An Introduction to the Electronic Structure of π-Conjugated Molecules and Polymers, and to the Concept of Electronic Bands

In this chapter, our main goal is to provide an introduction to the basic features of the electronic structure of π-conjugated systems and to the notion of electronic band structure in π-conjugated polymers. This approach allows us to make the bridge between the molecular aspects generally considered in the chemistry community and the condensed-matter aspects usually discussed in the physics community, which will be useful to grasp the broad range of concepts described in the other Chapters. We will describe the evolution of the electronic structure in going from π-conjugated molecules to infinite polymer chains. By considering simple approaches based on the Hückel model,1 we will: (i) define the implications of periodicity along an infinite polymer chain in the context of the orbital approximation; (ii) formulate Bloch's theorem and explain the notion of the Brillouin zone; (iii) relate the evolution of the molecular orbital energies as a function of increasing oligomer length to the band structure of a corresponding polymer; (iv) introduce the concepts of bond-length alternation and bond-order alternation (which will be relevant to the discussion in Chapter 11); and (v) illustrate the impact of the presence of electron-donor and electron-acceptor moieties on the electronic structure. The reader interested in the application of more sophisticated quantum-chemical approaches to polymers can find the related information, for instance, in the book by André et al.