# Stability of C59 Knockout Fragments from Femtoseconds to Infinity

Michael Gatchell<EMAIL_ADDRESS>Naemi Florin  Suvasthika Indrajith
José Eduardo Navarro Navarrete  Paul Martini  MingChao Ji  Peter Reinhed
Stefan Rosén  Ansgar Simonsson  Henrik Cederquist  Henning T. Schmidt  Henning
Zettergren  Department of Physics, Stockholm University, 106 91 Stockholm,
Sweden

###### Abstract

We have studied the stability of C59 anions as a function of time, from their
formation on femtosecond timescales to their stabilization on second
timescales and beyond, using a combination of theory and experiments. The
C${}_{59}^{-}$ fragments were produced in collisions between C60 fullerene
anions and neutral helium gas at a velocity of 90 km/s (corresponding to a
collision energy of 166 eV in the center-of-mass frame). The fragments were
then stored in a cryogenic ion-beam storage ring at the DESIREE facility where
they were followed for up to one minute. Classical molecular dynamics
simulations were used to determine the reaction cross section and the
excitation energy distributions of the products formed in these collisions. We
found that about 15 percent of the C${}_{59}^{-}$ ions initially stored in the
ring are intact after about 100 ms, and that this population then remains
intact indefinitely. This means that C60 fullerenes exposed to energetic atoms
and ions, such as stellar winds and shock waves, will produce stable, highly
reactive products, like C59, that are fed into interstellar chemical reaction
networks.

###### keywords:

Fullerenes , Knockout , Collision Induced Dissociation , Ion Storage Ring

###### MSC:

[2010] 00-01, 99-00

††journal: Carbon

##  1 Introduction

Fullerenes are classically defined as compounds solely composed of an even
number of carbon atoms in cage-like structures made up of twelve five-membered
rings and a number of six-membered rings, with the archetype being the C60
molecule of icosahedral symmetry [1, 2]. This definition leaves little room
for ambiguity, but it does raise the question as to what to call fullerene-
like structures with an odd number of carbon atoms other than in generic terms
such as fulleroids. This may seem like a purely hypothetical thought exercise,
but the fact is that odd-numbered, thermodynamically stable fullerene-like
species have been known to exist for nearly three decades [3]. C${}_{59}^{+}$
ions were first reported in experiments where N+ ions collided with C60
targets at center-of-mass energies close to 10 eV [3]. In these conditions,
the nitrogen ion is likely captured by the fullerene before the excited system
cools by emitting a CN-group, leaving behind a C${}_{59}^{+}$ product. These
experiments also identified substituted fullerenes such as C59N+ ions referred
to as “dopeyballs” [3]. Later studies produced similar results when studying
interactions between fullerenes and oxygen. Deng _et al._ identified
C${}_{53}^{-}$, C${}_{55}^{-}$, C${}_{57}^{-}$, and C${}_{59}^{-}$ in laser
ablation experiments on surfaces with deposited C60O [4]. Around the same
time, McElvany and coworkers produced C${}_{119}^{-}$, C${}_{129}^{-}$, and
C${}_{139}^{-}$ ions through the thermal desorption of soot samples in an
ozone atmosphere [5]. Odd-numbered fullerene fragments were also reported in
laser ablation studies of various fullerene-containing materials [6, 7].

The above-mentioned studies of odd-numbered fullerene fragments all involve a
chemical process where a classical fullerene is compromised by another element
(O or N) which leads to the removal of a C atom from the cage. There is,
however, at least one other mechanism that may lead to the formation of such
species: energetic collisions. In measurements performed at Aarhus University,
C60 anions were collided with rare gas targets at center-of-mass energies of a
few hundred eV, resulting in the production of C59 cations and anions in
addition to the usual even-numbered fragments [8, 9]. The mechanism leading to
appearance of these fragments in collisions is known as knockout [10, 11].
Knockout can occur when an energetic, massive particle, such as an atom or
ion, collides with a molecule. If the impacting particle directly strikes an
individual atom in the molecule, that atom may be permanently displaced or
even removed from the lattice in a prompt, quasi-elastic process on
femtosecond timescales [11]. Knockout-driven fragmentation differs from
statistical, thermally-driven dissociation processes in that energetically
unfavorable pathways may occur with a high probability. This is the case with
fullerenes, as the lowest energy dissociation pathways favor the loss of C2
fragments ($\sim 10$ eV dissociation energy [12, 13]) when the molecules are
excited rather than the loss of single C atoms (12–13 eV dissociation energy)
[13].

Knockout processes were later reported with cationic C60 molecular [13, 14]
and neutral [C60]k cluster [15, 16, 17, 18] targets colliding with energetic
atoms and ions, respectively. In the studies of clusters of fullerenes it was
shown that the fragments produced by knockout are highly reactive and readily
formed covalent bonds with neighboring molecules in the loosely bound
clusters, leading to the efficient production of, e.g., dumbbell-like
C${}_{119}^{+}$ products [15, 17]. For intact C60 molecules, the kinetic
energy threshold for fusing two colliding cages into a single molecule is
approximately 60 eV [19]. In contrast, the reaction barrier for forming
covalent bonds between a C59 molecule and an intact C60 neighbor is well below
1 eV [15, 17]. This dramatic difference readily demonstrates the high
reactivity of C59 in comparison to intact fullerenes.

