TABLE OF CONTENTS Vincent Crespi
Department of Physics and Materials Research Institute Pennsylvania State University, State College, PA
Since later chapters will cover the synthetic, electronic, and transport properties of carbon nanostructures in depth, here we take a different point of view and focus on the theory of their structure and geometry. The well-defined covalent bonding geometries of graphitic carbon lead to a simple set of geometrical rules that relate the global shape of a carbon nanostructure to the types of carbon rings within it.
Carbon is an unusual element. The isolated carbon atom has filled 1 s and 2 s states and two electrons in the 2 p state for a configuration of (1 s 22 s 22 p 2). Since carbon is a first-row element, the atom is very small and the Coulomb potential felt by the valence electrons is correspondingly high (remember the Coulomb potential energy varies as 1 /r). When carbon atoms are assembled into a larger structure, the potentials from nearby atoms perturb the 2 s and 2 p atomic orbitals and create bonding, nonbonding, and antibonding molecular orbitals formed from linear combinations (i.e., sums and differences) of the 2 s and 2 p states. Bonding occurs when the charge density of the electronic wavefunction occupies favorable areas, wherein the attractive atomic...
