Reprint of: Preparation and UV/visible spectra of fullerenes C60 and C70

AbstractThe preparation and isolation of pure fullerene-60 and fullerene-70 is described. The solution UV/visible absorption spectra of the two molecules are presented

Electronic Structure of Disclinated Graphene in an Uniform Magnetic Field

The electronic structure in the vicinity of the 1-heptagonal and 1-pentagonal defects in the carbon graphene plane is investigated. Using a continuum gauge field-theory model the local density of states around the Fermi energy is calculated for both cases. In this model, the disclination is represented by an SO(2) gauge vortex and corresponding metric follows from the elasticity properties of the graphene membrane. To enhance the interval of energies, a self-consistent perturbation scheme is used. The Landau states are investigated and compared with the predicted values.Comment: keywords: graphene, heptagonal defect, elasticity, carbon nanohorns, 13 page

Fullerene graphs have exponentially many perfect matchings

A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces. We show that fullerene graphs have exponentially many perfect matchings.Comment: 7 pages, 3 figure

Carbon clusters near the crossover to fullerene stability

The thermodynamic stability of structural isomers of $\mathrm{C}_{24}$, $\mathrm{C}_{26}$, $\mathrm{C}_{28}$ and $\mathrm{C}_{32}$, including fullerenes, is studied using density functional and quantum Monte Carlo methods. The energetic ordering of the different isomers depends sensitively on the treatment of electron correlation. Fixed-node diffusion quantum Monte Carlo calculations predict that a $\mathrm{C}_{24}$ isomer is the smallest stable graphitic fragment and that the smallest stable fullerenes are the $\mathrm{C}_{26}$ and $\mathrm{C}_{28}$ clusters with $\mathrm{C}_{2v}$ and $\mathrm{T}_{d}$ symmetry, respectively. These results support proposals that a $\mathrm{C}_{28}$ solid could be synthesized by cluster deposition.Comment: 4 pages, includes 4 figures. For additional graphics, online paper and related information see http://www.tcm.phy.cam.ac.uk/~prck

Molecular Dynamics Study of Bamboo-like Carbon Nanotube Nucleation

MD simulations based on an empirical potential energy surface were used to study the nucleation of bamboo-like carbon nanotubes (BCNTs). The simulations reveal that inner walls of the bamboo structure start to nucleate at the junction between the outer nanotube wall and the catalyst particle. In agreement with experimental results, the simulations show that BCNTs nucleate at higher dissolved carbon concentrations (i.e., feedstock pressures) than those where non-bamboolike carbon nanotubes are nucleated

Ab initio density functional investigation of B_24 cluster: Rings, Tubes, Planes, and Cages

We investigate the equilibrium geometries and the systematics of bonding in various isomers of a 24-atom boron cluster using Born-Oppenheimer molecular dynamics within the framework of density functional theory. The isomers studied are the rings, the convex and the quasiplanar structures, the tubes and, the closed structures. A staggered double-ring is found to be the most stable structure amongst the isomers studied. Our calculations reveal that a 24-atom boron cluster does form closed 3-d structures. All isomers show staggered arrangement of nearest neighbor atoms. Such a staggering facilitates $sp^2$ hybridization in boron cluster. A polarization of bonds between the peripheral atoms in the ring and the planar isomers is also seen. Finally, we discuss the fusion of two boron icosahedra. We find that the fusion occurs when the distance between the two icosahedra is less than a critical distance of about 6.5a.u.Comment: 8 pages, 9 figures in jpeg format Editorially approved for publication in Phys. Rev.

Renormalization Group Approach to the Coulomb Pseudopotential for C_{60}

A numerical renormalization group technique recently developed by one of us is used to analyse the Coulomb pseudopotential (${\mu^*}$) in ${{\rm C}_{60}}$ for a variety of bare potentials. We find a large reduction in ${\mu^*}$ due to intraball screening alone, leading to an interesting non-monotonic dependence of ${\mu^*}$ on the bare interaction strength. We find that ${\mu^*}$ is positive for physically reasonable bare parameters, but small enough to make the electron-phonon coupling a viable mechanism for superconductivity in alkali-doped fullerides. We end with some open problems.Comment: 12 pages, latex, 7 figures available from [email protected]

Restricted three body problems at the nanoscale

In this paper, we investigate some of the classical restricted three body problems at the nanoscale, such as the circular planar restricted problem for three C60 fullerenes, and a carbon atom and two C60 fullerenes. We model the van der Waals forces between the fullerenes by the Lennard-Jones potential. In particular, the pairwise potential energies between the carbon atoms on the fullerenes are approximated by the continuous approach, so that the total molecular energy between two fullerenes can be determined analytically. Since we assume that such interactions between the molecules occur at sufficiently large distance, the classical three body problems analysis is legitimate to determine the collective angular velocity of the two and three C60 fullerenes at the nanoscale. We find that the maximum angular frequency of the two and three fullerenes systems reach the terahertz range and we determine the stationary points and the points which have maximum velocity for the carbon atom for the carbon atom and the two fullerenes system