PAH cations

Lijun Hua,1 Xiaoyi Hu,2 Junfeng Zhen,3 Xuejuan Yang,1
1 Hunan Key Laboratory for Stellar and Interstellar Physics and School of
Physics and Optoelectronics,
Xiangtan University, Hunan 411105, China
2 Department of Chemical Physics, University of Science and Technology of
China, 96 Jinzhai RD., Hefei, Anhui 230026, China
3 Institute of Deep Space Sciences, Deep Space Exploration Laboratory, Hefei
230026, China
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

To investigate the gas-phase hydrogenation processes of large, astronomically
relevant cationic polycyclic aromatic hydrocarbon (PAH) molecules under the
interstellar environments, the ion-molecule collision reaction between six PAH
cations and H-atoms is studied. The experimental results show that the
hydrogenated PAH cations are efficiently formed, and no even-odd hydrogenated
mass patterns are observed in the hydrogenation processes. The structure of
newly formed hydrogenated PAH cations and the bonding energy for the
hydrogenation reaction pathways are investigated with quantum theoretical
calculations. The exothermic energy for each reaction pathway is relatively
high, and the competition between hydrogenation and dehydrogenation is
confirmed. From the theoretical calculation, the bonding ability plays an
important role in the gas-phase hydrogenation processes. The factors that
affect the hydrogenation chemical reactivity are discussed, including the
effect of carbon skeleton structure, the side-edged structure, the molecular
size, the five- and six-membered C-ring structure, the bay region structure,
and the neighboring hydrogenation. The IR spectra of hydrogenated PAH cations
are also calculated. These results we obtain once again validate the
complexity of hydrogenated PAH molecules, and provide the direction for the
simulations and observations under the coevolution interstellar chemistry
network. We infer that if we do not consider other chemical evolution
processes (e.g., photo-evolution), then the hydrogenation states and forms of
PAH compounds are intricate and complex in the interstellar medium (ISM).

###### keywords:

astrochemistry — methods: laboratory: molecular — ISM: atoms — ISM: molecules
— molecular processes

††pagerange: Gas-phase hydrogenation of large, astronomically relevant PAH
cations LABEL:lastpage

##  1 Introduction

Table 1: The molecular geometry of PAH molecules. The different edge structures are highlighted with different colors: solo (purple), duo (red), trio (green), and quarto (blue). Edge bonds without hydrogens attached correspond to bay regions (black), which can take different forms. PAHs | structures | solo | duo | trio | quarto | bay regons
---|---|---|---|---|---|---
Ovalene ($\rm{C_{32}H_{14}}$, m/z=398) |  | 2 | 6 | 0 | 0 | 0
Periflanthene ($\rm{C_{32}H_{16}}$, m/z=400) |  | 0 | 4 | 0 | 2 | 6
Tri-benzo-peropyrene (TBP, $\rm{C_{34}H_{16}}$, m/z=424) |  | 0 | 5 | 2 | 0 | 3
Tri-benzo-naphtho-pero-pyrene (TNPP, $\rm{C_{40}H_{18}}$, m/z=498) |  | 2 | 3 | 2 | 1 | 4
Hexa-benzo-coronene (HBC, $\rm{C_{42}H_{18}}$, m/z=522) |  | 0 | 0 | 6 | 0 | 6
Dicoronylene (DC, $\rm{C_{48}H_{20}}$, m/z=598) |  | 4 | 8 | 0 | 0 | 2

PAH molecules and their derivatives are abundant and ubiquitous in many
astronomical sources and are expected to account for $\sim$ 10% of cosmic
carbon in the ISM (Sellgren, 1984; Allamandola et al., 1989; Puget & Leger,
1989). The assignment of the aromatic infrared bands (AIBs) to PAHs has widely
been discussed and accepted (Leger & Puget, 1984; Allamandola et al., 1985,
1989; Peeters et al., 2004). The prominent 3.3 and 3.4 $\mu$m feature is
associated with aromatic and aliphatic CH stretches (Schutte et al., 1993;
Bernstein et al., 1996; Pendleton & Allamandola, 2002), and the 6.2 and 7.7
$\mu$m bands are linked to CC vibrations of aromatic rings. The 8.6 $\mu$m and
11.2 $\mu$m are assigned to CH in- and out-of-plane bending and (Peeters et
al., 2004; Tielens, 2008).And longer wavelength bands (>16 $\mu$m) are
assigned to CCC bending (Allamandola et al., 1989). The relative strength of
these bands depends on the chemical properties (e.g., size, structure, and
charge states) of PAH molecules (Allamandola et al., 1999; Draine & Li, 2001)
and their physical environment (e.g., the intensity and hardness of starlight
illuminating PAHs, electron density, and gas temperature) (Bakes & Tielens,
1994; Weingartner & Draine, 2001; Yang et al., 2021).

As a significant class of large organic interstellar molecules, PAHs play an
important role in the energy and ionization balance of the ISM (Tielens, 2008;
Berné et al., 2022b, and references therein), and catalyze the formation of
molecular H2 in photo-dissociation regions (PDRs; Boschman et al. (2012)).
Interstellar chemical-evolution processes, including collision reactions
(e.g., hydrogenation), photo-fragmentation, and ionization, further modify the
states and forms of these PAH compounds in interstellar environments that
various types of functional groups may be acquired and functionalize, such as
H/D, methyl (-CH3), vinyl (-CHCH2), methoxy (-OCH3), amino (-NH2),
cyano/isocyano (-CN, -NC), acid (-COOH), and hydroxyl (-OH) (Hollenbach &
Tielens, 1999; Tielens, 2013, and references therein).

PAHs and their associated derivate clusters may be formed through ion-molecule
reactions in interstellar space where PAH and other coexist atoms or molecules
(Petrie & Bohme, 1993; Böhme et al., 2016; Zhen et al., 2018, 2019). Hydrogen
is the most abundant element in the universe, and there are some regions in
the interstellar space where hydrogen (H) atoms are abundant, such as PDRs.
PDRs provide a natural laboratory for the study of the interaction of
interstellar UV radiation, hydrogen atoms, hydrogen ions, and other molecules
coexisting with carbonaceous species (Pety et al., 2005; Rapacioli et al.,
2005; Hollenbach & Tielens, 1999; Micelotta et al., 2010). Observations with
the Spitzer Space Telescope and the Herschel Space Observatory of the
prototypical PDR, NGC 7023, have revealed the important role of hydrogenation
processes of interstellar PAHs (Andrews et al., 2016).

When PAHs are in this high hydrogen density environment and are continuously
bombarded by H-atoms, there may be excess H-atoms on the periphery (Andrews et
al., 2016, and references therein), which are also known as super-hydrogenated
PAHs. The interaction between PAHs and H-atoms has been studied theoretically
(Cassam-Chenaï et al., 1994; Bauschlicher, 1998; E. Rauls, 2008; Sebree et
al., 2010; Yang et al., 2020a) and experimentally (Snow et al., 1998; Thrower
et al., 2012; Cazaux et al., 2016, 2019; Jensen et al., 2019), and these
studies indicate that super-hydrogenation of PAH cations is possible. In
addition, the IR vibrational spectra of mono-deuterated PAHs have also been
performed by theoretical calculations, and the intrinsic band strength of the
4.4 $\mu$m C-D stretch determined (Yang et al., 2020b, 2021). Furthermore, in
a combined experimental and theoretical study, coronene (C24H12) hydrogenation
follows a well-defined sequence of hydrogenation sites that has later been
confirmed by means of infrared spectroscopy (Cazaux et al., 2016, 2019).
Moreover, the gas-phase hydrogen/deuterium exchange on large, astronomically
relevant cationic PAHs (hexa-benzo-coronene cation, $\rm{[C_{42}H_{18}]}$+) is
also studied (Zhang et al., 2022).

To understand the reaction between PAH cations and H-atoms and further
investigate the coevolution network of the interstellar PAH chemistry
(Tielens, 2013; Zhang et al., 2023), in this work, by tracking the
hydrogenation processes of PAH compounds, we present an exploration study of
the chemical reactivity of six large, astronomically relevant PAH cations with
H-atoms. Furthermore, to investigate the formation mechanism of hydrogenated
PAH cations, the experimental results are illustrated together with the
results of the theoretical chemistry calculation.

In this work, ovalene ($\rm{C_{32}H_{14}}$), periflanthene
($\rm{C_{32}H_{16}}$), tri-benzo-peropyrene (TBP, $\rm{C_{34}H_{16}}$),
tribenzo-naphtho-pero-pyrene (TNPP, $\rm{C_{40}H_{18}}$), hexa-benzo-coronene
(HBC, $\rm{C_{42}H_{18}}$), dicoronylene (DC, $\rm{C_{48}H_{20}}$) are
selected, and the molecular geometry and edge structure information are
summarized in Table 1. These selected PAHs can be used as a prototypical
example for large(r) PAHs (Andrews et al., 2015; Croiset et al., 2016), and
its size, from 32 to 48 C-number, that lies within the astrophysically
relevant range (Kokkin et al., 2008; Steglich et al., 2011; Gredel et al.,
2011), and also allows us to unambiguously identify the hydrogenation
processes for PAHs with all types of molecular geometry.

##  2 Experimental and calculation results

The experiment was performed on the apparatus equipped with a quadrupole ion
trap and reflection TOF mass spectrometer, together with a heat-able oven for
the natural gas-phase PAH species (provided by Kentax, with a purity greater
than 99.5 %) (Zhang et al., 2023) (details in Appendix A). Evaporated natural
PAH molecules were ionized using electron impact ionization ($\sim$ 82 eV) and
transported into the ion trap via an ion-gate. A hydrogen atom source is
installed to produce the H-atoms (HABS; MBE-Komponenten GmbH; Tschersich &
Bonin (1998)). Based on the operating conditions, the H-atoms were expected to
have a flux of $\sim$ 4.0 * 1014 H-atoms cm-2s-1, and the volume density of
H-atoms is $\sim$ 5*109 cm-3. The resulting mass spectrum of large,
astronomically relevant hydrogenated cationic PAHs is obtained and presented
in the left panel of Figures 1-6.