A longstanding question since the knockout mechanism was identified is whether
or not the fragments formed when an atom is knocked out of a molecule can
survive in the gas phase on timescales longer than those of the typical
experiment (microseconds). Knockout processes often induce significant heating
of the damaged molecules. But if the fragments indeed are stable on extended
timescales, then their high chemical reactivity will enable new reaction
pathways which are far from being accessible for intact fullerenes. One such
environment where this may be important is the interstellar medium (ISM) where
complex carbon-based molecules such as fullerenes have been found to be
abundant [20, 21]. To achieve this, however, the fragments would need to
stabilize (cool) by, e.g., the emission of electrons (typically microsecond
timescales) or photons (up to millisecond timescales for vibronic de-
excitation).

A recent study involving the polycyclic aromatic hydrocarbon (PAH) molecule
coronene [22] investigated the long-term stability issue using the cryogenic
Double ElectroStatic Ion Ring ExpEriment (DESIREE) [23, 24]. In those
experiments, coronene cations were collided with He atoms at a center-of-mass
energy of 105 eV. Fragment ions that had lost a single C atom through knockout
were stored in the storage ring and the number of ions remaining in the ring
was monitored as a function of storage time. It was shown that a small
fraction of the fragments were lost on millisecond timescales due to their
high internal energy, but that approximately 80 percent of the stored
fragments stabilized to remain intact indefinitely in isolation. The
conclusion of that study was that knockout fragments such as those of coronene
formed in C24H12 \+ He $\rightarrow$ C23H${}_{x}^{+}$ \+ C + $\ldots$
collisions may stabilize in the ISM [22].

Here, we report on experiments where C${}_{59}^{-}$ ions are produced in
collisions between C${}_{60}^{-}$ and He atoms at center-of-mass energies of
166 eV and on the survival probability of these fragments on timescales
ranging up to one minute in one of the DESIREE storage rings. We find that
about 15 percent of the fragments formed in this way survive long enough to
stabilize radiatively in the gas phase.

Figure 1: Overview of the DESIREE storage rings. Mass-selected C60 anions with
kinetic energies of 30 keV passed through a gas cell containing a dilute He
gas in order to induce fragmentation in less than one percent of the fast
C${}_{60}^{-}$ ions. Selected beams of either C${}_{60}^{-}$, C${}_{59}^{-}$,
or C${}_{58}^{-}$ ions were stored in the rightmost DESIREE ion-beam storage
ring for stability measurements. Electrostatic beamline elements are indicated
by gray boxes and are labeled in the left ring. Neutral products formed along
the two straight sections (dashed blue arrows) were detected by microchannel
plate (MCP) detectors and dumped ions (solid blue line) were counted with the
centrally located detector. The cryogenic region is indicated by the thin gray
outline enclosing both rings.

##  2 Methods

###  2.1 Experimental methods

The experiments were carried out at the DESIREE facility at Stockholm
University [23, 24]. The centerpiece of the DESIREE facility is a pair of
cryogenically cooled electrostatic ion-beam storage rings with circumferences
of approximately 8.7 m each as outlined in Figure 1. Here, we largely followed
the experimental approach previously used to study the survival of PAH cations
damaged by single-carbon knockout in energetic collisions [22] and to study
the stability of C${}_{7}^{2-}$ dianions [25]. Anions of C60 were produced
using a custom-made electron-attachment ion source based on the design by
Yamada _et al._ [26]. The ions were accelerated by a 30 kV potential before a
beam chopper was used to produce ion pulses of suitable lengths for injection
into the storage ring. A 102∘ bending magnet was used to select C${}_{60}^{-}$
ions. These ions then passed through a 7 cm long gas cell containing He gas at
a pressure of $2\times 10^{-3}$ mbar. The 30 keV C${}_{60}^{-}$ ions impacted
the He target at a velocity of 90 km/s, corresponding to a collision energy of
166 eV in the center-of-mass reference frame.

Ions exiting the gas cell were analyzed and selected by scaling the voltages
of all ion-optical elements after the gas cell with the kinetic energy of the
anions, i.e. mass/initial mass corrected with a small energy loss in the gas
cell. The ions (C${}_{60}^{-}$, C${}_{59}^{-}$, and C${}_{58}^{-}$,
respectively) were injected one species at a time and stored in one of the
DESIREE storage rings for up to 100 s, during which the spontaneous emission
of neutral particles was monitored using the microchannel plate (MCP)
detectors that follow each of the two straight sections. Any neutral particles
formed along these straight sections will no longer be affected by the
electrostatic deflectors that are used to steer the ion beam and will continue
straight onto either detector as indicated by the dashed arrows in Fig. 1.

We also performed measurements where the ions were dumped onto one of the
detectors after a predetermined storage time. This was done by rapidly
switching off the 10∘ deflector that follows the common straight section of
the two ion storage rings (center of Figure 1). This caused the ions
circulating in the ring to continue straight onto the detector (the full arrow
pointing towards one of the MCP detectors in Fig. 1) that follows this section
and allowed the number of ions in the ring to be counted as individual hits.

The two DESIREE storage rings share a common enclosure that is shown as the
black outline in Figure 1. This entire region is cryogenically cooled to a
temperature of around 13 K. The residual gas pressure in this chamber was on
the order of $10^{-14}$ mbar, which corresponds to a density of 104 particles
(predominantly H2) per cubic centimeter. These conditions allow ions to
circulate in DESIREE over timescales ranging up to minutes or hours [27],
during which they are able to cool spontaneously with minimal environmental
influence, e.g., from black-body radiation or collisions with residual gas
particles [28].

