We present energy calculations of a ${\mathrm{C}}_{80}$ molecule with $D_{5d}$ symmetry encapsulated in a carbon nanotube. The approximation of a continuous tube rather than a rolled-up graphene sheet, justified by comparison with atomistic calculations, allows an expansion of the energy field into symmetry-adapted rotator functions. For a given tube radius $R$, we observe a strong dependence of the interaction energy on the molecular tilt angle and on the molecule’s lateral position in the tube. We observe a transition from on-axis lying orientations to tilted orientations at $R_1\approx 6.95$ Å and a subsequent transition to standing orientations at $R_2\approx 7.6$ Å. For tube radii larger than $R_3\approx 8.0$ Å, the molecule starts to occupy off-axis positions and assumes a lying orientation. Results are compared to the case of ${\mathrm{C}}_{70}$ molecules, with $D_{5h}$ symmetry. Our findings are consistent with recent high-resolution transmission electron microscopy measurements and are relevant for the design of new materials with tunable electronic properties.

• Received 28 October 2010

DOI:https://doi.org/10.1103/PhysRevB.83.045405