CURVATURE IN CARBON PI-CONJUGATED SYSTEMS: A THEORETICAL AND COMPUTATIONAL STUDY

My Ph.D. course has been focused on the theoretical study of curved-conjugated carbon nanostructures, with the purpose of providing a mathematically rigorous description of curvature and its effect on the chemical and physical properties. For a long time,  pi- conjugation and aromaticity were considered unique features of planar carbon structures. During the last decades, however, the progress in synthesis and material characterization has provided us with a large number of curved  pi-conjugated structures (annulenes, circulenes, coroannulenes, fullerenes, rippled graphene, etc), thus proving that  pi-conjugation - and its effect on chemical and physical properties - can exist also in a curved environment. This work was suggested by my supervisor Prof. R. Martinazzo, who recognized during my graduate work my great interest in Mathematics and invited me to join him in the discovery of the curved world. The topic was thus approached from two points of view: we selected some curved  pi-systems - that are interesting from both a fundamental and technological perspective - and we investigated their structures and reactivity through computational methods; meanwhile, we got our hands on maths, and in particular on a field called differential geometry, to track down those tools that allow to rigorously describe the curvature of carbon structures - something that, to the best of our knowledge, had not yet done in the literature. This work is organized into three Parts. Part I and Part II contain the results of our computational investigation. The main attention was given to the study of the H adsorption energetics, a simple reaction that is however relevant in disparate fields, from astrochemistry to hydrogen storage and graphene technology. In Part I, this reaction is considered in a "flat context", which allows us to introduce basic concepts - related to  -conjugation - that is important also for the understanding of the curved world. This Part is a natural development of my graduate Thesis work - which was focused on planar graphene - and is a report of my first year of Ph.D. activity. In particular, Chapter 1 and 2 are two introductory chapters that present known results on flat graphene and polycyclic aromatic hydrocarbons (PAHs) and the H sticking, together with their relevant applications. Chapter 4 contains the results of our Density Functional Theory (DFT) investigation of the stepwise H addition to the coronene molecule, a small flat PAH. The choice of the exchange-correlation (XC) functional represented an important part of the work on coronene and is thus extensively discussed in Chapter 3. Chapter 5 is dedicated instead to large PAH clusters. Part II is entirely devoted to curved systems. Chapter 6 sets the beginning of our journey through the curved world and is dedicated to the description of the main curved carbon nanostructure. Emphasis is given here to introduce the systems we investigated: curved PAH such as coroannulene, and the C/Si interface. Thus, Chapter 7 presents the study of the stepwise H addition to coroannulene. This Chapter is closely related to Chapter 4 since coroannulene can be considered as the curved analog of coronene. Chapter 8 describes the H sticking on a periodic system, namely graphene epitaxially grown on SiC, a.k.a. the C/Si interface. Here, the curvature is due to the interaction of graphene with the substrate. The subsequent Chapter describes a quantum dynamical investigation of the Eley-Rideal reaction - leading to the formation of molecular hydrogen - on the C/Si. interface. This work was done during my stay in Toulouse, as a visiting student in the group of Prof. D. Lemoine. In Part III, the problem of curvature is approached from a conceptual perspective. In particular, Chapter 11 introduces a new model we set up to describe the local curvature of carbon atoms and its relationship with hybridization - a first step in the development of a new theoretical framework for curved  -systems. The mathematics needed to understand our model is presented in Chapter 10. The latter grew larger than expected but the author used the time of writing as the right moment to re-organized what he learned with enthusiasm during the years of his Ph.D. Finally, in Chapter 12, we draw our conclusions from the work.