To illustrate the hydrogenation mechanism of large, astronomically relevant
PAH molecules, we theoretically study the reaction pathways between PAH
cations and H-atoms. The theoretical calculations were performed based on
density functional theory (DFT) with the hybrid density functional B3LYP
(Becke, 1992; Lee et al., 1988), as implemented in the Gaussian 16 program
(Frisch et al., 2016). The basis set of the 6-311++G** was selected and used
for all these systems. To account for the intermolecular interactions, the
dispersion-correction (D3, (Grimme et al., 2011)) is considered for each
system. All species’ geometries were optimized at the local minimum of their
potential energy surface in the calculation. Furthermore, the zero-point
vibrational energy (ZPVE) was obtained from the frequency calculation to
correct the molecular energy.

In addition, we note that due to the higher reactivity of H/D atoms with PAH
cations, the energy barrier in the accretion of H/D atoms on PAH cations is
very small, in the range of $\sim$10 to 30 meV, which have two orders of
magnitude smaller than the exothermic energy ($\sim$1.0 to 3.0 eV) (Cazaux et
al., 2016). In other words, the attachment energy barriers are almost
vanished, which we suppose it may be not play an important role in the
hydrogenation process. In addition, we suppose the collisional energy between
the PAH cations and H-atoms is not very high ($\sim$ 0.1 to 0.3 eV). So only
the exothermic energy for the reaction pathways needs to be considered in the
theoretical calculation (Cazaux et al., 2016; Schlathölter et al., 2020; Zhang
et al., 2023).

Furthermore, for the ion-atom collision reactions that under the gas phase
conditions, we consider the reaction collision can be happened if the
exothermic energy is around or higher than $\sim$ 1.0 eV. Given this, from our
obtained theoretical calculation results, the exothermic energy at each step
is all around or higher than $\sim$ 1.0 eV, so we regard the ion-atom
collision reaction rate between PAH cations and H atoms as the rate of
reaction in the gas phase (Schlathölter et al., 2020; Zhang et al., 2023).

The obtained calculation results of hydrogenated cationic large,
astronomically relevant PAHs are presented in the right panel of Figures 1-6
and Table 2-3. For all these PAH cations and hydrogenated PAH cations, the
doublet spin multiplicity is considered in the calculations.

$\rm{[C_{40}H_{18}]}^{+}$
---
Outer carbon sites
$\rm{[C_{40}H_{18}+H(1)]}^{+}$ |  -1.53 eV
$\rm{[C_{40}H_{18}+H(2)]}^{+}$ |  -1.54 eV
$\rm{[C_{40}H_{18}+H(3)]}^{+}$ |  -2.14 eV
$\rm{[C_{40}H_{18}+H(4)]}^{+}$ |  -1.54 eV
$\rm{[C_{40}H_{18}+H(5)]}^{+}$ |  -1.79 eV
$\rm{[C_{40}H_{18}+H(6)]}^{+}$ |  -2.10 eV
$\rm{[C_{40}H_{18}+H(7)]}^{+}$ |  -1.45 eV
$\rm{[C_{40}H_{18}+H(8)]}^{+}$ |  -2.11 eV
$\rm{[C_{40}H_{18}+H(9)]}^{+}$ |  -1.77 eV
Inner carbon sites
$\rm{[C_{40}H_{18}+H(a)]}^{+}$ |  -1.09 eV
$\rm{[C_{40}H_{18}+H(b)]}^{+}$ |  -1.30 eV
$\rm{[C_{40}H_{18}+H(c)]}^{+}$ |  -1.16 eV
$\rm{[C_{40}H_{18}+H(d)]}^{+}$ |  -0.93 eV
$\rm{[C_{40}H_{18}+H(e)]}^{+}$ |  -1.03 eV
$\rm{[C_{40}H_{18}+H(f)]}^{+}$ |  -1.37 eV
Center carbon sites
$\rm{[C_{40}H_{18}+H(A)]}^{+}$ |  -1.31 eV
$\rm{[C_{40}H_{18}+H(B)]}^{+}$ |  -1.19 eV
$\rm{[C_{40}H_{18}+H(C)]}^{+}$ |  -1.03 eV
$\rm{[C_{40}H_{18}+H(D)]}^{+}$ |  -1.22 eV
$\rm{[C_{40}H_{18}+H(E)]}^{+}$ |  -0.98 eV

Figure 1: Panel (A): evolution of the mass spectrum of the hydrogenated TNPP
cations with increasing H-atoms exposure time of 5.0, 10.0, 20.0, and 40.0 s;
panel (B): zoomed-in mass spectrum (40.0 s), revealing the presence of a
highly broadened mass distribution, and the large hydrogenated TNPP cations
$\rm[{C_{40}H_{18+18}}]^{+}$; right panel: the theoretical calculation results
for [C40H18]+ $+$ H.

$\rm{[C_{32}H_{14}]}^{+}$
---
Outer carbon sites
$\rm{[C_{32}H_{14}+H(1)]}^{+}$ |  -2.31 eV
$\rm{[C_{32}H_{14}+H(2)]}^{+}$ |  -1.84 eV
$\rm{[C_{32}H_{14}+H(3)]}^{+}$ |  -1.59 eV
$\rm{[C_{32}H_{14}+H(4)]}^{+}$ |  -1.82 eV
Inner carbon sites
$\rm{[C_{32}H_{14}+H(a)]}^{+}$ |  -0.94 eV
$\rm{[C_{32}H_{14}+H(b)]}^{+}$ |  -1.23 eV
Center carbon sites
$\rm{[C_{32}H_{14}+H(A)]}^{+}$ |  -0.98 eV
$\rm{[C_{32}H_{14}+H(B)]}^{+}$ |  -1.14 eV
$\rm{[C_{32}H_{14}+H(C)]}^{+}$ |  -0.96 eV

Figure 2: Panel (A): evolution of the mass spectrum of the hydrogenated
ovalene cations with increasing H atom exposure time of 5.0, 10.0, 20.0, and
40.0 s; panel (B): zoomed-in mass spectrum (40.0 s), revealing the presence of
a highly broadened mass distribution, and the large hydrogenated ovalene
cations $\rm[{C_{32}H_{14+14}}]^{+}$; right panel: the theoretical calculation
results for [C32H14]+ $+$ H.

$\rm{[C_{32}H_{16}]}^{+}$
---
Outer carbon sites
$\rm{[C_{32}H_{16}+H(1)]}^{+}$ |  -2.02 eV
$\rm{[C_{32}H_{16}+H(2)]}^{+}$ |  -1.45 eV
$\rm{[C_{32}H_{16}+H(3)]}^{+}$ |  -1.78 eV
$\rm{[C_{32}H_{16}+H(4)]}^{+}$ |  -1.94 eV
Inner carbon sites
$\rm{[C_{32}H_{16}+H(a)]}^{+}$ |  -1.12 eV
$\rm{[C_{32}H_{16}+H(b)]}^{+}$ |  -1.69 eV
$\rm{[C_{32}H_{16}+H(c)]}^{+}$ |  -1.48 eV
Center carbon sites
$\rm{[C_{32}H_{16}+H(A)]}^{+}$ |  -0.99 eV
$\rm{[C_{32}H_{16}+H(B)]}^{+}$ |  -1.39 eV

Figure 3: Panel (A): evolution of the mass spectrum of the hydrogenated
periflanthene cations with increasing H atom exposure time of 5.0, 10.0, 20.0,
and 40.0 s; panel (B): zoomed-in mass spectrum (40.0 s), revealing the
presence of a highly broadened mass distribution, and the large hydrogenated
periflanthene cations $\rm[{C_{32}H_{16+16}}]^{+}$; right panel: the
theoretical calculation results for [C32H16]+ $+$ H.

$\rm{[C_{34}H_{16}]}^{+}$
---
Outer carbon sites
$\rm{[C_{34}H_{16}+H(1)]}^{+}$ |  -1.78 eV
$\rm{[C_{34}H_{16}+H(2)]}^{+}$ |  -1.70 eV
$\rm{[C_{34}H_{16}+H(3)]}^{+}$ |  -1.43 eV
$\rm{[C_{34}H_{16}+H(4)]}^{+}$ |  -1.83 eV
$\rm{[C_{34}H_{16}+H(5)]}^{+}$ |  -2.10 eV
$\rm{[C_{34}H_{16}+H(6)]}^{+}$ |  -1.31 eV
$\rm{[C_{34}H_{16}+H(7)]}^{+}$ |  -2.10 eV
$\rm{[C_{34}H_{16}+H(8)]}^{+}$ |  -1.73 eV
Inner carbon sites
$\rm{[C_{34}H_{16}+H(a)]}^{+}$ |  -1.25 eV
$\rm{[C_{34}H_{16}+H(b)]}^{+}$ |  -1.22 eV
$\rm{[C_{34}H_{16}+H(c)]}^{+}$ |  -0.77 eV
$\rm{[C_{34}H_{16}+H(d)]}^{+}$ |  -0.92 eV
$\rm{[C_{34}H_{16}+H(e)]}^{+}$ |  -1.31 eV
Center carbon sites
$\rm{[C_{34}H_{16}+H(A)]}^{+}$ |  -1.01 eV
$\rm{[C_{34}H_{16}+H(B)]}^{+}$ |  -1.12 eV
$\rm{[C_{34}H_{16}+H(C)]}^{+}$ |  -0.96 eV
$\rm{[C_{34}H_{16}+H(D)]}^{+}$ |  -0.97 eV

Figure 4: Panel (A): evolution of the mass spectrum of the hydrogenated TBP
cations with increasing H atom exposure time of 5.0, 10.0, 20.0, and 40.0 s;
panel (B): zoomed-in mass spectrum (40.0 s), revealing the presence of a
highly broadened mass distribution, and the large hydrogenated TBP cations
$\rm[{C_{34}H_{16+16}}]^{+}$; right panel: the theoretical calculation results
for [C34H16]+ $+$ H.

