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

Abstract

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).