A Pariser–Parr–Pople Model Hamiltonian-Based Approach to the Electronic Structure and Optical Properties of Graphene Nanostructures

Abstract

The electronic structure of graphene and related nanostructures such as graphene nanoribbons and quantum dots is frequently described within the π-electron approaches such as the tight-binding model, which completely ignores the electron–electron interactions, or the Hubbard model which takes into account only the on-site part. In theoretical chemistry, Pariser–Parr–Pople (PPP) model Hamiltonian, which takes into account the long-range part of the inter-electron Coulomb interaction, has been employed extensively, and with considerable success, to study the electronic structure and optical properties of π-conjugated molecules and polymers. Therefore, with the aim of exploring the influence of long-range Coulomb interactions on the electronic structure and optical properties of graphene nanostructures, we have recently developed a numerical approach based upon the PPP model Hamiltonian and used it to study their band structure, magnetic order, and the linear optical absorption spectra. In this chapter, we describe our approach in detail and present its numerous applications ranging from finite systems such as fullerene C₆₀ and graphene quantum dots to infinitely long quasi-one-dimensional graphene nanoribbons. Our approach is computationally inexpensive and yields results in good agreement with the large-scale first-principles calculations reported by other authors. Furthermore, some of the novel predictions resulting from our approach are also discussed.