###  2.2 Theoretical methods

Following prior studies [13], simulations corresponding to the experiment were
made using the LAMMPS molecular dynamics simulator, colliding single C60
molecules with single He atoms. A non-periodic, cubic box with $40$ Å sides
was used, along with a timestep of 0.1 fs for the tracking of the motion of
all individual atoms. The box was shrink-wrapped, meaning that its boundaries
adjust in order to keep the atoms within it. A reactive empirical bond-order
(REBO) potential acts between the C atoms, while the interaction between C and
He is governed by a Ziegler-Biersack-Littmark (ZBL) potential. The former is
an empirical, short ranged many-body potential for hydrocarbons [29, 30, 31],
while the latter is a Coulombic potential developed to describe atomic high-
energy collisions [32]. In contrast to the experiment, the simulations were
made with a stationary C60 molecule being hit by a He atom of 166 eV
(corresponding to the 30 keV C${}_{60}^{-}$ projectile hitting He atoms at
rest in the lab frame).

Figure 2: Initial setup of a simulation. A helium atom is launched at a
stationary and randomly oriented C60 molecule with a velocity of 90 km/s. The
fullerene is centered at the origin of a three-dimensional coordinate system.
The initial position of the He atom is randomized in a square parallel to the
$xy$-plane (c.f. text).

The C60 structure, optimized with the REBO potential, was randomly rotated and
positioned at the center of the simulation box. The projectile was then
inserted with a fixed position in the $z$ direction and a randomized ($x,y$)
position. The randomized rotation of the C60 target relative to the randomized
position of projectile counts for all possible initial positions and
directions of the projectile in three-dimensional space. The initial position
of the projectile was limited to a $15$ Å $\times$ 15 Å square in order to
minimize the amount of runs where the projectile only transfers a negligible
energy to the target (see Figure 2). In total, data was collected for 100,000
simulation runs.

In contrast to the experiments, these simulations are defined for neutral
systems and do not take any electronic stopping into account. Fullerenes are
large molecules with many delocalized valence electrons. Dissociation energies
differ therefore only very slightly between neutral and anionic systems and in
previous studies there has generally been a very good agreement between these
types of simulations and experiments [13]. Furthermore, in the present energy
range, the energy transfer due to electronic stopping processes is negligible
in comparison to those due to the nuclear scattering processes simulated here
[11]. So, the exclusion of electronic stopping will not significantly
influence the results of the simulations.

##  3 Results and Discussion

A kinetic energy spectrum of negatively charged products exiting the collision
cell, measured using the 90∘ electrostatic deflector prior to injection into
DESIREE, is shown as the solid black line in Figure 3. The energies shown here
($E^{\text{lab}}_{\text{frag}}$) are all given in the laboratory reference
frame. The precursor C${}_{60}^{-}$ ions carry a kinetic energy of 30 keV with
some inherent spread from the ion source and acceleration stage. In the gas
cell, collisions with the He target introduce a recoil of varying degree
causing an offset and broadening of the peaks relative to the expected
positions based solely on mass loss. The small peak between 29.25 and 29.5 keV
in Figure 3 corresponds to C${}_{59}^{-}$, where a single C atom has been
knocked out, while the C${}_{58}^{-}$ fragments are centered around 28.9 keV.
Only the wing of the C${}_{60}^{-}$ peak is shown in the experimental spectrum
since its maximum is orders of magnitude higher in intensity than those of the
fragments. The intact C${}_{60}^{-}$ ions mainly stem from the portion of the
ion beam that passed through the gas cell without interacting with the dilute
He target.

Figure 3: Kinetic energy spectra of anionic fragments following collisions
between 30 keV C${}_{60}^{-}$ and a He gas target. The solid black line shows
the experimental spectrum and the histograms are from simulated collisions
where components from each of the C59 and C58 products can be distinguished.
The simulation data is shown in number of counts from 105 collisions with a
bin width of 20 eV. The normalization of the experimental data relative to the
theoretical spectra is done arbitrarily.

Corresponding spectra for C58 and C59 fragments from our MD simulations are
also shown in Figure 3. Here, the changes in center-of-mass motion of the
intact and damaged fullerene products caused by the collisions have been used
to estimate the width and position of each peak. The position of the simulated
C59 distribution is consistent with the experimental data. This supports past
observations that the knockout processes studied in the simulations are indeed
responsible for the C${}_{59}^{-}$ fragments detected in the experiments [8,
13, 14]. scales of the simulations, these excited systems remain intact,
contributing to the long tail in the energy spectrum.

Figure 4: Energy transfer distributions for C60, C59, and C58 products
determined from our MD simulations. For clarity, each distribution is
normalized to a total integrated yield of unity. Each bin has a width of 2 eV.
Median energies of each distribution ($\tilde{E}$) are given in the legend.

At first glance, the agreement between experiments and theory is rather poor
when it comes to the position and width of the C${}_{58}^{-}$ peak. The reason
for this is that, unlike in the experiments, _every_ C58 fragment formed in
the simulations originate from double knockout processes, collisions where a
single He atom knocks out two C atoms from the fullerene cage. Under the
conditions simulated here, the probability of this happening is smaller than
that of single C knockout. This is a particularly violent process, with a
large amount of energy being deposited into the cage. This can be seen in
particular in Figure 4 where the internal energy distribution of each fragment
type formed in the simulation is shown. The high energy transfer also results
in a significant broadening and shift of the C58 spectrum in Figure 3, with
the majority of the distribution falling outside of the range observed in the
experiments. The bulk of the C${}_{58}^{-}$ fragments detected in the
experiments must therefore come from other processes. For energetic reasons
this is most likely due to a later loss of a second C atom from the initially
formed C${}_{59}^{-}$.

