*Submitted to Chemical Physics Letters (3/97)
Published Chemical Physics Letters, 272 (1997) 18-24*

**Charge-exchange collisions of C _{60}^{z+
}: a probe of the ion charge distribution**

Douglas B. Cameron and __Joel H. Parks
__Rowland Institute for Science, Cambridge, MA
02142-1297, USA

We present measurements of charge-exchange collisions of Li, Cs and C

_{60 }with C_{60}^{z+}ions (z=1-3) at thermal collision energies. Relative charge-exchange rates were determined by measuring the decay of the multiply charged ions stored and cooled in a Paul trap during exposure to a neutral beam emitted by an effusive oven. Surprisingly, the measured rates for each neutral species are not proportional to the ion chargezas would be expected for Langevin collisions involving a charged point particle or a uniformly charged sphere. The observed rates suggest a nonuniform charge distribution over the surface of the gas phase C_{60}^{z+}ion. The relative rates can be reproduced by a model based on a symmetric distribution of point charges that are free to move on the ion surface during the neutral trajectory. Such behavior can be attributed to static and possibly dynamic Jahn-Teller effects in the gas phase fullerene cation.

Multiply charged C_{60}^{z+ }ions provide a unique opportunity to
observe charge- exchange interactions which exhibit a strong dependence on the
distribution and mobility of charge on the molecular microsurface. Since the diameter of C_{60}
(~7Å) is comparable to the range of the ion-neutral interaction during collisions, it
might be expected that the collision dynamics depend on characteristics of the ion charge
distribution. Studies of low energy charge-exchange between C_{60}^{+ }and
alkali atoms [1] and of C_{60}^{2+ }with small molecules^{ }[2]
have suggested models of a charge distribution that included charge motion on the ion
microsurface during the interaction trajectory. A symmetric distribution of *+z*
point charges on the C_{60} surface was proposed by Bohme and co-workers [3] to
describe the charge-exchange process from C_{60}^{z+} ions and was applied
to experimental results of fission (dissociation) reactions with 3z7 by
Märk and co-workers [4].

This letter presents experimental results which relate the long range ion-neutral
interaction to the ion charge distribution. Our results are not expected to depend on the
details of the curve-crossing dynamics where charge-exchange occurs. These crossings are
estimated to occur at ion-neutral separations shorter than the Langevin critical capture
distance arising in ion-induced dipole collisions. This is in contrast to the measurements
of C_{2}^{+ }fission [4] which require a model of the C_{60}^{z+}
ion distribution at the point of charge separation to estimate the fission dynamics.
However, both fission and the collision interactions of C_{60}^{z+} can be
described with a distribution of equidistant point charges on the ion surface. In
addition, the collision rates obtained from our experiments imply that the charge
distribution is free to undergo rigid rotation about the C_{60} microsurface
during the collision trajectory. The experimental implications of a nonuniform charge
distribution and its apparent rapid rotation during the collision are discussed in the
context of Jahn-Teller effects, previously studied for anions, cations and neutral triplet
states of C_{60}.

The experimental arrangement used for these measurements has been described elsewhere
[1,5]. C_{60}^{z+} ions and C_{60-2m}^{z+} fragments^{ }were
loaded into a radio frequency Paul trap by electron ionization of an effusive beam of C_{60}
entering through an aperture in the ring electrode. Multiply-charged ions (£ 10^{3} ions) were produced by an electron beam current
density of ~2 mA/cm^{2 }at ~100 eV energy for exposure times of 0.5-1 s. The trap
was maintained at 300 K and ions were stored within a background He gas at pressures of
~10^{-4} Torr, adequate to thermalize the translational and vibrational degrees of
freedom. [1] The ions were then exposed to a thermal beam of alkali atoms or C_{60}
molecules that traverses the trap through two apertures in the ring electrode for an
exposure interval set by a solenoid driven shutter.

**Figure 1.** The mass spectrum of trapped C_{60}^{z+
}and associated fragments are shown. Ions are loaded into the trap by e-beam
ionization of neutral C_{60} and the spectrum is detected by resonant ejection of
the ions into an electron multiplier.

