Energy barriers of Be and B in passing through the C₆₀ fullerene cage

We have studied the potential barriers for the penetration of atomic beryllium or boron inside the C₆₀ fullerene by performing density functional theory (DFT) calculations with three variants for the exchange and correlation: B3LYP (hybrid functional), PW91, and PBE. Four principal trajectories to the inner part of C₆₀ for the penetrating atom have been considered: through the center of six-member-carbon ring (hexagon), five-member-carbon ring (pentagon), and also through the center of the double C–C bond (D-bond) and the center of the single C–C bond (S-bond). Averaging over the three DFT variants yields the following barriers for beryllium penetrating inside a deformable fullerene: 3.2 eV (hexagon), 4.8 eV (S-bond), 5.3 eV (D-bond), 5.9 eV (pentagon). These barriers correspond to the slow and adiabatic penetration of Be, in contrast to the fast (non-adiabatic) penetration through the rigid cage of C₆₀ resulting in 5.6 eV (hexagon), 16.3 eV (pentagon), 81.8 eV (S-bond), and 93.4 eV (D-bond). The potential barriers for the boron penetrating inside deformable/rigid C₆₀ are 3.7/105.4 eV (D-bond), 4.0/86.8 eV (S-bond), 4.7/7.8 eV (hexagon), 6.8/14.0 eV (pentagon).