$\rm{[C_{42}H_{18}]}^{+}$
---
Outer carbon sites
$\rm{[C_{42}H_{18}+H(1)]}^{+}$ |  -2.05 eV
$\rm{[C_{42}H_{18}+H(2)]}^{+}$ |  -1.62 eV
Inner carbon sites
$\rm{[C_{42}H_{18}+H(a)]}^{+}$ |  -1.25 eV
Center carbon sites
$\rm{[C_{42}H_{18}+H(A)]}^{+}$ |  -1.51 eV
$\rm{[C_{42}H_{18}+H(B)]}^{+}$ |  -1.18 eV

Figure 5: Panel (A): evolution of the mass spectrum of the hydrogenated HBC
cations with increasing H atom exposure time of 5.0, 10.0, 20.0, and 40.0 s;
panel (B): zoomed-in mass spectrum (40.0 s), revealing the presence of a
highly broadened mass distribution, and the large hydrogenated HBC cations
$\rm[{C_{42}H_{18+14}}]^{+}$; right panel: the theoretical calculation results
for [C42H18]+ $+$ H.

$\rm{[C_{48}H_{20}]}^{+}$
---
Outer carbon sites
$\rm{[C_{48}H_{20}+H(1)]}^{+}$ |  -2.08 eV
$\rm{[C_{48}H_{20}+H(2)]}^{+}$ |  -1.74 eV
$\rm{[C_{48}H_{20}+H(3)]}^{+}$ |  -1.47 eV
$\rm{[C_{48}H_{20}+H(4)]}^{+}$ |  -1.46 eV
$\rm{[C_{48}H_{20}+H(5)]}^{+}$ |  -1.77 eV
Inner carbon sites
$\rm{[C_{48}H_{20}+H(a)]}^{+}$ |  -1.04 eV
$\rm{[C_{48}H_{20}+H(b)]}^{+}$ |  -0.80 eV
$\rm{[C_{48}H_{20}+H(c)]}^{+}$ |  -1.16 eV
$\rm{[C_{48}H_{20}+H(d)]}^{+}$ |  -0.86 eV
Center carbon sites
$\rm{[C_{48}H_{20}+H(A)]}^{+}$ |  -1.06 eV
$\rm{[C_{48}H_{20}+H(B)]}^{+}$ |  -0.70 eV
$\rm{[C_{48}H_{20}+H(C)]}^{+}$ |  -1.02 eV
$\rm{[C_{48}H_{20}+H(D)]}^{+}$ |  -0.67 eV
$\rm{[C_{48}H_{20}+H(E)]}^{+}$ |  -0.75 eV

Figure 6: Panel (A): evolution of the mass spectrum of the hydrogenated DC cations with increasing H atom exposure time of 5.0, 10.0, 20.0, and 40.0 s; panel (B): zoomed-in mass spectrum (40.0 s), revealing the presence of a highly broadened mass distribution, and the large hydrogenated DC cations $\rm[{C_{48}H_{20+20}}]^{+}$; right panel: the theoretical calculation results for [C48H20]+ $+$ H. Table 2: The theoretical calculation results (outer side-edged carbon sites) for [C40H18]+ $+$ H and [C40H19]+ $+$ H.The doublet spin multiplicity is considered in all calculations in this table. sites diagram |  edge structure | add the first H-atoms | E(eV) | add the second H-atoms | E(eV)
---|---|---|---|---|---
| solo | $\rm{[C_{40}H_{18}+H(3)]}^{+}$ | -2.14 |  $\rm{[C_{40}H_{18}]}^{+}$ \+ $\rm{H_{2}}$ | -2.09
duo | $\rm{[C_{40}H_{18}+H(4)]}^{+}$ | -1.54 | $\rm{[C_{40}H_{18}+H(4,5)]}^{+}$ | -2.70
$\rm{[C_{40}H_{18}]}^{+}$ \+ $\rm{H_{2}}$ | -2.70
$\rm{[C_{40}H_{18}+H(5)]}^{+}$ | -1.79 | $\rm{[C_{40}H_{18}+H(5,4)]}^{+}$ | -2.44
$\rm{[C_{40}H_{18}]}^{+}$ \+ $\rm{H_{2}}$ | -2.44
$\rm{[C_{40}H_{18}+H(9)]}^{+}$ | -1.77 | $\rm{[C_{40}H_{18}+H(9,9^{\prime})]}^{+}$ | -2.44
$\rm{[C_{40}H_{18}]}^{+}$ \+ $\rm{H_{2}}$ | -2.46
trio | $\rm{[C_{40}H_{18}+H(6)]}^{+}$ | -2.10 | $\rm{[C_{40}H_{18}+H(6,7)]}^{+}$ | -1.81
$\rm{[C_{40}H_{18}+H(6,8)]}^{+}$ | -1.60
$\rm{[C_{40}H_{18}]}^{+}$ \+ $\rm{H_{2}}$ | -2.14
$\rm{[C_{40}H_{18}+H(7)]}^{+}$ | -1.45 | $\rm{[C_{40}H_{18}+H(7,6)]}^{+}$ | -2.46
$\rm{[C_{40}H_{18}+H(7,8)]}^{+}$ | -2.47
$\rm{[C_{40}H_{18}]}^{+}$ \+ $\rm{H_{2}}$ | -2.78
$\rm{[C_{40}H_{18}+H(8)]}^{+}$ | -2.11 | $\rm{[C_{40}H_{18}+H(8,6)]}^{+}$ | -1.80
$\rm{[C_{40}H_{18}+H(8,7)]}^{+}$ | -1.82
$\rm{[C_{40}H_{18}]}^{+}$ \+ $\rm{H_{2}}$ | -2.13
quarto | $\rm{[C_{40}H_{18}+H(1)]}^{+}$ |  -1.53 | $\rm{[C_{40}H_{18}+H(1,1^{\prime})]}^{+}$ | -1.98
$\rm{[C_{40}H_{18}+H(1,2)]}^{+}$ | -2.34
$\rm{[C_{40}H_{18}]}^{+}$ \+ $\rm{H_{2}}$ | -2.70
$\rm{[C_{40}H_{18}+H(2)]}^{+}$ | -1.54 | $\rm{[C_{40}H_{18}+H(2,1)]}^{+}$ | -2.33
|  $\rm{[C_{40}H_{18}]}^{+}$ \+ $\rm{H_{2}}$ | -2.70

###  2.1 Experimental results and calculation for the hydrogenation of PAH
cations

####  2.1.1 Experimental results and calculation for TNPP cations ([C40H18]+)
$+$ H

In Figure 1, the evolution of the mass spectrum of hydrogenated TNPP cations
is presented in the range of m/z=484-540. A series of hydrogenated TNPP
cations, [C40H18+n]+, are observed. As shown in Figure 1(A), the black line is
the TNPP cation mass spectrum before hydrogenation. In addition to the main
TNPP mass peak, some residual TNPP fragments (peaks due to H loss) were also
measured, such as C${}_{40}{\rm{H}_{16/17/18/19}}^{+}$, which are byproducts
of the electron impact ionization and fragmentation processes (Zhen et al.,
2014). This phenomenon is also present in the other mass spectra measured in
this paper for the same reason. By varying the H-atoms’ exposure time (from
5.0 to 10.0, 20.0, and 40.0 s), the hydrogenation degree of TNPP cations
changes. The m/z distribution exhibits the expected shift to higher masses,
which indicates that H-atoms are being added to TNPP cations. With H atom
exposure time increasing, the average intensity of each peak decreases, but
the total intensity of ions trapped in the ion trap is almost unchanged. As
shown in Figure 1(B), a zoomed-in mass spectrum (the H atom exposure time is
40.0 s) reveals a highly broadened mass distribution and the presence of newly
formed large hydrogenated TNPP cations: m/z=516, [C40H18+18]+, n=18, which
suggest that 18 H-atoms are being added to TNPP cations, the hydrogenated TNPP
cations are efficiently formed. In addition, no even-odd hydrogenated mass
patterns are observed in the hydrogenation experiments.

Meanwhile, there is no clear mass peaks that can attribute to the PAH
fragments (e.g., loss of C2H2) in our obtained mass spectrometry. We suppose
that the non-appearance of fragmentation mainly attributes to the superior
stability of large PAHs (listed in Table 1) upon hydrogenation compared to
smaller PAH (e. g., C16H10) (Schlathölter et al., 2020). And due to that, the
large PAHs may play an important role as an ideal catalyst for hydrogen
formation without destruction in the ISM (Tielens, 2013).