Charge-exchange collisions between C_{60}^{z+} ions and alkali atoms
resulted in a decay of the number of trapped ions. Previous experiments [1] demonstrated
that this was the only significant process responsible for ion decay. The trapped ion
lifetime was several minutes in the absence of neutral flux and contributed negligible
loss to these measurements. After exposing the trapped ions to the neutral beam for a
specific time interval, the number of remaining ions was determined by resonantly ejecting
all trapped ions into an electron multiplier. Simultaneous measurements on ions having
different charge states *z* could be made by trapping a range of *m/z* ions.
This allowed an accurate determination of the decay rates of C_{60}^{z+}
relative to C_{60}^{+}. These relative rates eliminate the dependence on
the neutral flux which, although required for absolute rates, was found to be difficult to
calibrate accurately. [1]^{ }Figure 1 displays the mass spectrum of trapped ions
before exposure to neutral flux. The trapped ion spectrum in Fig. 1 spans a trap parameter
range of 0.21£q_{z}£0.84
and the number of ions for each species is proportional to the integrated peak signal. By
performing these measurements as a function of exposure interval, the relative
charge-exchange rate of each ion species was determined.

The charge-exchange channels observed in these experiments resulted from reactions

(1)

for* z=1-4*, *m=0-5*. Resonant ion ejection from the Paul trap permitted either
individual masses or mass distributions to be isolated for study. When C_{60}^{+}
or C_{60}^{2+} was mass isolated in the trap prior to exposure, the decay
of either ion was observed to be a single exponential extending over 2-3 orders of
magnitude. However, exposure of the complete multiply-charged mass spectrum shown in Fig.
1 results in more complex behavior since it includes the cascade of ions to lower charge
states.

**Figure 2.** The decay curves for charge-exchange of C_{60}^{z+}
with Li are shown for *z=1* by filled circles, *z=2* by filled squares and *z=3*
by filled triangles. The solid curves are determined by parameter fits of the decay rates
k_{1}, k_{2} and k_{3} shown next to curve. The data points were
obtained by integrating the mass spectrum peaks of C_{60}^{z+} for each
charge state *z* at each Li exposure time.

Charge-exchange rates were extracted from the analysis of multiply-charged mass spectra
by comparing the measured time dependent population of each species with the solution of a
coupled set of differential equations involving collision rate parameters. The decay rate
of each species was then independently determined as fit parameters to these solutions. As
an example, the decay of C_{60}^{z+} ions (*z=1-3*) during Li flux
exposure is shown in Fig. 2. Each data point is an average of ~5 measurements and exhibits
scatter arising from statistical fluctuations. The cascade of +2 to +1 ions is clearly
evident in the initial increase of the +1 species. The experimental rates derived from
exponential fits of the decay curves shown in Fig. 2 are k_{1 }= 1.88 sec^{-1},^{
}k_{2 }= 2.21 sec^{-1}, k_{3 }= 2.48 sec^{-1} for *z=+1,
+2, +3* respectively with an uncertainty of ±15%. Note that these rates are clearly
not proportional to the ion charge *z*.

Precautions in these decay measurements was taken to ensure that the sequential
resonant ejection of different charge states with comparable mass results in quantitative
ion detection. Within the trap, space charge fields couple the overlapping ion clouds of
different species. As a result, the ejection of a dense inner cloud of low *m/z* ions
through a surrounding cloud of higher *m/z* can destabilize the outer cloud and
affect the quantitative detection of the higher *m/z* species. This is evident in
Fig. 2 as larger scatter in the C_{60}^{+} signal at short exposure times
when comparable quantities of C_{60}^{2+} are present. These effects were
minimized by loading smaller initial quantities (<1000) of the lower *m/z* ions.
Decay rates were determined from ion data which did not exhibit large fluctuations, such
as the *z=2* and *z=3* decays and data taken at longer exposure times for *z=1*
as shown in Fig. 2. As a final confirmation that the analysis yielded reliable rates, the
decay rates of individually trapped ion species were compared with the rates obtained from
a multiply-charged mass spectrum and found to be the same within experimental uncertainty.

