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

Abstract

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.

Statistics of work and orthogonality catastrophe in discrete level systems: an application to fullerene molecules and ultra-cold trapped Fermi gases

“…As shown in Figure 1, the valence electronic structure of the neutral and ionized clusters is made of discrete energy levels separated by an average energy difference of about 0.2 eV. The predicted band gap value of 1.82 eV for C 60 is consistent with experiments [47] and previous calculations [18]. Core ionization leads to a decrease of the band gap in of about 0.5 eV (Table 1).…”

“…The former is expressed by the photo-current probability, involving the initial core state and the final photo electron state. The latter is manifested by the work distribution in Equation 2, which can be interpreted as the probability density that the work is used to excite valence electrons at the expense of the kinetic energy of the photoelectron, ε [17][18][19]. Indeed, P(W) accounts for the N − 1 electrons that do not directly participate in the ionization process.…”

“…The corresponding kinetic energy spectrum was observed to have an asymmetric peak at the binding energy of the core level with a power-law singularity, which has then become known as the Fermi edge singularity [7]. Similar patterns were afterwards identified in a large number of coreionized systems [8,9], including organic molecules [10] and carbon-based nanomaterials [11][12][13][14][15][16][17][18][19], where an additional signature of the Anderson orthogonality catastrophe are the secondary peaks, or shake-up satellites, in the core level spectra. Despite the diversity of contexts in which Fermi edge resonance and Anderson orthogonality catastrophe occur [20][21][22][23][24][25][26][27][28][29][30], the same generic physics has been recently observed in the controllable domain of ultra-cold trapped gases, as a response to the embedding of a single probe qubit, i.e., a two-level impurity [31,32].…”

“…To depict the rearrangement of the valence electronic structure, we use a DFT approach in which we replace the core electrons of a specific atom in the molecule with an effective core potential (ECP) of the Stevens-Basch-Krauss (SBK) type [40], whose parameters are adjusted to describe neutral and core-ionized atomic carbon [10]. The valence electrons in this reference atom are described by a d-polarized double split-valence pseudo-basis, being specifically designed for the considered ECP and optimized for the neutral (C 60 ) and ionized ( ) clusters [18,19]. As for the core and valence electrons of all other atoms in the compound, we select the d-polarized triple split-valence basis set denoted 6-311G* [41].…”

“…The average core energy ε c for C 60 overestimates the experimental C 1s energy by a percentage error of about 7%. Possible causes for this discrepancy are discussed in [18]. The valence states are of the form and , where and are the valence-eigenvectors of coefficients for C 60 and , respectively.…”