Modeling vacancies in graphite via the Hückel method

It is known that when irradiating a graphite surface with ions the predominant source of defects are vacancies. Vacancies are also formed in a growing graphite sheet and cannot be filled. The theoretical work that has been carried out so far on the properties of these defects has only involved quite small model systems. Calculations on graphite, or closely related carbon phases like nanotubes, with randomly distributed vacancies require very large systems allowing only the simplest model to be used. We have used the H\"uckel method to model vacancies, both ordinary and hydrogenated, by fitting the H\"uckel energy levels to those resulting from a valence effective Hamiltonian calculation. The three atoms neighboring a vacancy are treated as pseudo-π orbitals and our calculations suggest that they together contribute with one extra π electron to the system. Using this model optical and electronic properties of a graphite sheet as a function of vacancy density have been calculated.