The internal energy distributions ($E^{\text{int}}_{\text{frag}}$) for each of
the main products, calculated from the MD simulations, are shown in Figure 4.
As expected, the internal energy distribution of intact C60 after the
collisions is biased towards 0 eV as many of the collisions, even with the box
size used here, are at most glancing with little energy transfer. There is,
however, a long tail extending past 100 eV. The lowest dissociation energy of
C60 ions is about 10 eV for C2 loss [33], and about 40 eV is required to
activate these processes on microsecond timescales [34]. Furthermore, the
electron affinity of C60 is only 2.7 eV [12, 35]. Thus, the hottest C60 anions
that survive the initial collisions with the He target will rapidly decay,
either by electron emission or by fragmentation.

The relaxation behavior of C${}_{59}^{-}$ is to some extant similar to that of
C${}_{60}^{-}$. The knockout of a single C atom is potentially a destructive
process, but a significant fraction of these trajectories result in a clean
hit with a relatively small amount of energy transfer to the rest of the
fullerene cage. The differences between the C59 and C60 distributions are thus
relatively small considering the excess counts near 0 eV in the latter case.
In comparison, the aforementioned energy distribution for the C58 fragments is
significantly wider and peaks near 60 eV. Here, only two simulation runs give
C58 double knockout with internal energies less than 20 eV. Compared to
similar studies with coronene, the energy transfer for the different products
follow similar trends. The main difference is that the double knockout
products here (C58) display a stronger heating, relative to the other
products, than was observed for the planar PAH and its fragments [22]. This is
a result of the three-dimensional structure of the fullerene cage which
increases the likelihood of multiple interactions between the projectile (He)
and a single C60 target molecule..

Due to the internal energies of the intact and damaged fullerenes leaving the
collision cell, a portion of the ions stored in DESIREE will spontaneously
decay. Neutral products from this decay, either dissociation or electron
emission, are detected using one of the particle detectors situated after each
of the straight sections (Fig. 1). The neutral signal from these processes
tends to follow a ${\sim 1/t}$ behavior as a function of the storage time due
to the broad internal energy distribution of the population of stored ions
[36]. The measured decay curves for stored C${}_{60}^{-}$, C${}_{59}^{-}$, and
C${}_{58}^{-}$ ions are given in the supplementary material as their
interpretation is outside the scope of this work.

While the neutral particle yield from the stored ions provides insight into
ongoing decay processes, it does not represent the behavior of the full
ensemble of ions in the ring. Ions that cool by other means, e.g., photon
emission, or that have a low enough internal energy to be stable for the
timescale of the experiment, will not decay, making them invisible to the
neutral particle measurements. To probe the actual number of ions in the
storage ring at any given time we instead use a technique where one of the
ten-degree deflectors is switched to ground on a microsecond timescale, which
effectively dumps the entire content of the ring onto one of the particle
detectors (lower center of Fig. 1).

Figure 5: Number of C${}_{59}^{-}$ ions stored on average after different
storage times, measured by dumping the contents of the ring onto a detector.
Each point is the result of 500 measurement cycles (ion injection, storage,
and beam dump). The solid line shows a fit to Eq. 1, with the two components
shown as the dotted and dashed lines, respectively. Note the logarithmic
horizontal scale that spans six orders of magnitude in time.

The signal of dumped C${}_{59}^{-}$ ions, as function of time from their
formation, is shown in Figure 5 as the number of ions counted per measurement
cycle. The shortest measurement achievable is when the ions were dumped after
half of a turn in the ring, 160 $\mu$s after they were produced. At the
opposite end of the scale, the longest measurement involved storing the ions
for 100 s. It is immediately clear that the signal drops by about an order of
magnitude during the first few hundred milliseconds before leveling out. At
longer times, the ion-beam storage lifetime becomes a limiting factor, causing
the signal to taper off once again. To quantify these processes we fit an
expression of the type

$I(t)=A\times t^{p}+B\times e^{-t/\tau}$ (1)

to the data. Here, $t$ is the time since ion production (in the gas cell),
while $A$, $B$, $p$, and $\tau$ are free parameters. The $p$ parameter is
related to the rate at which a portion of the ions spontaneously decay due to
their internal energies. The lifetime $\tau$ is the measured ion-beam storage
lifetime that is dictated by the storage parameters and background conditions,
and the parameter $B$ represents the expected ion signal in the absence of the
storage-limited loss of ions. The fit of Eq. 1 is shown as the solid line in
Figure 5. The key finding from this fit is the value of $B=2.05\pm 0.02$. This
value gives the average number of ions remaining in the ring when spontaneous
loss of hot ions no longer occurs. This means that of the $12.6\pm 0.1$
C${}_{59}^{-}$ ions that are counted after half of a turn in the ring for each
injection, $10.5\pm 0.2$ of them (about 85 percent) will dissociate or
neutralize spontaneously on average. The two remaining ions, however, will
remain intact indefinitely in isolation, i.e., in the gas phase. In our
measurements, the number of remaining ions in the ring remains a constant for
nearly three orders of magnitude in time, from approximately 100 ms to 10 s
after the C${}_{59}^{-}$ fragments are formed. After this the signal drops off
due to imperfections in the storage conditions. The conditions at DESIREE
allow for storage lifetimes on the order of hours [27, 37], but the small
number of ions present in the present experiment makes optimizing the ring
parameters for longer lifetimes difficult. The $107\pm 11$ s beam lifetime
measured here thus represents an instrument optimization limitation and not a
residual-gas limited ion-beam lifetime or a finite lifetime of the
C${}_{59}^{-}$ fragments.