Regarding the hydrogenation pathway of TNPP cations, we believe that these
hydrogenated TNPP cations are formed through ion-molecule reaction pathways,
i.e., [C40H18]+ $+$ H-atoms. The reaction process between TNPP cations and
H-atoms occurs through sequential steps and repeatedly adds H-atoms. In
addition, from previous studies (Petrie et al., 1992; Le Page et al., 2001;
Cazaux et al., 2016; Zhang et al., 2023), the competition between
hydrogenation and dehydrogenation has been observed in the ion-molecule
reaction pathways, i.e., H2 is formed as a secondary product through the
reaction pathway as follows:

$\displaystyle[\rm{C_{40}H_{18}}]^{+}\stackrel{{\scriptstyle\rm
H}}{{\longrightarrow}}[\rm{C_{40}H_{18+n}}]^{+}+m*H_{2}$

As shown in Figure 1, TNPP (C40H18) has 18 outer (solo, duo, trio, and quarto
side-edged structures), 12 inner, and 10 center carbon sites, and we identify
each carbon skeleton structure’s effect on the hydrogenation processes. The
carbon reaction sites in symmetrical positions have similar reaction activity.
According to that, 20 reaction pathways are considered and obtained in the
theoretical calculations. The reaction sites are highlighted with different
colors and labeled: solo (purple, 3), duo (red, 4, 5, and 9), trio (green, 6,
7, and 8), and quarto (blue, 1, and 2), inner (a, b, c, d, e, and f) and
center (A, B, C, D, and E).

The binding energies of the mono-hydrogenated TNPP cations obtained are given
in the right panel of Figure 1. These 20 mono-hydrogenated TNPP cations are
divided into three groups: outer carbon edge, inner carbon edge, and center
carbon edge.

The first group is for the outer carbon edge, and we can see that all the
reaction pathways are exothermic. For quarto side-edged carbon sites, with
-1.53 and -1.54 eV for [C40H18 \+ H(1/2)]+; For solo side-edged carbon sites,
with -2.14 eV for [C40H18 \+ H(3)]+; For duo side-edged carbon sites, with
-1.54, -1.79, and -1.77 eV for [C40H18 \+ H(4/5/9)]+; For trio side-edged
carbon sites, with -2.10, -1.45, and -2.11 eV for [C40H18 \+ H(6/7/8)]+; The
second group is for the inner carbon edge, we can see all the reaction
pathways are exothermic. With -1.09, -1.30, -1.16, -0.93, -1.03, and -1.37 eV
for [C40H18 \+ H(a/b/c/d/e/f)]+. The third group is for the center carbon
edge, and we can see that all the reaction pathways are exothermic. With
-1.31, -1.19, -1.03, -1.22, and -0.98 eV for [C40H18 \+ H(A/B/C/D/E)]+,
respectively.

The exothermic energy for the formation of [C40H19]+, in the range of
0.93-2.14 eV, is relatively higher and can stabilize the whole molecules. The
ion-molecule reactions between TNPP cations and H-atoms readily occur, and we
propose that [C40H19]+ formed in the lab are a mixture with different possible
isomers.

####  2.1.2 Experimental results and calculation for ovalene cations
([C32H14]+) $+$ H

In Figure 2, the evolution of the mass spectrum of hydrogenated ovalene
cations is presented in the range of m/z=384-440. A series of hydrogenated
ovalene cations, [C32H14+n]+, are observed. As shown in Figure 2(A), by
varying the H-atoms’ exposure time (from 5.0 to 10.0, 20.0, and 40.0 s), the
hydrogenation degree of ovalene cations changes. The m/z distribution exhibits
the expected shift to higher masses, which indicates that H-atoms are being
added to ovalene cations. With H atom exposure time increasing, the average
intensity of each peak decreases, but the total intensity of ions trapped in
the ion trap is almost unchanged. As shown in Figure 2(B), a zoomed-in mass
spectrum (the H-atoms exposure time is 40.0 s) reveals a highly broadened mass
distribution and the presence of newly formed large hydrogenated ovalene
cations: m/z=412, [C32H14+14]+, n=14, which suggest that 14 H-atoms are being
added to ovalene cations, the hydrogenated ovalene cations are efficiently
formed.

Regarding the hydrogenation pathway of ovalene cations, similar to the TNPP
cations and previous work (Cazaux et al., 2016; Zhang et al., 2023), we
believe that these hydrogenated ovalene cations are formed through ion-
molecule reaction pathways, i.e., [C32H14]+ $+$ H-atoms. The reaction process
between ovalene cations and H-atoms occurs through sequential steps and
repeatedly adds H-atoms. In addition, H2 is formed as a secondary product
through the reaction pathway as follows:

$\displaystyle[\rm{C_{32}H_{14}}]^{+}\stackrel{{\scriptstyle\rm
H}}{{\longrightarrow}}[\rm{C_{32}H_{14+n}}]^{+}+m*H_{2}$

As shown in Figure 2, ovalene ($\rm{C_{32}H_{14}}$) has 14 outer (solo and duo
side-edged structures), 8 inner, and 10 center carbon sites, and we will
identify each carbon skeleton structure’s effect on the hydrogenation
processes. The carbon reaction sites in symmetrical positions have similar
reaction activity. According to that, 9 reaction pathways are considered and
obtained in the theoretical calculations. The reaction sites are highlighted
with different colors and labeled solo (purple, 1), duo (red, 2, 3, and 4),
inner (a and b), and center (A, B, and C).

The binding energies of the mono-hydrogenated ovalene cations are given in the
right panel of Figure 2. These 9 mono-hydrogenated ovalene cations are divided
into three hydrogenation groups: outer carbon edge, inner carbon edge, and
center carbon edge. The first group is for the outer carbon edge, and we can
see that all the reaction pathways are exothermic. For solo side-edged carbon
sites, with -2.31 eV for [C32H14 \+ H(1)]+; For duo side-edged carbon sites,
with -1.84, -1.59, and -1.82 eV for [C32H14 \+ H(2/3/4)]+; The second group is
for the inner carbon edge, we can see all the reaction pathways are
exothermic. With -0.94, and -1.23 eV for [C32H14 \+ H(a/b)]+, respectively.
The third group is for the center carbon edge, and we can see that all the
reaction pathways are exothermic. With -0.98, -1.14, and -0.96 eV for [C32H14
\+ H(A/B/C)]+, respectively.

The exothermic energy for the formation of [C32H15]+, in the range of
0.94-2.31 eV, is relatively higher and can stabilize the whole molecules. The
ion-molecule reactions between ovalene cations and H-atoms readily occur, and
so we propose that [C32H15]+ formed in the lab are a mixture with different
possible isomers.

####  2.1.3 Experimental results and calculation for periflanthene cations
([C32H16]+) $+$ H

In Figure 3, the evolution of the mass spectrum of hydrogenated periflanthene
cations is presented in the range of m/z=388-444. A series of hydrogenated
periflanthene cations, [C32H16+n]+, are observed. As shown in Figure 3(A), by
varying the H-atoms’ exposure time (from 5.0 to 10.0, 20.0, and 40.0 s), the
hydrogenation degree of periflanthene cations changes. The m/z distribution
exhibits the expected shift to higher masses, which indicates that H-atoms are
being added to periflanthene cations. As shown in Figure 3(B), a zoomed-in
mass spectrum (the H atom exposure time is 40.0 s) reveals a highly broadened
mass distribution and the presence of newly formed large hydrogenated
periflanthene cations: m/z=416, [C32H16+16]+, n=16, which suggest that 16
H-atoms are being added to periflanthene cations, the hydrogenated
periflanthene cations are efficiently formed.

Regarding the hydrogenation pathway of periflanthene cations, we believe that
these hydrogenated periflanthene cations are formed through ion-molecule
reaction pathways, i.e., [C32H16]+ $+$ H-atoms. The reaction process between
periflanthene cations and H-atoms occurs through sequential steps and
repeatedly adds H-atoms. In addition, H2 is formed as a secondary product
through the reaction pathway as follows:

$\displaystyle[\rm{C_{32}H_{16}}]^{+}\stackrel{{\scriptstyle\rm
H}}{{\longrightarrow}}[\rm{C_{32}H_{16+n}}]^{+}+m*H_{2}$

As shown in Figure 3, periflanthene (C32H16) has 16 outer (duo and quarto
side-edged structures), 12 inner, and 4 center carbon sites, and we identify
each carbon skeleton structure’s effect on the hydrogenation processes. The
reaction sites in symmetrical positions have similar reaction activity.
According to that, 9 reaction pathways are considered and obtained in the
theoretical calculations. The reaction sites are highlighted with different
colors and labeled duo (red, 1, and 2), quarto (blue, 3, and 4), inner (a, b,
and c), and center (A and B).

The binding energies of the mono-hydrogenated periflanthene cations are given
in the right panel of Figure 3. These 9 mono-hydrogenated periflanthene
cations are divided into three hydrogenation groups: outer edge, inner edge,
and center edge. The first group is for the outer carbon edge, and we can see
that all the reaction pathways are exothermic. For duo side-edged carbon
sites, with -2.02 and -1.45 eV for [C32H16 \+ H(1/2)]+; For quarto side-edged
carbon sites, with -1.78 and -1.94 eV for [C32H16 \+ H(3/4)]+; The second
group is for the inner carbon edge, we can see all the reaction pathways are
exothermic. With -1.12, -1.69, and -1.48 eV for [C32H16 \+ H(a/b/c)]+. The
third group is for the center carbon edge, and we can see that all the
reaction pathways are exothermic. With -0.99 and -1.39 eV for [C32H16 \+
H(A/B)]+, respectively.

The exothermic energy for the formation of [C32H17]+, in the range of
0.99-2.02 eV, is relatively higher and can stabilize the whole molecules. The
ion-molecule reactions between ovalene cations and H-atoms readily occur, and
so we propose that [C32H17]+ formed in the lab are a mixture with different
possible isomers.

