Energetics and structural characterization of ${\mathrm{C}}_{60}$ polymerization in BN and carbon nanopeapods

As in the case of carbon nanotubes, also boron nitride nanotubes may host arrays of ${\mathrm{C}}_{60}$ molecules and form a nanopeapod (NPP). The observed separation between ${\mathrm{C}}_{60}$ molecules in BN NPP’s is consistently shorter than in carbon NPP’s, which influences their electronic properties. Here we report on total-energy pseudopotential density functional theory (DFT) calculations for polymerized and nonpolymerized ${\mathrm{C}}_{60}$ chains, and optimize their atomic structures to provide a description of their energetic landscape. A fully polymerized ${\mathrm{C}}_{60}$ chain and a ${\mathrm{C}}_{60}$ dimer are found to be more stable than nonpolymerized ${\mathrm{C}}_{60}$, respectively, by 0.89 and $0.38\mathrm{eV}∕{\mathrm{C}}_{60}$. The geometry and energetics of an encapsulated ${\mathrm{C}}_{60}$ chain is not significantly different with respect to the isolated molecule. Encapsulation energies in BN and carbon NPP’s are, respectively, 1.56 and $1.67\mathrm{eV}∕{\mathrm{C}}_{60}$, which are significantly larger than the calculated activation energy for ${\mathrm{C}}_{60}$ polymerization, supporting the hypothesis that encapsulated ${\mathrm{C}}_{60}$’s in NPP’s are partially polymerized. Band structure analysis show that polymerization does not affect the gap width of the ${\mathrm{C}}_{60}$ chain. BN NPP’s are semiconductors with a gap width determined by the ${\mathrm{C}}_{60}$. The lowest unoccupied ${\mathrm{C}}_{60}$ states lie just above the Fermi level in metallic carbon NPP’s and charge transfert could take place, affecting the ${\mathrm{C}}_{60}$ geometry.

Figure 1

Atomic structures of (a) a polymerized chain of ${\mathrm{C}}_{60}$ molecules; (b) a ${\left({\mathrm{C}}_{60}\right)}_2$ dimer. The center-to-center distance in the polymer is $d$, the intermolecular bond length or shortest intermolecular distance is $l$, and the dimer length is $L$.

Figure 2

Energetic landscape of a ${\mathrm{C}}_{60}$ chain, representing the dependence of the total energy of two possible configurations with respect to center-to-center distance $d$ and shortest intermolecular distance $l$: dotted, non-polymerized chain; dashed, polymerized chain. The solid curves represent the profile of the potential barriers between the two configurations for various values of $d$. In the inset details of the total energy dependence on $d$ are given.

Figure 3

Energetic landscape of a dimer ${\left({\mathrm{C}}_{60}\right)}_2$, representing the dependence of the total energy of two possible configurations with respect to the dimer length $L$ and shortest intermolecular distance $l$: dotted, nonpolymerized chain; dashed, polymerized chain. The solid curves represent the profile of the potential barrier between the two configurations for various values of $L$. In the inset details of the total energy dependence on $L$ are given.

Figure 4

Band structures in the region close to the electronic gap for the equilibrium configurations of (a) a non-bonded ${\mathrm{C}}_{60}$ chain; (b) a polymerized ${\mathrm{C}}_{60}$ chain. The position of the Fermi level is indicated by a dashed line. In (a), labels indicate the symmetry of the molecular states corresponding to the bands in proximity of the gap.

Figure 5

Band structures in the region close to the electronic gap for the equilibrium configurations of: (a) a nonbonded ${\mathrm{C}}_{60}$ dimer encapsulated in a (10,10) carbon nanotube; (b) a double-bonded ${\mathrm{C}}_{60}$ dimer encapsulated in a (10,10) carbon nanotube. The position of the Fermi level is indicated by a dashed line.