From acene to graphene spectrum of $\pi$ electrons with the use of the Green's function

Abstract

Origin of the spectrum of $\pi$ electrons that results from coupling of $N$ $\cal N$-long acenes via C-C covalent bonding have been traced with the use of the Green function formalism. Exact expressions of acene and graphene Green's functions, which are useful for analysis of electronic properties of these macromolecules, are obtained and advanced to the form suitable for instructive applications.