The results are in line with those found when coronene cation fragments were
produced under similar experimental conditions [22]. The main difference is
that there, as many as 80 percent of the fragments resulting from single
C-loss stabilize during the first second of storage and will thus remain
intact indefinitely. Here, the fraction is significantly smaller, with only 15
percent of the C${}_{59}^{-}$ ions entering the ring remaining intact after
this time. This difference is largely due to the storage of anion fragments in
the present experiments. Cationic fragments can either release excess energy
by photon emission or by dissociation. For anions, the activation energy for
electron emission is typically much lower than for cations, which opens
another possible decay channel. The electron affinity of C59 is about 3.5 eV
(the energy varies slightly between the two main isomers [13]). This is lower
than the lowest dissociation energy for C${}_{59}^{-}$, which is about 4.5 eV
for additional C-loss [13]. Electron detachment is therefore expected to be
the dominant decay channel until radiative cooling quenches any further
depletion of the ion population. Following the scheme by Andersen _et al._ for
estimating the detachment rate of excited fullerene anions as a function of
internal energy [38], we can theoretically estimate the fraction of
C${}_{59}^{-}$ fragments that survive under our present experimental
conditions. The connection between temperature (for $T>1000$ K) and internal
energy, $E^{\text{int}}$, for an individual fullerene molecule can to be
approximated by

$T[\text{K}]=1000+(E^{\text{int}}[\text{eV}]-7.4)/C,$ (2)

where $C$ is the heat capacity of the fullerene ion. The effective
temperature, correcting for the finite size of the system [39], is then given
by $T_{\text{eff}}=T-E_{b}/2C$, where $E_{b}=3.5$ eV is the electron affinity
of C59 [38]. The heat capacity of C59 is estimated by scaling the value for
C60 (0.0138 eV/K [38]) by the reduced number of internal degrees of freedom,
171 vs. 174, giving $C=0.0136$ eV/K. Assuming a statistical decay processes,
the rate of electron emission as a function of internal temperature can then
be determined from an Arrhenius rate equation

$k=\nu e^{-E_{b}/k_{\text{B}}T_{\text{eff}}}.$ (3)

Here, $k_{\text{B}}$ is the Boltzmann constant and the pre-exponential factor
is taken to be the same as for C60, $\nu=10^{13}$ s-1 [40]. From Figure 5, we
can see that the ion decay is quenched after about 100 ms. Using eq. (3), the
maximum internal energy a C${}_{59}^{-}$ can have while surviving on these
timescales is $E^{\text{int}}\approx 15$ eV. In our molecular dynamics
simulations (Figure 4), 20 percent of the C59 fragments formed by knockout of
a C atom have internal energies less than 15 eV, which is close to the
measured fraction of about 15 percent of stored C${}_{59}^{-}$ ions surviving.
There are good reasons to believe that the surviving fractions for neutral or
cationic C59 would be larger than for the corresponding anion when they are
produced through knockout. These findings thus suggest that exotic and
reactive C59 fragments could be present and survive in regions where
fullerenes are processed by energetic particles.

##  4 Conclusions

We have studied the stability of C${}_{59}^{-}$ fragments formed in energetic
collisions between C60 anions and He atoms at a velocity of 90 km/s. Despite
the violent process in which they are formed, about 15 percent of the
C${}_{59}^{-}$ ions formed remain stable on timescales of seconds or longer,
at which point they no longer decay. The ions lost during this time are
expected to primarily decay via electron emission into neutral C59, so the
actual fraction of odd-numbered fullerene fragments produced in this process
is presumably higher than the measured value. The intact C${}_{59}^{-}$ ions,
however, will remain so indefinitely in isolation, stabilized by photoemission
processes, e.g., vibrational de-excitation.

Fullerenes are known to be widely abundant in interstellar and circumstellar
environments [20, 21], regions of space where particle fluxes from stellar
winds and shock waves are often present [41, 42]. The velocities of particles
in these regions are of the same order of magnitude as those studied in the
present experiments. It is therefore likely that knockout processes occur and,
as our results have shown, that odd-numbered fullerene radicals such as C59
(neutral or ions) are present there as well. If they are, then their increased
chemical reactivity compared to intact fullerenes [15, 16, 17] could play an
important role in reaction networks involving complex, carbonaceous molecules.

## Acknowledgments

This work was performed at the Swedish National Infrastructure, DESIREE
(Swedish Research Council Contract Nos. 2017-00621 and 2021-00155). M.G.,
H.C., H.S., and H.Z. acknowledge support from the Swedish Research Council
(contracts 2020-03104, 2019-04379, 2022-02822, and 2020-03437, respectively).
It is a part of the project “Probing charge- and mass-transfer reactions on
the atomic level”, supported by the Knut and Alice Wallenberg Foundation
(Grant no. 2018.0028). This article is based upon work from COST Actions
CA18212 – Molecular Dynamics in the GAS phase (MD-GAS) and CA21101 – Confined
Molecular Systems: From a New Generation of Materials to the Stars (COSY),
supported by COST (European Cooperation in Science and Technology).