The Langevin model [6,7] is a useful starting point to describe thermal energy
collisions between an ion and a polarizable neutral particle. Charge-exchange collision
rates between C_{60}^{+} and alkali atoms at thermal energies have been
shown [1] to scale with polarizability and reduced mass as predicted by the Langevin model
[6,7]. However these measurements exhibited larger rates than this model estimates. In
this model, the neutral is attracted by a charge-induced dipole interaction which results
in a capture trajectory for impact parameters less than a critical value b^{*}
determined by the collision energy E_{0 }and_{ }neutral_{ }polarizability a. However, the collision separation at which charge-exchange occurs
r_{c} is determined by the specific potential curve crossing involved. It is
useful to compare r_{c }with b^{*} to obtain a clearer interpretation of
the collision process. For the collision models described below, the calculated critical
impact parameters were in the range b^{*}~ 10-20 Å. The neutral-ion separation at
the curve crossing can be estimated as in Ref.[8] for collisions involving multiply
charged ions at thermal energies. For collisions of C_{60}^{2+} with Li,
we estimate a crossing separation of r_{c}~ 5-7 Å from ion center, assuming two
point charges on the ion surface. Consequently, in the present experiments, b^{*}_{
}is sufficiently greater than r_{c} that the collision rates are expected to
be more dependent on the ion charge distribution through the ion-neutral interaction than
on details of the charge-exchange curve crossing. This is in contrast to the measurements
determining details of C_{60}^{z+} fission energetics [4] and
charge-exchange measurements of C_{60}^{2+} with^{ }C_{60}^{
}at high collision energies [9] both of which are more strongly dependent on the
details of the charge dynamics at the point of charge-exchange. As a result of these
considerations, the following analysis will concentrate on characterizing the dependence
of the long range charge-induced dipole interaction on the ion charge distribution. Decay
rate measurements will be compared with calculated collision rates derived from different
assumptions of this charge distribution.

In the case of multiply-charged^{ }ions, the Langevin model predicts collision
rates proportional to ion charge *z*. However, as indicated in Fig. 2, the measured
relative decay rates of C_{60}^{3+}, C_{60}^{2+ }and C_{60}^{+}
are clearly inconsistent with this simple Langevin model. Considering that the diameter of
C_{60}^{z+} (~7Å) is only a factor of 2-3 smaller than the critical
impact parameter b^{*}, we propose that this departure from the Langevin model
arises from an increased sensitivity to the nonuniformity of the ion charge distribution.
As will be discussed more thoroughly below, a nonuniform ion charge distribution can arise
from Jahn-Teller distortions of the icosahedral ion structure. Consequently, an analysis
of the collision process will require a more detailed description of the ion charge
distribution.

In many environments C_{60} behaves as a delocalized p-electron
system with a polarizability comparable to that of a metal sphere of the same diameter
[10]. If C_{60}^{z+ }is modeled as a rigid metallic sphere of 3.55 Å
radius, during the collision it becomes polarized by the fields of the induced dipole
giving rise to an induced charge which is nonuniformly distributed on the microsurface.
However, this nonuniformity was calculated and found to produce insignificant deviations
from the Langevin cross sections (<1%) for impact parameters comparable to b^{*}~
15 Å.

In order to consider greater variations in the charge distribution, we chose to
construct a distribution based on an assembly of point charges. Minimal energy
configurations for a set of like charges on the surface of a sphere have been considered
previously [11] and recently applied to charge-exchange [3], electrochemical reduction
[12] and dissociation [4] of C_{60}^{z+}. Only the simpler geometries for
2 charges at opposite ends of a diameter, and 3 charges at the vertices of an equilateral
triangle will be relevant to our analysis of doubly and triply ionized species. We present
the following modifications of the Langevin model which involve point charge
approximations of the charge distribution. Although each distribution is based upon a
minimal energy configuration, these alternative models cover the two extremes of fixed and
mobile charges.

Figure 3.The model geometry used to describe the interaction of C_{60}^{3+ }having mass M with a neutral species of mass m and polarizability a is shown. Point charges are positioned on the ion microsurface at radii R_{i }and angular separations which minimize the repulsive Coulomb interaction. The interaction potential between the point charges and the induced dipole moment, p, is defined in Eq.(2).