####  2.1.4 Experimental results and calculation for TBP cations ([C34H16]+)
$+$ H

In Figure 4, the evolution of the mass spectrum of hydrogenated TBP cations is
presented in the range of m/z=408-464. A series of hydrogenated TBP cations,
[C34H16+n]+, are observed. As shown in Figure 4(A), by varying the H-atoms’
exposure time (from 5.0 to 10.0, 20.0, and 40.0 s), the hydrogenation degree
of TBP cations changes. The m/z distribution exhibits the expected shift to
higher masses, which indicates that H-atoms are being added to TBP cations. As
shown in Figure 4(B), a zoomed-in mass spectrum (the H-atoms exposure time is
40.0 s) reveals a highly broadened mass distribution and the presence of newly
formed large hydrogenated TBP cations: m/z=440, [C34H16+16]+, n=16, which
suggest that 16 H-atoms are being added to TBP cations, the hydrogenated TBP
cations are efficiently formed.

Regarding the hydrogenation pathway of TBP cations, we believe that these
hydrogenated TBP cations are formed through ion-molecule reaction pathways,
i.e., [C34H16]+ $+$ H-atoms. The reaction process between TBP cations and
H-atoms occurs through sequential steps and repeatedly adds H-atoms. In
addition, H2 is formed as a secondary product through the reaction pathway as
follows:

$\displaystyle[\rm{C_{34}H_{16}}]^{+}\stackrel{{\scriptstyle\rm
H}}{{\longrightarrow}}[\rm{C_{34}H_{16+n}}]^{+}+m*H_{2}$

As shown in Figure 4, TBP (C34H16) has 16 outer (duo and trio side-edged
structures), 10 inner, and 8 center carbon sites, and we identify each carbon
skeleton structure’s effect on the hydrogenation processes. The reaction sites
in symmetrical positions have similar reaction activity. According to that, 17
reaction pathways are considered and obtained. The reaction sites are
highlighted with different colors and labeled: duo (red, 1, 2, 3, 4, and 8),
trio (green, 5, 6, and 7), inner (a, b, c, d, and e) and center (A, B, C, and
D).

The binding energies of the mono-hydrogenated TBP cations are given in the
right panel of Figure 4. These 17 mono-hydrogenated TBP cations are divided
into three hydrogenation groups: outer carbon edge, inner carbon edge, and
center carbon edge. The first group is for the outer carbon edge, and we can
see that all the reaction pathways are exothermic. For duo side-edged carbon
sites, with -1.78, -1.70, -1.43, -1.83, and -1.73 eV for [C34H16 \+
H(1/2/3/4/8)]+; For trio side-edged carbon sites, with -2.10, -1.31, and -2.10
eV for [C34H16 \+ H(5/6/7)]+; The second group is for the inner carbon edge,
we can see all the reaction pathways are exothermic. With -1.25, -1.22, -0.77,
-0.92, and -1.31 eV for [C34H16 \+ H(a/b/c/d/e)]+. The third group is for the
center carbon edge, and we can see that all the reaction pathways are
exothermic. With -1.01, -1.12, -0.96, and -0.97 eV for [C34H16 \+
H(A/B/C/D)]+, respectively.

The exothermic energy for the formation of [C34H17]+, in the range of
0.77-2.10 eV, is relatively higher and can stabilize the whole molecules. The
ion-molecule reactions between ovalene cations and H-atoms readily occur, and
so we propose that [C34H17]+ formed in the lab are a mixture with different
possible isomers.

####  2.1.5 Experimental results and calculation for HBC cations ([C42H18]+)
$+$ H

In Figure 5, the evolution of the mass spectrum of hydrogenated HBC cations is
presented in the range of m/z=504-560. A series of hydrogenated HBC cations,
[C42H18+n]+, are observed. As shown in Figure 5(A), by varying the H-atoms’
exposure time (from 5.0 to 10.0, 20.0, and 40.0 s), the hydrogenation degree
of HBC cations changes. The m/z distribution exhibits the expected shift to
higher masses, which indicates that H-atoms are being added to HBC cations. As
shown in figure 5(B), a zoomed-in mass spectrum (the H-atoms exposure time is
40.0 s) reveals a highly broadened mass distribution and the presence of newly
formed large hydrogenated HBC cations: m/z=536, [C42H18+14]+, n=14, which
suggest that 14 H-atoms are being added to HBC cations, the hydrogenated HBC
cations are efficiently formed.

Regarding the hydrogenation pathway of HBC cations, we believe that these
hydrogenated HBC cations are formed through ion-molecule reaction pathways,
i.e., [C42H18]+ $+$ H-atoms. The reaction process between HBC cations and
H-atoms occurs through sequential steps and repeatedly adds H-atoms. In
addition, H2 is formed as a secondary product through the reaction pathway as
follows:

$\displaystyle[\rm{C_{42}H_{18}}]^{+}\stackrel{{\scriptstyle\rm
H}}{{\longrightarrow}}[\rm{C_{42}H_{18+n}}]^{+}+m*H_{2}$

As shown in Figure 5, HBC (C42H18) has 18 outer (trio side-edged structures),
12 inner, and 12 center carbon sites, and we identify each carbon skeleton
structure’s effect on the hydrogenation processes. The reaction sites in
symmetrical positions have similar reaction activity. According to that, 5
reaction pathways are considered and obtained. The reaction sites are
highlighted with different colors and labeled trio (green, 1 and 2), inner
(a), and center (A and B).

The binding energies of the mono-hydrogenated HBC cations are given in the
right panel of Figure 5. These 5 mono-hydrogenated HBC cations are divided
into three hydrogenation groups: outer edge, inner edge, and center edge. The
first group is for the outer carbon edge, and we can see that all the reaction
pathways are exothermic. For trio side-edged carbon sites, with -2.05 and
-1.62 eV for [C42H18 \+ H(1/2)]+; The second group is for the inner carbon
edge, we can see the reaction pathway is exothermic. With -1.25 eV for [C42H18
\+ H(a)]+. The third group is for the center carbon edge, and we can see that
all the reaction pathways are exothermic. With -1.51 and -1.18 eV for [C42H18
\+ H(A/B)]+, respectively.

The exothermic energy for the formation of [C42H19]+, in the range of
1.18-2.05 eV, is relatively higher and can stabilize the whole molecules. The
ion-molecule reactions between ovalene cations and H-atoms readily occur, and
so we propose that [C42H19]+ formed in the lab are a mixture with different
possible isomers. In addition, the gas-phase hydrogen/deuterium exchange on
HBC cations is studied (Zhang et al., 2022). The exothermic energy for
deuteration and dedeuteration reaction pathway is relatively high, and the
value of exothermic energy is consistent with the results that obtained in
here.

####  2.1.6 Experimental results and calculation for DC cations ([C48H20]+)
$+$ H

In Figure 6, the evolution of the mass spectrum of hydrogenated DC cations is
presented in the range of m/z=580-636. A series of hydrogenated DC cations,
[C48H20+n]+, are observed. As shown in Figure 6(A), by varying the H-atoms’
exposure time (from 5.0 to 10.0, 20.0, and 40.0 s), the hydrogenation degree
of DC cations changes. The m/z distribution exhibits the expected shift to
higher masses, which indicates that H-atoms are being added to DC cations. As
shown in Figure 6(B), a zoomed-in mass spectrum (the H-atoms exposure time is
40.0 s) reveals a highly broadened mass distribution and the presence of newly
formed large hydrogenated DC cations: m/z=616, [C48H20+20]+, n=20, which
suggest that 20 H-atoms are being added to DC cations, the hydrogenated DC
cations are efficiently formed.

Regarding the hydrogenation pathway of DC cations, we believe that these
hydrogenated DC cations are formed through ion-molecule reaction pathways,
i.e., [C48H20]+ $+$ H-atoms. The reaction process between DC cations and
H-atoms occurs through sequential steps and repeatedly adds H-atoms. In
addition, H2 is formed as a secondary product through the reaction pathway as
follows:

$\displaystyle[\rm{C_{48}H_{20}}]^{+}\stackrel{{\scriptstyle\rm
H}}{{\longrightarrow}}[\rm{C_{48}H_{20+n}}]^{+}+m*H_{2}$

As shown in Figure 6, DC (C48H20) has 20 outer (solo and duo side-edged
structures), 14 inner, and 14 center carbon sites, and we identify each carbon
skeleton structure’s effect on the hydrogenation processes. The reaction sites
in symmetrical positions have similar reaction activity. According to that, 14
reaction pathways are considered and obtained. The reaction sites are
highlighted with different colors and labeled: solo (purple, 1), duo (red, 2,
3, 4, and 5), inner (a, b, c, and d), and center (A, B, C, D, and E).

The binding energies of the mono-hydrogenated DC cations are given in the
right panel of Figure 6. These 14 mono-hydrogenated DC cations are divided
into three hydrogenation groups: outer edge, inner edge, and center edge. The
first group is for the outer carbon edge, and we can see that all the reaction
pathways are exothermic. For solo side-edged carbon sites, with -2.08 eV for
[C48H20 \+ H(1)]+; For duo side-edged carbon sites, with -1.74, -1.47, -1.46,
and -1.77 eV for [C48H20 \+ H(2/3/4/5)]+; The second group is for the inner
carbon edge, we can see the reaction pathway is exothermic. With -1.04, -0.80,
-1.16, and -0.86 eV for [C48H20 \+ H(a/b/c/d)]+. The third group is for the
center carbon edge, and we can see that all the reaction pathways are
exothermic. With -1.06, -0.70, -1.02, -0.67, and -0.75 eV for [C48H20 \+
H(A/B/C/D/E)]+, respectively.

The exothermic energy for the formation of [C48H21]+, in the range of
0.67-2.08 eV, is relatively higher and can stabilize the whole molecules. The
ion-molecule reactions between ovalene cations and H-atoms readily occur, and
so we propose that [C48H21]+ formed in the lab are a mixture with different
possible isomers.