## References

  * [1] G. P. Moss, P. A. S. Smith, D. Tavernier, Glossary of class names of organic compounds and reactivity intermediates based on structure (iupac recommendations 1995), Pure and Applied Chemistry 67 (8-9) (1995) 1307–1375.  doi:10.1351/pac199567081307.
  * [2] A. L. Goodson, C. L. Gladys, D. E. Worst, Numbering and naming of fullerenes by chemical abstracts service, Journal of Chemical Information and Computer Sciences 35 (6) (1995) 969–978.  doi:10.1021/ci00028a004.
  * [3] J. F. Christian, Z. Wan, S. L. Anderson, Nitrogen ion (n+) + c60 fullerene reactive scattering: substitution, charge transfer, and fragmentation, The Journal of Physical Chemistry 96 (26) (1992) 10597–10600.
  * [4] J. P. Deng, D. D. Ju, G. R. Her, C. Y. Mou, C. J. Chen, Y. Y. Lin, C. C. Han, Odd-numbered fullerene fragment ions from c60 oxides, The Journal of Physical Chemistry 97 (45) (1993) 11575–11577.  doi:10.1021/j100147a002.
  * [5] S. W. McElvany, J. H. Callahan, M. M. Ross, L. D. Lamb, D. R. Huffman, Large odd-numbered carbon clusters from fullerene-ozone reactions, Science 260 (5114) (1993) 1632–1634.
  * [6] L. Zhu, S. Wang, Y. Li, Formation of anomalous odd‐numbered carbon cluster ions in the gas‐phase coalescence reactions of fullerenes, The Journal of Chemical Physics 101 (10) (1994) 8592–8595.  doi:10.1063/1.468054.
  * [7] Q. Kong, L. Zhao, J. Zhuang, J. Xu, S. Qian, Y. Li, R. Cai, H. Hou, J. Wang, Formation of odd-numbered fullerene-related species and its relation to the formation of metallofullerenes, International Journal of Mass Spectrometry 209 (1) (2001) 69–79.  doi:https://doi.org/10.1016/S1387-3806(01)00477-8.
  * [8] M. Larsen, P. Hvelplund, M. Larsson, H. Shen, Fragmentation of fast positive and negative C60 ions in collisions with rare gas atoms, The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics 5 (2) (1999) 283–289.  doi:10.1007/s100530050257.
  * [9] S. Tomita, P. Hvelplund, S. B. Nielsen, T. Muramoto, C59-ion formation in high-energy collisions between cold C${}_{60}^{-}$ and noble gases, Physical Review A 65 (2002) 043201.  doi:10.1103/PhysRevA.65.043201.
  * [10] M. H. Stockett, H. Zettergren, L. Adoui, J. D. Alexander, U. Bērziņš, T. Chen, M. Gatchell, N. Haag, B. A. Huber, P. Hvelplund, A. Johansson, H. A. B. Johansson, K. Kulyk, S. Rosén, P. Rousseau, K. Støchkel, H. T. Schmidt, H. Cederquist, Nonstatistical fragmentation of large molecules, Physical Review A 89 (2014) 032701.  doi:10.1103/PhysRevA.89.032701.
URL http://link.aps.org/doi/10.1103/PhysRevA.89.032701

  * [11] M. Gatchell, H. Zettergren, Knockout driven reactions in complex molecules and their clusters, Journal of Physics B: Atomic, Molecular and Optical Physics 49 (16) (2016) 162001.  doi:10.1088/0953-4075/49/16/162001.
  * [12] K. Støchkel, J. U. Andersen, Photo excitation and laser detachment of C${}_{60}^{-}$ anions in a storage ring, The Journal of Chemical Physics 139 (16) (2013) 164304.  doi:10.1063/1.4826097.
  * [13] M. H. Stockett, M. Wolf, M. Gatchell, H. T. Schmidt, H. Zettergren, H. Cederquist, The threshold displacement energy of buckminsterfullerene c60 and formation of the endohedral defect fullerene he@c59, Carbon 139 (2018) 906 – 912.  doi:10.1016/j.carbon.2018.07.073.
  * [14] M. Gatchell, M. Stockett, P. Rousseau, T. Chen, K. Kulyk, H. Schmidt, J. Chesnel, A. Domaracka, A. Méry, S. Maclot, L. Adoui, K. Støchkel, P. Hvelplund, Y. Wang, M. Alcamí, B. Huber, F. Martín, H. Zettergren, H. Cederquist, Non-statistical fragmentation of pahs and fullerenes in collisions with atoms, International Journal of Mass Spectrometry 365–366 (0) (2014) 260 – 265, special issue: Tilmann Märk.  doi:10.1016/j.ijms.2013.12.013.
  * [15] H. Zettergren, P. Rousseau, Y. Wang, F. Seitz, T. Chen, M. Gatchell, J. D. Alexander, M. H. Stockett, J. Rangama, J. Y. Chesnel, M. Capron, J. C. Poully, A. Domaracka, A. Méry, S. Maclot, H. T. Schmidt, L. Adoui, M. Alcamí, A. G. G. M. Tielens, F. Martín, B. A. Huber, H. Cederquist, Formations of dumbbell c118 and c119 inside clusters of c60 molecules by collision with $\alpha$ particles, Physical Review Letters 110 (2013) 185501.  doi:10.1103/PhysRevLett.110.185501.
  * [16] F. Seitz, H. Zettergren, P. Rousseau, Y. Wang, T. Chen, M. Gatchell, J. D. Alexander, M. H. Stockett, J. Rangama, J. Y. Chesnel, M. Capron, J. C. Poully, A. Domaracka, A. Méry, S. Maclot, V. Vizcaino, H. T. Schmidt, L. Adoui, M. Alcamí, A. G. G. M. Tielens, F. Martín, B. A. Huber, H. Cederquist, Ions colliding with clusters of fullerenes—decay pathways and covalent bond formations, The Journal of Chemical Physics 139 (3) (2013) 034309\.  doi:10.1063/1.4812790.
  * [17] Y. Wang, H. Zettergren, P. Rousseau, T. Chen, M. Gatchell, M. H. Stockett, A. Domaracka, L. Adoui, B. A. Huber, H. Cederquist, M. Alcamí, F. Martín, Formation dynamics of fullerene dimers ${\mbox{c}}_{118}^{+}$, ${\mbox{c}}_{119}^{+}$, and ${\mbox{c}}_{120}^{+}$, Physical Review A 89 (2014) 062708.  doi:10.1103/PhysRevA.89.062708.
  * [18] R. Delaunay, M. Gatchell, A. Mika, A. Domaracka, L. Adoui, H. Zettergren, H. Cederquist, P. Rousseau, B. A. Huber, Shock-driven formation of covalently bound carbon nanoparticles from ion collisions with clusters of c60 fullerenes, Carbon 129 (2018) 766–774.  doi:10.1016/j.carbon.2017.12.079.
  * [19] E. E. B. Campbell, Fullerene-Fullerene Collisions, Springer Netherlands, Dordrecht, 2003, pp. 161–189.  doi:10.1007/1-4020-2524-6{\\_}9.
URL https://doi.org/10.1007/1-4020-2524-6_9