In contrast to the metallic model, we assume that the *z* charges are localized to
points on the C_{60}^{z+} surface. The collision model based on this
distribution was evaluated by explicitly integrating the trajectory to determine the cross
section. To accomplish this, forces were computed for the charge-induced dipole
configuration as shown in Fig. 3 for *z=3*. Charges on C_{60}^{3+}
with radius *R* induce a dipole *p* on the neutral particle of polarizability a. The induced dipole is expressed in terms of the net field from the
point charges,** **. The potential
energy V is expressed by

, (2)

and the force **F**_{i }on m due to the charge located at** r**_{i }is
given by

(3)

where **n**_{i }is a unit vector in the direction of **r**_{i}.
The total force is then given by and the
resulting ion rotation follows from the torque equation **.**

To determine the cross sections for each charge state *z=1-3*, a particular
orientation of the charge distribution was selected and the critical impact parameter b^{*}
was determined from the outcome of successive trajectories which varied the impact
parameter. This evaluation was repeated for random selections of orientation and initial
velocity in a Monte Carlo fashion to average the cross section over all orientations and
the velocity distribution of the neutral beam. This average cross section <s_{z} > is then related to the collision rate where is the neutral flux for atoms with speeds between *v* and *v+dv*.

It is essential to point out here that rotational averaging of the ion charge
distribution and the resulting charge-neutral interaction will not occur during the
collision trajectory of alkali atoms or C_{60} since the rotational period of ~20
ps at 300K is a factor of ~30 longer than the collision duration for Li, and a factor of
~3 for C_{60}.

In this case, the charges are considered sufficiently mobile for the distribution to maintain an orientation determined by the induced dipole. Such a model is based on the assumption that the net torque exerted by the induced dipole on the charges is capable of maintaining the distribution of point charges in the lowest energy configuration. In this configuration, one charge is oriented nearest the dipole throughout the neutral trajectory and the remaining charges are positioned to minimize the repulsive energy but otherwise free to rotate about the collision line of centers. In this orientation, the net force is a central force so that the net torque vanishes and calculation of the collision cross section reduces to the solution of a quartic equation which can be performed without the need for Monte Carlo methods. However, the calculations were performed both ways as a check on the Monte Carlo asymptote, and very close agreement was found.

**Figure 4.** A plot of experimental ratios of decay rates for
multiply-charged ions is compared with calculations based on different models of the ion
charge distribution. The data indicated by filled circles refer to Li measurements and
open circles to Cs measurements of C_{60}^{z+ }decay rates. Several decay
measurements for fragments C_{56}^{z+ }and C_{58}^{z+ }are
also shown. Calculated ratios indicated by open circles refer to the Langevin model,
filled (open) squares to Li (Cs) decay in the stationary charge model and filled (open)
triangles to Li (Cs) decay in the mobile charge model. Symbols refer to each individual
charge state but are offset from the x-axis marker for clarity. Dashed lines are guides
for the eye indicating trends of the model calculations.

The relative rates k_{z}/k_{1} for Li and Cs collisions with C_{60}^{z+}
are compared in Fig. 4. Rates calculated with the stationary charge model are observed to
agree closely with those calculated by the Langevin model. This was found to be the case
even for the absolute rates with different *z*. This is a consequence of averaging
over random orientations which yields an effective spherical charge distribution. In
general, any model relying on a stationary charge distribution will approach the Langevin
result after such averaging over random orientations. However, the experimental
measurements are in sharp disagreement with both these calculations.

Relative rates for the mobile charge model are also shown in Fig. 4 and these
calculated rates display close agreement with experimental results. Collisions of Li and
Cs with C_{58}^{z+}, C_{56}^{z+} fragments demonstrate
similar agreement with the mobile model calculations. Charge-exchange collisions of C_{60}^{z+
}with neutral C_{60} were also measured. It was observed that the
charge-exchange of C_{58}^{+2 }with C_{60} resulted in *equal*
product densities of C_{60}^{+ }and C_{58}^{+} confirming
that stable products are formed in these collisions between heavy particles. In addition,
the symmetric exchange of C_{60}^{+ }with C_{60 }was observed to
occur without loss of C_{60}^{+} so that only the loss rates for C_{60}^{3+
}and C_{60}^{2+} could be determined. The ratio of these rates was
measured to be (k_{3}/k_{2}) = 1.38±0.08 and the mobile charge model
yields a ratio of 1.37, in close agreement with measurement. It is evident that motion of
the charge distribution during the trajectory plays an essential role in the physics of
this collision process and that a nonuniform charge distribution alone is not sufficient
to explain this phenomena.

