Microscopic mechanism of fullerene fusion Seungwu Han, 1 Mina Yoon, 2 Savas Berber, 2 Noejung Park, 3 Eiji Osawa, 4 Jisoon Ihm, 3 and David Tománek 2, * 1 Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544, USA and Department of Physics, Ewha Womans University, Seoul 120-750, Korea 2 Physics and Astronomy Department, Michigan State University, East Lansing, Michigan 48824-2320, USA 3 School of Physics, Seoul National University, Seoul 151-742, Korea 4 NanoCarbon Research Institute, Chosei, Chiba 299435, Japan (Received 28 June 2004; published 22 September 2004) Combining total energy calculations with a search of phase space, we investigate the microscopic fusion mechanism of C 60 fullerenes. We find that the 2+2 cycloaddition reaction, a necessary precursor for fullerene fusion, may be accelerated inside a nanotube. Fusion occurs along the minimum energy path as a finite sequence of Stone-Wales transformations, determined by a graphical search program. Search of the phase space using the “string method” indicates that Stone-Wales transformations are multistep processes, and provides detailed information about the transition states and activation barriers associated with fusion. DOI: 10.1103/PhysRevB.70.113402 PACS number(s): 81.05.Tp The discovery of fullerenes 1 and nanotubes 2 has ignited strong interest in these and related carbon nanostructures. Due to the unusual stability of the graphitic sp 2 bond, large- scale structural changes in bulk fullerene crystals occur only under extremely high pressures and temperatures. 3,4 On the other hand, fullerenes in nanotube peapods 5 have been ob- served to fuse 6,7 at relatively low temperatures near 1100 ° C, significantly below the decomposition temperature of fullerenes 8 or graphite 9 near 4000 °C. No information is available about the detailed fusion process except the obvi- ous conclusion that strong sp 2 bonds should not be broken during structural rearrangements leading to fusion. In view of the fact that even minor structural changes in carbon nano- structures may modify significantly their physical properties, including magnetism, 10,11 there is additional interest in un- derstanding fusion as a way to control large-scale structural transformations. Here we study the microscopic fusion mechanism of fullerenes. We show that large-scale structural changes, in- cluding fusion, can be achieved by a finite sequence of gen- eralized Stone-Wales transformations, which involve only bond rotations and avoid bond breaking. Using a graphical search program, 12 we determine the optimum reaction path- way for thermal fusion of fullerenes. Search of the phase space by the “string method” provides detailed information about the optimum pathway, including the identification of activation barriers and transition-state geometries. We find the fusion process to be exothermic. The fusion dynamics is fast in spite of the formidable total activation barrier close to 5 eV, associated with each Stone-Wales transformation. These bond rotations turn out to be multistep processes with lower individual activation barriers. We calculate the total energy of the fullerene system using an electronic Hamiltonian that had been applied successfully to describe the formation of peapods, 13 multiwall nanotubes, 14 the dynamics of the “bucky shuttle,” 15 and the melting of fullerenes. 8 Our numerical results are compared to those of ab initio density functional calculations, which use a numerical basis to represent localized atomic orbitals, 16 and which have been applied successfully to nanotubes and fullerenes. 17 Structural optimization is performed using the conjugate gradient technique. Our total energy formalism de- scribes accurately not only the covalent bonding within the sp 2 bonded fullerenes, but also the weak interaction between fullerenes. We find it crucial to use an electronic Hamiltonian in this study, since analytical bond-order potentials do not describe the rehybridization during the fusion process with a sufficient precision. The fusion of two C 60 molecules to a C 120 capsule, which has been observed in peapods, 6,7 is driven by the energy gain associated with reducing the local curvature in the system. Still, this reaction involves a large-scale morphological change and will only occur, if the required activation barrier is small. A previous study, 18 based on minimizing the classical ac- tion, suggests that the fusion reaction should be a multistep process. Due to the computational limitations associated with the formidable task to find a contiguous minimum-energy path in the 360-dimensional configurational space of the sys- tem, and to anticipate the optimum one-to-one atomic map- ping between the initial and the final structure, we expect the “true” activation barrier for this reaction to lie below the relatively high postulated value of 8 eV. Combining a very similar total energy functional with a method to identify all intermediate steps, we identify in the following an alternate reaction path with lower activation barriers. It appears that the most likely fusion path may involve a sequence of bond rotations, called generalized Stone-Wales (GSW) transformations. GSW transformations are known to require much lower activation energies than processes in- volving bond breaking, and have been studied extensively in sp 2 bonded carbon structures. 12,19,20 A possible GSW path- way for fusion has been suggested based on a “qualitative reasoning assisted search” for structures along the minimum- energy path. 21 The initial step in that study, however, is a reaction between two pentagons facing each other, which is energetically unaccessible. In order to obtain microscopic insight into the fusion re- action, avoiding the above shortcomings, we investigated the optimum reaction path for the the 2C 60 → C 120 fusion. It is PHYSICAL REVIEW B 70, 113402 (2004) 1098-0121/2004/70(11)/113402(4)/$22.50 ©2004 The American Physical Society 70 113402-1