  * [20] J. Cami, J. Bernard-Salas, E. Peeters, S. E. Malek, Detection of C60 and C70 in a young planetary nebula, Science 329 (5996) (2010) 1180–1182.  doi:10.1126/science.1192035.
  * [21] E. K. Campbell, M. Holz, D. Gerlich, J. P. Maier, Laboratory confirmation of C${}_{60}^{+}$ as the carrier of two diffuse interstellar bands, Nature 523 (7560) (2015) 322–323.  doi:10.1038/nature14566.
  * [22] M. Gatchell, J. Ameixa, M. Ji, M. H. Stockett, A. Simonsson, S. Denifl, H. Cederquist, H. T. Schmidt, H. Zettergren, Survival of polycyclic aromatic hydrocarbon knockout fragments in the interstellar medium, Nature Communications 12 (1) (2021) 6646.  doi:10.1038/s41467-021-26899-0.
  * [23] R. D. Thomas, H. T. Schmidt, G. Andler, M. Björkhage, M. Blom, L. Brännholm, E. Bäckström, H. Danared, S. Das, N. Haag, P. Halldén, F. Hellberg, A. I. S. Holm, H. A. B. Johansson, A. Källberg, G. Källersjö, M. Larsson, S. Leontein, L. Liljeby, P. Löfgren, B. Malm, S. Mannervik, M. Masuda, D. Misra, A. Orbán, A. Paál, P. Reinhed, K.-G. Rensfelt, S. Rosén, K. Schmidt, F. Seitz, A. Simonsson, J. Weimer, H. Zettergren, H. Cederquist, The double electrostatic ion ring experiment: A unique cryogenic electrostatic storage ring for merged ion-beams studies, Review of Scientific Instruments 82 (6) (2011) 065112.  doi:10.1063/1.3602928.
URL http://scitation.aip.org/content/aip/journal/rsi/82/6/10.1063/1.3602928

  * [24] H. T. Schmidt, R. D. Thomas, M. Gatchell, S. Rosén, P. Reinhed, P. Löfgren, L. Brännholm, M. Blom, M. Björkhage, E. Bäckström, J. D. Alexander, S. Leontein, D. Hanstorp, H. Zettergren, L. Liljeby, A. Källberg, A. Simonsson, F. Hellberg, S. Mannervik, M. Larsson, W. D. Geppert, K.-G. Rensfelt, H. Danared, A. Paál, M. Masuda, P. Halldén, G. Andler, M. H. Stockett, T. Chen, G. Källersjö, J. Weimer, K. Hansen, H. Hartman, H. Cederquist, First storage of ion beams in the double electrostatic ion-ring experiment: Desiree, Review of Scientific Instruments 84 (5) (2013) 055115.  doi:10.1063/1.4807702.
  * [25] P. K. Najeeb, M. H. Stockett, E. K. Anderson, M. K. Kristiansson, P. Reinhed, A. Simonsson, S. Rosén, R. D. Thomas, K. C. Chartkunchand, H. Gnaser, R. Golser, D. Hanstorp, A. Larson, H. Cederquist, H. T. Schmidt, H. Zettergren, Stability and cooling of the ${\mathrm{c}}_{7}^{2-}$ dianion, Phys. Rev. Lett. 131 (2023) 113003.  doi:10.1103/PhysRevLett.131.113003.
URL https://link.aps.org/doi/10.1103/PhysRevLett.131.113003