Table 3: The theoretical calculation results for the bay region and non-bay region structures. Using ovalene ($\rm{C_{32}H_{14}}$) and periflanthene ($\rm{C_{32}H_{16}}$) as a comparable example. The doublet spin multiplicity is considered in all calculations in this table. edge structure and sites diagram | as the first H added | E(eV) | as the third H added | E(eV)
---|---|---|---|---
Ovalene, non-bay region | $\rm{[C_{32}H_{14}+H(1)]}^{+}$ | -2.31 | $\rm{[C_{32}H_{14}+2H(2,3)+H(1)]}^{+}$ | -2.00
$\rm{[C_{32}H_{14}+H(4)]}^{+}$ | -1.81 | $\rm{[C_{32}H_{14}+2H(2,3)+H(4)]}^{+}$ | -1.63
periflanthene, with bay region | $\rm{[C_{32}H_{16}+H(1^{\prime})]}^{+}$ | -1.78 | $\rm{[C_{32}H_{16}+2H(1,2)+H(1^{\prime})]}^{+}$ | -1.96
$\rm{[C_{32}H_{16}+H(3)]}^{+}$ | -2.02 | $\rm{[C_{32}H_{16}+2H(1,2)+H(3)]}^{+}$ | -1.92

###  2.2 Calculation for the subsequent hydrogenation pathways

For the subsequent hydrogenation pathways of the hydrogenated PAH cations,
based on the molecular structural symmetry and the previous theoretical
calculation results, we assume that further H-atom attachment and abstraction
tend to occur on the outer carbon sites. In addition, the subsequent
hydrogenation of hydrogenated PAH cations has many possible reaction pathways;
for simplicity, we only chose the subsequent react carbon sites that are close
to the already hydrogenated carbon sites (Petrie et al., 1992; Le Page et al.,
2001; Cazaux et al., 2016; Zhang et al., 2023).

####  2.2.1 The hydrogenation pathways for the hydrogenated TNPP cations
([C40H19]+) $+$ H

For the subsequent hydrogenation pathways of the hydrogenated PAH cations, we
take TNPP as a typical example to calculate the hydrogenation processes. As
shown in Table 1, TNPP has all kinds of CH groups, and the different edge
structures are highlighted with different colors, which allows us to identify
the edge effect on the hydrogenation processes for such a molecular geometry.
Based on the obtained calculation results of hydrogenated TNPP cations
([C40H19]+) $+$ H-atoms in Figure 1. For simplicity, to the subsequent adduct
reaction pathways, hydrogenated TNPP cations ([C40H19]+) $+$ H-atoms are
calculated, and the calculation results are presented in Table 2.

Two types of reaction pathways are obtained: one reacts with its neighbor
carbon sites (CH group) that add the H-atoms directly and form a CH2 unit; the
other one reacts with the hydrogenated group (CH2) the CH unit is newly
formed, and H2 is formed as a secondary product.

To the solo edge, only one reaction pathways is obtained, [C40H18 \+ H(3)]+ \+
H $\rightarrow$ [C40H18]+ \+ H2, the exothermic energy is 2.09 eV; To the duo,
trio, and quarto edge, two type reaction pathway obtained, one is add the
second H-atoms in its neighbor carbon sites, the other one is form H2. We can
see that all the reaction pathways are exothermic. The exothermic energy for
the formation of [C40H20]+, in the range of 1.60-2.70 eV, is relatively higher
and can stabilize the whole molecules. The ion-molecule reactions between
C40H19 cations and H-atoms readily occur, and so we propose that [C40H20]+
formed in the lab are a mixture with different possible isomers.

H2 is efficiently formed as a secondary product, and the exothermic energies
for the dehydrogenated pathway are around $\sim$ 2.3 eV. Given the results
presented in this work, the potential for large PAH cations to act as
catalysts for molecular H2 formation is confirmed (Boschman et al., 2012;
Thrower et al., 2019; Pantazidis et al., 2019). In addition, except for the
trio edge, all the exothermic energies for the second are higher than the
first one. The higher exothermic energies suggest that after adding the first
H-atom, its neighbor carbon site becomes more chemically active. The trio edge
structure, mainly due to the hydrogenation of the middle trio carbon site,
destroys the aromaticity of the whole C-ring.

####  2.2.2 The hydrogenation pathways for the hydrogenated PAH cation with
the bay region and non-bay region structures

For PAHs with the bay region and non-bay region structures, we take ovalene
($\rm{C_{32}H_{14}}$), periflanthene ($\rm{C_{32}H_{16}}$) as a comparable
example with the same size to calculate the hydrogenation processes. As shown
in Table 1, ovalene has a non-bay region structure, and periflanthene has six
bay-region structures. This allows us to identify the bay-region effect on the
hydrogenation processes for such a molecular geometry.

For simplicity, the calculation results are presented in Table 3. To ovalene
cations, two reaction pathways are calculated, [C32H14 \+ 2H(2,3)]+ \+ H
$\rightarrow$ [C32H14 +3H(2,3,1)]+ and [C32H14 \+ 2H(2,3)]+ \+ H $\rightarrow$
[C32H14 \+ 3H(2,3,4)]+. We can see the reaction pathway is exothermic, with
-2.00 and -1.63 eV. To periflanthene cations, two reaction pathways are
calculated, [C32H16 \+ 2H(1,2)]+ \+ H $\rightarrow$ [C32H16 +3H(1,2,1’)]+ and
[C32H16 \+ 2H(1,2)]+ \+ H $\rightarrow$ [C32H16 \+ 3H(1,2,3)]+. We can see the
reaction pathway is exothermic, with -1.96 and -1.92 eV.

We can see, when compared with the first H-atoms, the exothermic energies of
hydrogenation reaction pathways on the bay or non-bay region of hydrogenated
cations located in a similar range and have no differences.

Figure 7: The influencing factors that affect the hydrogenation chemical
reactivity: panel (A): carbon skeleton structure’s effect: outer, inner, and
center; panel (B): side-edged structures’ effect: solo, duo, trio, and quarto;
panel (C): molecular size’s effect.  Figure 8: Computed vibrational normal
modes for the mono-hydrogenated TNPP cations: panel (A) is the spectrum of
[C40H18]+; panel (B-J) is the spectrum of [C40H18+H]+ (H atom added to outer
carbon sites); panel (K-M) is the spectrum of [C40H18+H]+ (H atom added to
inner carbon sites); panel (N-P) is the spectrum of [C40H18+H]+ (H atom added
to center carbon sites). The vibrational band positions are scaled by a
constant factor of 0.9670. Figure 9: Computed vibrational normal modes for the
di-hydrogenated TNPP cations ([C40H18+2H]+). The vibrational band positions
are scaled by a constant factor of 0.9670.

###  2.3 Results discussion

Overall, the results obtained from the theoretical calculation are consistent
with the experimental results. The obtained exothermic energy for each
hydrogenation reaction pathway is relatively high, which is consistent with
the results we observed in our experiments that the ion-molecule collision
reactions between PAH cations and H-atoms readily occur. From the calculation
results on the hydrogenation processes of the hydrogenated PAH cations, we
conclude that adding H-atoms to the carbon skeleton of PAH cations is a
relatively independent event. As these reaction pathways are relatively
independent and random events, the chance of their occurrence is entirely
determined by the already hydrogenated carbon sites and the remaining
hydrogenated carbon sites on the carbon skeleton of large cationic PAHs
(Cazaux et al., 2016, 2019; Zhang et al., 2023). In addition, the competition
between hydrogenation and dehydrogenation is confirmed that H2 is efficiently
formed as a secondary product. Given the results presented in this work, the
potential for large PAH cations to act as catalysts for molecular H2 formation
is confirmed (Boschman et al., 2012; Thrower et al., 2019; Pantazidis et al.,
2019).

From the theoretical calculation, bonding ability plays an important role in
the hydrogenation processes. Accordingly, some hydrogenation reaction pathways
have higher exothermic energies, which means that these hydrogenation
processes are more likely to occur, i.e., the carbon sites for hydrogenation
have relatively high chemical reactivity. In the following subsections, we
will discuss the factors that affect the chemical reactivity of these carbon
reaction sites, including the effect of carbon skeleton structure, the side-
edged structure, the molecular size, the bay region structure, and the
neighboring hydrogenation, as presented in Figure 7.

####  2.3.1 Carbon skeleton structure’s effect: outer, inner, and center

The exothermic energies of all these carbon sites for the hydrogenation are
presented in Figure 7(A) as a function of carbon skeleton structures. We can
see the exothermic energies of hydrogenation reaction pathways on the
different types of carbon skeleton (e.g., outer, inner, and center carbon
sites) have some differences: the exothermic energies of inner and center
carbon sites are similar that located in the range of 0.6-1.6 eV, while the
exothermic energies of outer carbon sites are mainly located in the range of
1.3-2.3 eV. Although there is some overlap in their energy ranges, the higher
exothermic energies of outer than inner and center suggest that outer carbon
sites have relatively higher chemical reactivity than the inner and center
carbon sites, i.e., the outer carbon sites will more easily be hydrogenated.
The H atom attachment and abstraction tend to occur on the outer carbon sites
according to previous investigations (Elias et al., 2009; Cazaux et al.,
2016).

However, in terms of the total number of carbon sites, the sum of inner and
center carbon sites is more than that of outer, especially as the PAH becomes
larger and more compact, the proportion of inner and center carbon sites will
increase, i.e., the proportion of outer carbon sites in the total number will
affect the collision reaction probability.

####  2.3.2 Side-edged structure’s effect: solo, duo, trio, and quarto

The exothermic energies of all these outer side-edged carbon sites for the
hydrogenation are presented in Figure 7(B) as a function of side-edged
structures. We can see the exothermic energies of hydrogenation reaction
pathways on the different types of side-edged structures (e.g., solo, duo,
trio, and quarto) have some differences: the exothermic energies of solo are
located in the range of 2.1-2.3 eV; the exothermic energies of duo are mainly
located in the range of 1.3-2.0 eV; the exothermic energies of trio are mainly
located in the range of 1.2-2.1 eV; the exothermic energies of quarto are
mainly located in the range of 1.7-1.9 eV.

