Formation dynamics of fullerene dimers $C_{118}^{+}$, $C_{119}^{+}$, and $C_{120}^{+}$

Dumbbell-shaped fullerene dimers $C_{118}^{+}$ and $C_{119}^{+}$ have recently been observed in mass spectra resulting from collisions between clusters of C${}_{60}$ molecules and keV He${}^{2+}$ or Ar${}^{2+}$ ions [H. Zettergren et al., Phys. Rev. Lett. 110, 185501 (2013) and F. Seitz et al., J. Chem. Phys. 139, 034309 (2013)]. To unveil the formation mechanisms of these fullerene dimers, systematic molecular dynamics (MD) simulations based on the self-consistent charge density functional tight-binding method have been performed for C${}_n^{+}$ + C${}_{60}$ ($n=58,59,60$) collisions following prompt atom knockouts by the fast ions. The statistics from the MD simulations indicate a much higher reactivity of $C_{59}^{+}$ and $C_{58}^{+}$ fragments compared to that of $C_{60}^{+}$. It is found that the covalently bonded dumbbell-shaped fullerene dimers $C_{118}^{+}$ and $C_{119}^{+}$ can be formed at very low-collision energies within 1 ps and are stable enough to survive on the microsecond time scale of the experiment. The thermodynamic and kinetic stabilities, as well as the bonding features, have been investigated for the most stable dumbbell dimers $C_{118}^{+}$, $C_{119}^{+}$, and $C_{120}^{+}$.

Figure 1

(a) The five representative reacting sites in the C${}_{60}$ cage: hexagonal ring centers (H), pentagonal ring centers (P), vertices (V), hexagon-hexagon bond centers (hh), and pentagon-hexagon bond centers (ph). (b) A schematic example of an initial configuration for an MD simulation for a V-hh $C_{60}^{+}$ + C${}_{60}$ collision with rotational angle $\theta$.

Figure 2

Schlegel diagrams showing the closed-cage structures of the fragments $C_{59}^{+}$ and $C_{58}^{+}$. The dashed line shows the bond formed after the cage closing process. The full circle in $C_{59}^{+}$ represents the unsaturated bivalent carbon atom. The letters P, N, H, and O indicate pentagonal, nonagonal, hexagonal, and octagonal rings, respectively.

Figure 3

Upper panel: The variation of potential energy of the $C_{59}^{+}$ fragment as a function of time. As a comparison, the B3LYP/6-31G(d) energies are also given (as empty circles), based on the geometries selected from the DFTB MD trajectory. Lower panel: The distances between the pair of atoms among the three carbon atoms C1, C2, and C3 (as labeled in the Schlegel diagram) as a function of time. In both panels, the vertical dashed line indicates the estimated cage closing time.

Figure 4

Formation probabilities of (a) $C_{120}^{+}$ and (b) $C_{119}^{+}$, $C_{118}^{+}$, as functions of center-of-mass collision KE. The results were obtained from the DFTB MD simulations.

Figure 5

Changes in potential energy of (a) $C_{60}^{+}$ + C${}_{60}$ $$ $C_{120}^{+}$ (KE = 60 eV), (b) $C_{59}^{+}$ + C${}_{60}$ $$ $C_{119}^{+}$ (KE = 5 eV), and hh-$C_{58}^{+}$ + C${}_{60}$ $$ $C_{118}^{+}$ (KE = 5 eV), as functions of time (upper panel). The B3LYP/6-31G(d) energies are given (as discrete points) for comparison, based on the geometries sampled from the DFTB MD trajectory. In the lower panel of each figure, the corresponding center-to-center distance between the two cages, $R$, is also plotted as a function of simulation time.

Figure 6

Upper panel: The probability of knocking out two carbon atoms at different positions (indicated by empty circles in the illustrated structures of fullerenes) in the C${}_{60}$ cage. Lower panel: The corresponding probability of forming $C_{118}^{+}$ dimer from the collision between $C_{58}^{+}$ and C${}_{60}$ with a collision KE of 1 eV.

Figure 7

The most stable dumbbell fullerene dimers, $C_{120}^{+}$, $C_{119}^{+}$, and $C_{118}^{+}$, produced in fullerene collisions. The red color highlights the $s{p}^3$ carbon atoms. Point groups are given in parentheses. Atomic coordinates can be found in the Supplemental Material [76].

Figure 8

Potential energy as a function of intercage distance along the dissociation and the formation paths for (a) C${}_{60}$ + C${}_{60}$, (b) C${}_{59}$ + C${}_{60}$, and (c) C${}_{58}$ + C${}_{60}$ reactions, calculated using the SCC-DFTB-D method. The crossing point of the dissociation and the formation energy curves gives an upper estimate of the transition state (TS) energy.