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The intershell and interlayer interaction (complexation) energies of C60 inside C240 (C60@C240) and of graphene sheets are investigated by all-electron density functional theory (DFT) using generalized gradient approximation (GGA) functionals and a previously developed empirical correction for dispersion (van der Waals) effects (DFT−D method). Large Gaussian basis sets of polarized triple-ζ quality that provide very small basis set superposition errors (<10% of ΔE) are employed. The theoretical approach is first applied to graphene sheet model dimers of increasing size (up to (C216H36)2). The interaction energies are extrapolated to infinite lateral size of the sheets. The value of −66 meV/atom obtained for the interaction energy of two sheets supports the most recent experimental estimate for the exfoliation energy of graphite (−52 ± 5 meV/atom). The interlayer equilibrium distance (334 ± 3 pm) is also obtained accurately. The binding energy of C60 inside C240 is calculated to be −184 kcal mol-1 which is about 89% of the corresponding value of a similarly sized graphene sheet model dimer. Geometric relaxation of the monomers upon complexation and nonadditivity (multilayer) effects are found to be negligible. The various contributions to the binding (Pauli exchange repulsion, electrostatic and induction, dispersion) are comparatively analyzed for the sheets and for C60@C240. The binding in both systems is that of typical van der Waals complexes; that is, the dispersion contributions play a major role as also indicated by the fact that conventional GGA functionals yield purely repulsive interactions. The plots of the electrostatic potential of the fragments often used as tools for analysis lead here to qualitatively wrong conclusions. The relatively large binding energy of C60@C240 can be explained by favorable dispersion, induction, and charge-transfer interaction contributions but reveals no special role of the π orbitals. According to population analyses, about 0.67 electrons are transferred from the inner to the outer cage in C60@C240 upon complex formation.
Grimme et al. (Fri,) studied this question.