Although there is some overlap in their energy ranges, the higher exothermic
energies of solo carbon sites are higher than others, and the solo carbon
sites have relatively higher chemical reactivity than others. The exothermic
energies of duo and quarto carbon sites are quite similar, suggesting that duo
and quarto carbon sites have relatively similar chemical reactivity. The
exothermic energies of trio carbon sites are scattered in a relatively large
range that the middle carbon sites are $\sim$ 0.5 eV smaller than the side,
which suggests that side carbon sites have relatively higher chemical
reactivity than the middle position of trios. Based on that, the solo carbon
sites and the side carbon sites of the trio edge will more easily be
hydrogenated. However, in terms of each PAH, the proportion of each side-edged
structure in the total number will affect the collision reaction probability.

####  2.3.3 Molecular size’s effect

The exothermic energies of all these outer side-edged carbon sites for the
hydrogenation are presented in Figure 7(C) as a function of molecular size.
The exothermic energies of hydrogenation reaction pathways on different sizes
(e.g., from 32 to 48 C-number) are located in a similar range and have no
differences. PAHs with different molecular sizes have a relatively similar
chemical reactivity, i.e., no molecular size effect on the hydrogenation
processes. The no molecular size effect conclusion is working in the size
range (32-48 C-atoms) that is presented here, but it may not work in other
molecular size ranges.

####  2.3.4 Five- and six-membered C-ring structure’s effect

As presented in Figure 2 and Figure 3, ovalene and periflanthene have 32
C-atoms, but their molecular structure is different. Ovalene is a
pericondensed PAH with six-member C-ring, and periflanthene is a catacondensed
PAH with two five-membered C-ring (only for the inner and center carbon
sites). From the obtained calculation results, we can see the exothermic
energies of hydrogenation reaction pathways on five-membered C-ring and six-
membered C-ring have some differences: with -1.69 and -1.48 eV for [C32H16 \+
H(b/c)]+, -1.39 eV for [C32H16 \+ H(B)]+, respectively; while with -0.94 and
-1.23 eV for [C32H14 \+ H(a/b)]+,-0.98, -1.14 and -0.96 eV for [C32H14 \+
H(A/B/C)]+, respectively. The five-membered C-ring carbon sites have
relatively higher chemical reactivity than the six-membered C-ring.

####  2.3.5 Neighboring hydrogenation’s effect

As presented in Table 2, from our calculations, except for the trio edge, all
the exothermic energies for the second (in the neighbor carbon sites) are
higher than the first one, i.e., the carbon site becomes more chemically
active by its neighboring carbon site’s hydrogenation. The trio edge
structure, mainly due to the hydrogenation of the middle carbon site, destroys
the aromaticity of the whole C-ring. We note that we performed only some of
these related theoretical calculations. When the amount of hydrogen addition
is higher, some intramolecular interactions and other reaction formation
pathways may also exist.

####  2.3.6 Bay region structure’s effect

From previous work (Castellanos et al., 2018), the bay and non-bay region
structure have a very important impact on dehydrogenation. However, as
presented in Table 3, from our calculations, the exothermic energies of
hydrogenation reaction pathways with bay or non-bay structures have no
differences. PAHs with bay or non-bay structures have a similar chemical
reactivity, i.e., no bay region structure’s effect on the hydrogenation
processes. These reaction pathways are relatively independent and random
events, and the chance of their occurrence is entirely determined by the
already hydrogenated carbon sites and the remaining hydrogenated carbon sites
on the carbon skeleton of large cationic PAHs (Cazaux et al., 2016; Zhang et
al., 2023).

##  3 IR spectra of hydrogenated PAH cations

These possible newly formed hydrogenated PAH cations obtained above may also
be the candidates of the observed IR interstellar bands (Schutte et al.,
1993). They may exist in the same interstellar area through an evolutionary
ion-molecular reaction network between PAHs and H-atoms that may contribute to
the observed interstellar spectrum, which motivates the spectroscopic studies
(Peeters et al., 2004; Tielens, 2013, and references therein). Based on the
calculation results and to obtain the IR spectra of these molecules after the
hydrogenation processes, the IR spectra of these molecules were obtained. For
these newly formed molecules, the calculations were performed with the
6-311++G(d, p) basis set. The vibrational band positions are scaled by a
uniform factor of 0.9670, and the black line is the spectra simulated by
Gaussians with a full-width half-maximum of 8 cm-1 (Boersma et al., 2014).

###  3.1 IR spectra of mono-hydrogenated PAH cations

The computed vibrational normal modes for the mono-hydrogenated TNPP cations
are presented in Figure 8, in the range of 0$-$3500 cm-1: panel (A) is the IR
spectrum of [C40H18]+ (without hydrogenation); panel (B-J, red) is the IR
spectrum of [C40H18+H]+ (H atom added to outer carbon sites); panel (K-M,
pink) is the IR spectrum of [C40H18+H]+ (H atom added to inner carbon sites);
panel (N-P, blue) is the IR spectrum of [C40H18+H]+ (H atom added to center
carbon sites). For further comparison, the IR spectra of other mono-
hydrogenated PAH cations are provided in Appendix B (Figures B1-B5).

The IR spectra of [C40H18+H]+ are very complex, and we only conclude two
characteristic peaks: 3.4-3.5 $\mu$m is the stretch vibration of CH2 when the
H-atoms are added to the outer carbon sites of TNPP cations; 3.6-3.7 $\mu$m is
the stretch vibration of CH when the H-atoms are added to the inner and center
carbon sites of TNPP cations. As can be seen in Figure 8, the spectral
intensity of hydrogenated TNPP cations becomes weaker when compared to that of
C40H18+ (without hydrogenation) (e.g., the strength of C-C stretch).

###  3.2 IR spectra of di-hydrogenated PAH cations

The computed vibrational normal modes for the di-hydrogenated TNPP cations are
presented in Figure 9, in the range of 0$-$3500 cm-1. As can be seen in Figure
9, 3.3-3.6 $\mu$m are the characteristic stretch vibrations of CH2 when the
TNPP cations attached with 2 extra H atoms, which is a wider range than that
of mono-hydrogenated TNPP cations. Moreover, the spectral intensity of di-
hydrogenated TNPP cations (except [C40H18+2H(1,2)]+) becomes weaker when
compared to that of C40H18+ (without hydrogenation). It has no significant
differences when compared to that of [C40H18+H]+ (mono-hydrogenated TNPP
cations) (e.g., the strength of C-C stretch).

In general, the IR spectra of the TNPP cations are relatively similar to the
newly formed hydrogenated TNPP cations. Some new vibrational modes were
preserved, while others were not, and some newly vibrational modes were
formed, and the vibrational peaks were variable due to the influence of their
surrounding environment. These obtained spectra reveal the complexity of
molecule structure and the complexity of their infrared spectra, which also
illustrates the important role of the complex organic molecules in the carbon
skeleton and the connection type of clusters.

##  4 Astronomical implications

As a complex molecular system, PAH compounds have very complex molecular
evolution characteristics and spatial distribution in interstellar space
(Tielens, 2013, and references therein). In the chemical evolution network,
PAH molecules are affected and constrained by the interstellar UV radiation,
the flux of H-atoms, hydrogen ions, and other coexisting molecules during the
different interstellar evolution periods (Tielens, 2013; Zhang et al., 2023).
The evolution of PAH molecules in response to H atom bombardment is very
complex. In the present paper, we demonstrate the processes taking place in
PAH molecules in response to H atom bombardment from different perspectives,
including in experiments and quantitative calculations. In contrast to our
laboratory studies, hydrogenation of PAHs in PDRs is similar to that, mainly
due to H-atom bombardment in the gas phase. Hence, our experiments can be
directly applied to understand the hydrogenation processes of PAHs in space.

Six large, astronomically relevant PAHs are selected in this work. These
selected six PAHs are used here as prototypical examples for large(r) PAHs
(Andrews et al., 2015; Croiset et al., 2016), and their size, from 32 to 48
C-number, that lies within the astrophysically relevant range (Kokkin et al.,
2008; Steglich et al., 2011; Gredel et al., 2011). The experimental results
show that the collision reactions between PAH cations and H-atoms can
efficiently occur in the gas phase, and the hydrogenated PAH cations are
formed through a sequential-step pathway. Unlike the photo-dehydrogenation
processes that lead to the predominance of even-mass fragments (Zhen et al.,
2014), there are no even-odd hydrogenated mass patterns observed in the gas-
phase hydrogenation processes.

The results of the theoretical calculations are consistent with the
experimental results. From the theoretical calculation, the exothermic energy
for each reaction pathway is relatively higher, meaning that the ion-molecule
reactions between the PAH and H atoms are mainly one-off collision reactions.
The molecular structure of hydrogenated PAH cations is diverse. The relative
chemical activity is very important in the ion-molecular reaction formation
process and reaction evolution network, which affects the abundance ratio of
formed species (Jäger et al., 2009; Montillaud et al., 2013; Zhen et al.,
2019). From the obtained results, we infer that the formation of aliphatic C-H
bonds plays an important role in the chemical evolution process of PAHs.

Furthermore, the calculated exothermic energy for each formation steps are
very high. The exothermic energy can quickly be transferred as the vibrational
energy of ground states to "heat" the molecules, resulting in an increase in
the temperature of molecules (Tielens, 2013). In our experimental condition,
the exothermic energy is mainly released through collision with He atoms
(buffer gas); IR fluorescence may not play an important role in the exothermic
energy release processes. In contrast to our laboratory studies, in the
astrophysical environments, due to the low density of molecules, the
exothermic energy is mainly released through IR fluorescence. However,
irrespective of which energy release pathways are involved, it will always
leave the species with lower vibrationally excited from which it relaxes
either through collision relaxation or IR fluorescence.

