Core-hole effects in fullerene molecules and small-diameter conducting nanotubes: a density functional theory study

Core-hole induced electron excitations in fullerene molecules, and small-diameter conducting carbon nanotubes, are studied using density functional theory with minimal, split-valence, and triply-split-valence basis sets plus the generalized gradient approximation by Perdew-Burke-Ernzerhof for exchange and correlation. Finite-size computations are performed on the carbon atoms of a C(60) Bucky ball and a piece of (3, 3) armchair cylindrical network, terminated by hydrogen atoms, while periodically boundary conditions are imposed on a (3, 3) nanotube unit cell. Sudden creation of the core state is simulated by replacing a 1s electron pair, localized at a central site of the structures, with the effective pseudo-potentials of both neutral and ionized atomic carbon. Excited states are obtained from the ground-state (occupied and empty) electronic structure of the ionized systems, and their overlaps with the ground state of the neutral systems are computed. These overlaps enter Fermi's golden rule, which is corrected with lifetime and finite-temperature effects to simulate the many-electron response of the nanoobjects. A model based on the linked cluster expansion of the vacuum persistence amplitude of the neutral systems, in a parametric core-hole perturbation, is developed and found to be reasonably consistent with the density functional theory method. The simulated spectrum of the fullerene molecule is found to be in good agreement with x-ray photoemission experiments on thick C(60) films, reproducing the low energy satellites at excitation energies below 4 eV within a peak position error of ca. 0.3 eV. The nanotube spectra show some common features within the same experiments and describe well the measured x-ray photoelectron lineshape from nanotube bundles with an average diameter of 1.2 nm.