Self-consistent LCAO calculation of the electronic properties of graphite. II. Point vacancy in the two-dimensional crystal

Abstract

The electronic properties of a point vacancy in the two-dimensional graphite crystal are investigated within the small-periodic-cluster approach using a self-consistent all-valence-electron LCAO (linear combination of atomic orbitals) scheme previously employed for the calculations of the band structure and optical spectra of the regular lattice (part I). Eight crystal bands, 54-96 $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$ points in the Brillouin zone, selected according to the mean value theorem and ${2}^{2}$-${5}^{2}$ primitive unit cells around the site are allowed to interact. A doubly degenerate singly occupied $\ensuremath{\sigma}$ level is shown to appear in the $\ensuremath{\sigma}\ensuremath{-}{\ensuremath{\sigma}}^{*}$ band gap, 3.5 eV above the $\ensuremath{\sigma}$ band edge, with a wave function that is about 80% localized on the three nearest-neighbor atoms. The density of electronic states, charge distribution and Poisson electrostatic potential of the structure are computed and used to discuss the characteristic feature of the in connection with Coulson's defect molecule model and with current models of electron trapping mechanisms used to interpret the experimental data on Hall coefficient, resistivity and diamagnetic susceptibility of damaged graphite. Both symmetric and Jahn-Teller lattice distortions are introduced around the site, the results being used to interpret the experimentally observed decrease in lattice constant, the observed optical absorption and the vibronic parameters of the Jahn-Teller effect. Symmetric lattice relaxations are shown to have a moderate effect on the lattice energy and on the position of the level, these changes being mainly due to the response of the $\ensuremath{\pi}$ subsystem to accumulation of excess $\ensuremath{\pi}$ charge on the surrounding bonds, while Jahn-Teller distortions are shown to have a small effect on the system due to the relative rigidity of the $\ensuremath{\sigma}$ skeleton. The energy of vacancy formation as well as the energy of atom displacement and vacancy migration are directly computed from the change in total lattice energy, the results being in good agreement with experiment. The importance of introducing charge self-consistency in treating the charge redistribution in the system as well as the significance of allowing more distant atoms to interact with the vacancy electrons, is emphasized.