The AIBs, which are key PDR signatures in the near- and mid-IR regions, are
mainly attributed to PAHs and related species that are heated by the
absorption of UV photons (Leger & Puget, 1984; Allamandola et al., 1985).
Therefore, most of the galactic and extragalactic observations obtained with
the newly launched infrared James Webb Space Telescope (JWST) will encompass
PDR emissions and will help astrochemical researchers to elucidate the
distribution and molecular and spatial evolution characteristics of PAH
molecules in interstellar environments (Berné et al., 2022a). Especially for
these IR spectra of the hydrogenated PAH cations obtained in this work, their
spectral profile contributions and the spectral features may offer some
insights for the tentative detection in the ISM.

##  5 Conclusions

Overall, combining experiments with quantum chemical calculations, the
hydrogenation processes between six large, astronomically relevant PAH cations
and H-atoms are studied in this work. The hydrogenated PAH cations are
efficiently formed through an ion-molecule collision reaction in the gas
phase. Through theoretical quantum calculations, the structure of newly formed
hydrogenated PAH cations and the bonding energies of their reaction pathways,
together with the IR spectra, are obtained.

The effect of carbon skeleton structure, the side-edged structure, the
molecular size, the five- and six-membered C-ring structure, the bay region
structure, and the neighboring hydrogenation are discussed based on the
calculation results:

  1. 1.

The outer carbon sites have relatively higher chemical reactivity than the
inner and center carbon sites, i.e., the outer carbon sites will be
hydrogenated more easily.

  2. 2.

The solo and the side carbon sites of the trio edges will more easily be
hydrogenated.

  3. 3.

PAHs with different molecular sizes have a relatively similar chemical
reactivity, i.e., no molecular size effect on the hydrogenation processes.

  4. 4.

The five-membered C-ring carbon sites have relatively higher chemical
reactivity than the six-membered C-ring.

  5. 5.

The carbon site becomes more chemically active by its neighboring carbon
site’s hydrogenation.

  6. 6.

PAHs with bay or non-bay structures have a similar chemical reactivity, i.e.,
large PAHs do not have the bay region structure’s effect on the hydrogenation
processes.

The results we obtained once again validate the complexity of interstellar
molecules, and the evolution of PAH molecules under the constraints of the
factors of H-atoms is very complex. Hence, if these PAHs are present in space,
the formation of hydrogenated PAH cations could produce an extended family of
large molecules. As part of the coevolution of interstellar chemistry, the
hydrogenation and dehydrogenation reaction modes should be considered where
these PAHs are located when further reacting with H-atoms in the interstellar
environment, which provides data support and direction for our future
treatment of interstellar evolution simulations, especially for the
interstellar coevolution simulations.

Furthermore, these hydrogenated PAH cations may also provide candidates of
interest for the IR interstellar bands. From the theoretical results, we can
see that more aliphatic C-H bonds formed with its new vibrational modes.
Therefore, their role in the spectral profile contributions and the spectral
features for tentative detection in the ISM is warranted (Tielens, 2008; Berné
et al., 2022a; Chown et al., 2024).

## Acknowledgements

This work is supported by the National Natural Science Foundation of China
(NSFC, Grant No. 12333005, 12122302, and 12073027). Theoretical calculations
were performed at the Supercomputing Center of the University of Science and
Technology of China.

## Data availability

All data generated or analyzed during this study are included in this article.

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##  Appendix A Experimental methods

Here, we provide a brief description of the experimental methods used in this
study (Zhang et al., 2023). Neutral PAHs were converted into the gas phase by
heating PAHs in powdered form (provided by Kentax, with a purity greater than
99.5 %) in an oven. The temperature of oven is $\sim$ 473, 473, 503, 553, 573,
and 603 K for ovalene ($\rm{C_{32}H_{14}}$), periflanthene
($\rm{C_{32}H_{16}}$), tri-benzo-peropyrene (TBP, $\rm{C_{34}H_{16}}$),
tribenzo-naphtho-pero-pyrene (TNPP, $\rm{C_{40}H_{18}}$), hexa-benzo-coronene
(HBC, $\rm{C_{42}H_{18}}$), and dicoronylene (DC, $\rm{C_{48}H_{20}}$),
respectively. Subsequently, evaporated PAH molecules were ionized and
transported into the ion trap via an ion-gate. During this procedure, helium
gas was introduced continuously into the trap via a leaking valve to
thermalize the ion cloud through collisions ($\sim$ 300 K). A high-precision
delay generator (SRS DG535) was used to control the full-timing sequence.

A hydrogen atom beam source (HABS; MBE-Komponenten GmbH; Tschersich & Bonin
(1998)) was installed to produce the H atoms. The H-atoms were formed by
cracking H2 gas (with a purity greater than 99.99 %) using a tungsten
capillary at $\sim$ 2173 K. The chamber pressure during the H atom beam
exposition was $\sim$ 1.2 * 10-6 mbar with H2 flowing through the HABS (the
typical background pressure in the chamber was $\sim$ 6.0 * 10-7 with helium
gas). The working distance from the end of the tungsten capillary to the
center of the ion trap was $\sim$ 5.0 cm. The H-atoms flux was incident into
the ion trap through a 2.4 mm aperture in the ion trap ring electrode. Based
on the operating conditions, the H-atoms were expected to have a flux of
$\sim$ 4.0 * 1014 H-atoms cm-2s-1, and the volume density of H-atoms is $\sim$
5*109 cm-3.

A delay generator controls the full-timing sequence. Our setup is operated
with a frequency of 0.2, 0.1, 0.05, or 0.025 Hz, i.e., one complete measuring
cycle lasts 5.0, 10.0, 20.0, or 40.0 s, respectively. In each experiment, the
ion gate is opened, allowing the ion trap to fill with a certain amount of
ions. Hydrogenated PAH cations are formed in the ion trap, and adduct
formation presumably occurs. A negative square pulse is applied to the end cap
at the end of each cycle, and the resulting mass fragments are measured.

##  Appendix B Vibration modes and corresponding infrared intensity of other
hydrogenated PAH cations

The IR spectra of other hydrogenated PAH cations are presented in Figures
B1-B5, in the range of 0$-$3500 cm-1. The vibrational band positions are
scaled by a constant factor of 0.9670, and the black line represents the
spectra simulated by Gaussians with a full width at half maximum of 8 cm-1
(Boersma et al., 2014).

In Figure B1, the computed vibrational normal modes for the mono-hydrogenated
ovalene cations ([C32H14+H]+) are presented. In Figure B2, the computed
vibrational normal modes for the mono-hydrogenated periflanthene cations
([C32H16+H]+) are presented. In Figure B3, the computed vibrational normal
modes for the mono-hydrogenated TBP cations ([C34H16+H]+) are presented. In
Figure B4, the computed vibrational normal modes for the mono-hydrogenated HBC
cations ([C42H18+H]+) are presented. In Figure B5, the computed vibrational
normal modes for the mono-hydrogenated DC cations ([C48H20+H]+) are presented.

Figure 10: Computed vibrational normal modes for the mono-hydrogenated ovalene
cations: panel (A) is the spectrum of [C32H14]+; panel (B-E) is the spectrum
of [C32H14+H]+ (H atom added to outer carbon sites); panel (F-G) is the
spectrum of [C32H14+H]+ (H atom added to inner carbon sites); panel (H-J) is
the spectrum of [C32H14+H]+ (H atom added to center carbon sites). The
vibrational band positions are scaled by a constant factor of 0.9670.  Figure
11: Computed vibrational normal modes for the mono-hydrogenated periflanthene
cations: panel (A) is the spectrum of [C32H16]+; panel (B-E) is the spectrum
of [C32H16+H]+ (H atom added to outer carbon sites); panel (F-H) is the
spectrum of [C32H16+H]+ (H atom added to inner carbon sites); panel (I-J) is
the spectrum of [C32H16+H]+ (H atom added to center carbon sites). The
vibrational band positions are scaled by a constant factor of 0.9670.  Figure
12: Computed vibrational normal modes for the mono-hydrogenated TBP cations:
panel (A) is the spectrum of [C34H16]+; panel (B-I) is the spectrum of
[C34H16+H]+ (H atom added to outer carbon sites); panel (J-N) is the spectrum
of [C34H16+H]+ (H atom added to inner carbon sites); panel (O-R) is the
spectrum of [C34H16+H]+ (H atom added to center carbon sites). The vibrational
band positions are scaled by a constant factor of 0.9670.  Figure 13: Computed
vibrational normal modes for the mono-hydrogenated HBC cations: panel (A) is
the spectrum of [C42H18]+; panel (B-C) is the spectrum of [C42H18+H]+ (H atom
added to outer carbon sites); panel (D) is the spectrum of [C42H18+H]+ (H atom
added to inner carbon sites); panel (E-F) is the spectrum of [C42H18+H]+ (H
atom added to center carbon sites). The vibrational band positions are scaled
by a constant factor of 0.9670.  Figure 14: Computed vibrational normal modes
for the mono-hydrogenated DC cations: panel (A) is the spectrum of [C48H20]+;
panel (B-F) is the spectrum of [C48H20+H]+ (H atom added to outer carbon
sites); panel (G-J) is the spectrum of [C48H20+H]+ (H atom added to inner
carbon sites); panel (K-O) is the spectrum of [C48H20+H]+ (H atom added to
center carbon sites). The vibrational band positions are scaled by a constant
factor of 0.9670.