Reduction of activation energy barrier of Stone-Wales transformation in endohedral metallofullerenes

Using ab initio calculations, we examine effects of encapsulated metal atoms inside a ${\mathrm{C}}_{60}$ molecule on the activation energy barrier for the Stone-Wales transformation. The encapsulated metal atoms we study are K, Ca, and La which nominally donate one, two, and three electrons to the ${\mathrm{C}}_{60}$ cage, respectively. We find that isomerization of the endohedral metallofullerene via the Stone-Wales transformation can occur more easily than that of the empty fullerene owing to the charge transfer. When K, Ca, and La atoms are encapsulated inside the fullerene, the activation energy barriers are lowered by 0.30, 0.55, and $0.80\mathrm{eV}$, respectively compared with that of empty ${\mathrm{C}}_{60}$ $\left(7.16\mathrm{eV}\right)$. The lower activation energy barrier of the Stone-Wales transformation implies the higher probability of isomerization and coalescence of metallofullerenes, which require a series of Stone-Wales transformations.

Figure 1

Schematic energy diagram and the atomic configuration along the reaction coordinate in the Stone-Wales transformation of empty ${\mathrm{C}}_{60}$. (a) Energy profile along the reaction coordinate. The dots represent the energies of the replicas in the SW transformation in the NEB method. (b) Atomic rearrangement from the $I_h$ isomer to the $C_{2v}$ isomer of the empty ${\mathrm{C}}_{60}$ molecule. Here, the rotating carbon dimer is shown in black.

Figure 2

(Color online) Density of states (DOS) for ${\mathrm{C}}_{60}$ and $\mathrm{La}@{\mathrm{C}}_{60}$ in the transition state [(a) and (c), respectively] and the isodensity surface plots of particular states for ${\mathrm{C}}_{60}$ and $\mathrm{La}@{\mathrm{C}}_{60}$ [(b) and (d)]. The energy levels of the wave functions in (b) and (d) are indicated by arrows in (a) and (c), respectively. The isodensity value is $0.0014e∕{\mathrm{\AA }}^3$ and the surface is color-coded according to the sign of the wave functions.

Figure 3

(Color online) Atomic structures of the transition state configuration for (a) ${\mathrm{C}}_{60}$ and (b) $\mathrm{La}@{\mathrm{C}}_{60}$, and PDOS of two atoms [labeled $A$, $B$ and $A^{\prime }$, $B^{\prime }$ in (a) and (b), respectively] which have dangling bonds in the transition state, for (c) ${\mathrm{C}}_{60}$ and (d) $\mathrm{La}@{\mathrm{C}}_{60}$. The defect states due to the dangling bonds or distorted bonding configurations are indicated by arrows. The red solid and blue dotted lines are the PDOS onto $2p$ orbitals of $A$, $A^{\prime }$ and $B$, $B^{\prime }$ atoms, respectively.