As shown in Fig. 4, both measurements and mobile model calculations exhibit relative
rates only fractionally larger than unity, which suggests that the single charge nearest
the neutral during the trajectory effectively determines the collision rate. The absolute
rates calculated for Li collisions with the mobile charge model are larger than the
Langevin rates by a factor of 2.1 for C_{60}^{+}, 1.3 for C_{60}^{2+
}and 1.1 for C_{60}^{3+}, and similar results were found for Cs. This
result is expected as the multiply charged ions more closely approximate a uniform charge
distribution with increasing *z*. These calculations are consistent with previous
measurements [1] of alkali charge-exchange with C_{60}^{+} which indicated
absolute rates in excess of the Langevin model by a factor of 2-3. Bohme [2,13] also
measured occasional ion-neutral collision rates larger than Langevin rates for collisions
of C_{60}^{+} and C_{60}^{2+ }with several organic
species.

Delocalized charges on the C_{60}^{z+} ion surface have been neglected
in our calculations. Dielectric screening by these charges would reduce the fields at the
position of the neutral leading to a smaller induced dipole and as a result slower
collision rates. In the stationary charge model, the average over random orientations will
tend to average out screening effects in the relative rates. However, in the mobile charge
model for *z=1-3*, only the closest charge contributes significantly to the induced
dipole, so that the effect of screening will be roughly independent of *z*. In this
case, the relative rate analysis depending on rate ratios would be insensitive to the
presence of screening. Furthermore, C_{60}^{z+} fission measurements [4]
indicate that screening effects were observed only for z6.

It is also important to point out that the charge-exchange collisions studied here with
*z>1* occur without an energy barrier imposed by coulomb repulsion [2,3]. The
estimated ion-neutral separation at the charge-exchange curve crossing of r_{c}~
5-7 Å and the neutral ionization potentials of Cs (3.9 eV), Li (5.4 eV) and C_{60}
(7.6 eV) result in an exothermic process which probably leaves the C_{60}^{(z-1)+
}ion in an excited electronic state.

The close agreement observed between the theoretical model and measured collision rates
is surprising since the ability for charge to freely move about on the ion surface would
seem to be inconsistent with the presence of a nonuniform charge distribution. However,
such a model of the charge dynamics becomes quite plausible upon considering the
consequences of both static and dynamic Jahn-Teller effects in C_{60}^{z+}.
Recent *ab initio* calculations have shown that both positive [14] and negative [15]
ions of C_{60 }with open electronic shells undergo static Jahn-Teller distortions
which lower the icosahedral_{ }symmetry of the neutral molecule. These distortions
are predicted to introduce changes in the bond lengths and associated charge distributions
near an equator of the molecular cage. The ion models introduced here which treat point
charges confined to the spherical surface may be considered as a simple representation of
these distortions. Dynamic Jahn-Teller effects have been indicated in photoemission
measurements [16] of C_{60}^{-} and also as the basis for the weak
temperature dependence of electron paramagnetic resonance (EPR) spectra of triplet state C_{60}
[17-19]. The EPR linewidth variation with temperature is characteristic of a rotation of
the symmetry axis about the direction of the magnetic field. This observation is
interpreted to result from rapid (~10^{-14} -^{ }10^{-13} s)
tunneling [19] among nearly degenerate vibronic states associated with different symmetry
axes. In the case of C_{60}^{z+ }collisions, a similar tunneling among
states with different axes of molecular symmetry could reorient the charge inhomogeneity
during the collision trajectory. Such a pseudorotation of the charge distribution would
provide the apparent charge mobility suggested by our collision model. Further
investigations are planned to detect the presence of dynamic Jahn-Teller effects in
collisions by measuring the dependence of the collision rates on the vibrational
temperature of trapped C_{60}^{z+} over a range of 10 to 300K.

To summarize, charge-exchange collisions of C_{60}^{z+} with both
alkali atoms and C_{60} are observed to occur with rates which are relatively
insensitive to the charge state. This result contradicts calculations based upon a uniform
charge distribution including the standard Langevin model. A theoretical model which
closely predicts measurements of the relative rates incorporates an array of point charges
on the C_{60}^{z+} surface to approximate the non-uniform distribution. In
addition, the model includes the property of charge mobility which allows the distribution
to reorient during the collision trajectory. These characteristics of charge localization
and mobility, although seemingly contradictory, are both required in the collision model
to describe experimental results. Jahn-Teller effects including distortion of the ion
charge distribution as well as a pseudorotation of this distribution yield a plausible
basis for the physics characterized by the model.

We would like to thank Michael Burns, Mordechai Rokni and Abraham Szöke for relevant discussions during the progress of this work. This research was fully supported by The Rowland Institute for Science.

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