  * [26] K. Yamada, A. Chiba, Y. Hirano, Y. Saitoh, Development of an electron-attachment-type negative fullerene ion source, AIP Conference Proceedings 2011 (1) (2018) 050020.  doi:10.1063/1.5053318.
  * [27] E. Bäckström, D. Hanstorp, O. M. Hole, M. Kaminska, R. F. Nascimento, M. Blom, M. Björkhage, A. Källberg, P. Löfgren, P. Reinhed, S. Rosén, A. Simonsson, R. D. Thomas, S. Mannervik, H. T. Schmidt, H. Cederquist, Storing kev negative ions for an hour: The lifetime of the metastable ${{}^{2}P}_{1/2}^{o}$ level in ${{}^{32}\mathrm{S}}^{-}$, Physical Review Letters 114 (2015) 143003.  doi:10.1103/PhysRevLett.114.143003.
URL http://link.aps.org/doi/10.1103/PhysRevLett.114.143003

  * [28] H. T. Schmidt, G. Eklund, K. C. Chartkunchand, E. K. Anderson, M. Kamińska, N. de Ruette, R. D. Thomas, M. K. Kristiansson, M. Gatchell, P. Reinhed, S. Rosén, A. Simonsson, A. Källberg, P. Löfgren, S. Mannervik, H. Zettergren, H. Cederquist, Rotationally cold ${\mathrm{oh}}^{-}$ ions in the cryogenic electrostatic ion-beam storage ring desiree, Phys. Rev. Lett. 119 (2017) 073001.  doi:10.1103/PhysRevLett.119.073001.
URL https://link.aps.org/doi/10.1103/PhysRevLett.119.073001

  * [29] D. W. Brenner, Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Physical Review B 42 (1990) 9458–9471.  doi:10.1103/PhysRevB.42.9458.
  * [30] D. W. Brenner, Erratum: Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Physical Review B 46 (1992) 1948–1948.  doi:10.1103/PhysRevB.46.1948.2.
  * [31] D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, S. B. Sinnott, A second-generation reactive empirical bond order (rebo) potential energy expression for hydrocarbons, Journal of Physics: Condensed Matter 14 (4) (2002) 783.
  * [32] J. F. Ziegler, J. P. Biersack, U. Littmark, In The Stopping and Range of Ions in Matter, Pergamon, New York, 1985.
  * [33] S. Tomita, J. U. Andersen, C. Gottrup, P. Hvelplund, U. V. Pedersen, Dissociation energy for ${c}_{2}$ loss from fullerene cations in a storage ring, Physical Review Letters 87 (7) (2001) 073401–.  doi:10.1103/PhysRevLett.87.073401.
  * [34] D. B. Qian, X. Ma, Z. Chen, B. Li, X. L. Zhu, S. F. Zhang, S. Martin, R. Brédy, J. Bernard, L. Chen, Multistage transformation and charge effect during the fragmentation phase transition in atomic clusters, Phys. Rev. A 87 (2013) 063201.  doi:10.1103/PhysRevA.87.063201.
  * [35] D.-L. Huang, P. D. Dau, H.-T. Liu, L.-S. Wang, High-resolution photoelectron imaging of cold C${}_{60}^{-}$ anions and accurate determination of the electron affinity of C60, The Journal of Chemical Physics 140 (22) (2014) 224315.  doi:10.1063/1.4881421.
  * [36] K. Hansen, Decay dynamics in molecular beams, Mass Spectrometry Reviews 40 (6) (2021) 725–740.  doi:https://doi.org/10.1002/mas.21630.
URL https://doi.org/10.1002/mas.21630

  * [37] M. K. Kristiansson, S. Schiffmann, J. Grumer, J. Karls, N. de Ruette, G. Eklund, V. Ideböhn, N. D. Gibson, T. Brage, H. Zettergren, D. Hanstorp, H. T. Schmidt, Experimental and theoretical studies of excited states in Ir-, Physical Review A 103 (6) (2021) 062806–.  doi:10.1103/PhysRevA.103.062806.
  * [38] J. U. Andersen, C. Gottrup, K. Hansen, P. Hvelplund, M. O. Larsson, Radiative cooling of fullerene anions in a storage ring, The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics 17 (2) (2001) 189–204.  doi:10.1007/s100530170022.
URL https://doi.org/10.1007/s100530170022

  * [39] C. E. Klots, Kinetic methods for quantifying magic, Zeitschrift für Physik D Atoms, Molecules and Clusters 21 (4) (1991) 335–342.  doi:10.1007/BF01438406.
URL https://doi.org/10.1007/BF01438406

  * [40] J. U. Andersen, E. Bonderup, Classical dielectric models of fullerenes and estimation of heat radiation, The European Physical Journal D \- Atomic, Molecular, Optical and Plasma Physics 11 (3) (2000) 413–434.  doi:10.1007/s100530070070.
URL https://doi.org/10.1007/s100530070070

  * [41] E. R. Micelotta, A. P. Jones, A. G. G. M. Tielens, Polycyclic aromatic hydrocarbon processing in a hot gas, Astronomy and Astrophysics 510 (2010) A37.  doi:10.1051/0004-6361/200911683.
URL http://dx.doi.org/10.1051/0004-6361/200911683

  * [42] E. R. Micelotta, A. P. Jones, A. G. G. M. Tielens, Polycyclic aromatic hydrocarbon processing in interstellar shocks, Astronomy and Astrophysics 510 (2010) A36.  doi:10.1051/0004-6361/200911682.
URL http://dx.doi.org/10.1051/0004-6361/200911682