Recursion and Path-Integral Approaches to the Analytic Study of the Electronic Properties of C60C_{60}

The recursion and path-integral methods are applied to analytically study the electronic structure of a neutral $C_{60}$ molecule. We employ a tight-binding Hamiltonian which considers both the $s$ and $p$ valence electrons of carbon. From the recursion method, we obtain closed-form {\it analytic} expressions for the $\pi$ and $\sigma$ eigenvalues and eigenfunctions, including the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states, and the Green's functions. We also present the local densities of states around several ring clusters, which can be probed experimentally by using, for instance, a scanning tunneling microscope. {}From a path-integral method, identical results for the energy spectrum are also derived. In addition, the local density of states on one carbon atom is obtained; from this we can derive the degree of degeneracy of the energy levels.Comment: 19 pages, RevTex, 6 figures upon reques

Computational study of the thermal conductivity in defective carbon nanostructures

We use non-equilibrium molecular dynamics simulations to study the adverse role of defects including isotopic impurities on the thermal conductivity of carbon nanotubes, graphene and graphene nanoribbons. We find that even in structurally perfect nanotubes and graphene, isotopic impurities reduce thermal conductivity by up to one half by decreasing the phonon mean free path. An even larger thermal conductivity reduction, with the same physical origin, occurs in presence of structural defects including vacancies and edges in narrow graphene nanoribbons. Our calculations reconcile results of former studies, which differed by up to an order of magnitude, by identifying limitations of various computational approaches

Molecular geometry optimization with a genetic algorithm

We present a method for reliably determining the lowest energy structure of an atomic cluster in an arbitrary model potential. The method is based on a genetic algorithm, which operates on a population of candidate structures to produce new candidates with lower energies. Our method dramatically outperforms simulated annealing, which we demonstrate by applying the genetic algorithm to a tight-binding model potential for carbon. With this potential, the algorithm efficiently finds fullerene cluster structures up to ${\rm C}_{60}$ starting from random atomic coordinates.Comment: 4 pages REVTeX 3.0 plus 3 postscript figures; to appear in Physical Review Letters. Additional information available under "genetic algorithms" at http://www.public.iastate.edu/~deaven

Prismane C_8: A New Form of Carbon?

Our numerical calculations on small carbon clusters point to the existence of a metastable three-dimensional eight-atom cluster C$_8$ which has a shape of a six-atom triangular prism with two excess atoms above and below its bases. We gave this cluster the name "prismane". The binding energy of the prismane equals to 5.1 eV/atom, i.e., is 0.45 eV/atom lower than the binding energy of the stable one-dimensional eight-atom cluster and 2.3 eV/atom lower than the binding energy of the bulk graphite or diamond. Molecular dynamics simulations give evidence for a rather high stability of the prismane, the activation energy for a prismane decay being about 0.8 eV. The prismane lifetime increases rapidly as the temperature decreases indicating a possibility of experimental observation of this cluster.Comment: 5 pages (revtex), 3 figures (eps

Theory of Spontaneous Polarization of Endohedral Fullerenes

A pseudo-Jahn-Teller model describing central atom distortions is proposed for endohedral fullerenes of the form A@C$_{60}$ where A is either a rare gas or a metal atom. A critical (dimensionless) coupling $g_c$ is found, below which the symmetric configuration is stable and above which inversion symmetry is broken. Vibronic parameters are given for selected endohedral fullerenes.Comment: 4 pages, REVTEX, 1 Postscript figure. [Phys. Rev. Lett. (in press)

Unusually High Thermal Conductivity of Carbon Nanotubes

Combining equilibrium and non-equilibrium molecular dynamics simulations with accurate carbon potentials, we determine the thermal conductivity $\lambda$ of carbon nanotubes and its dependence on temperature. Our results suggest an unusually high value ${\lambda}{\approx}6,600$~W/m$\cdot$K for an isolated (10,10) nanotube at room temperature, comparable to the thermal conductivity of a hypothetical isolated graphene monolayer or diamond. Our results suggest that these high values of $\lambda$ are associated with the large phonon mean free paths in these systems; substantially lower values are predicted and observed for the basal plane of bulk graphite.Comment: 4 pages 3 figures (5 postscript files), submitted for publicatio

Thermal effects on atomic friction

We model friction acting on the tip of an atomic force microscope as it is dragged across a surface at non-zero temperatures. We find that stick-slip motion occurs and that the average frictional force follows $|\ln v|^{2/3}$, where $v$ is the tip velocity. This compares well to recent experimental work (Gnecco et al, PRL 84, 1172), permitting the quantitative extraction of all microscopic parameters. We calculate the scaled form of the average frictional force's dependence on both temperature and tip speed as well as the form of the friction-force distribution function.Comment: Accepted for publication, Physical Review Letter

Anomalous Thermal Stability of Metastable C_20 Fullerene

The results of computer simulation of the dynamics of fullerene C_20 at different temperatures are presented. It is shown that, although it is metastable, this isomer is very stable with respect to the transition to a lower energy configuration and retains its chemical structure under heating to very high temperatures, T ~ 3000 K. Its decay activation energy is found to be E_a ~ 7 eV. Possible decay channels are studied, and the height of the minimum potential barrier to decay is determined to be U = 5.0 eV. The results obtained make it possible to understand the reasons for the anomalous stability of fullerene C_20 under normal conditions.Comment: Slightly corrected version of the paper submitted to Phys. Solid Stat

Magic Numbers of Silicon Clusters

A structural model for intermediate sized silicon clusters is proposed that is able to generate unique structures without any dangling bonds. This structural model consists of bulk-like core of five atoms surrounded by fullerene-like surface. Reconstruction of the ideal fullerene geometry results in the formation of crown atoms surrounded by $\pi$-bonded dimer pairs. This model yields unique structures for \Si{33}, \Si{39}, and \Si{45} clusters without any dangling bonds and hence explains why these clusters are least reactive towards chemisorption of ammonia, methanol, ethylene, and water. This model is also consistent with the experimental finding that silicon clusters undergo a transition from prolate to spherical shapes at \Si{27}. Finally, reagent specific chemisorption reactivities observed experimentally is explained based on the electronic structures of the reagents.Comment: 4 pages + 3 figures (postscript files after \end{document}