On the Binding properties and HOMO-LUMO gaps of Polycyclic Aromatic Hydrocarbon clusters through DFT calculations

The mechanism of soot particle formation in combustion can be depicted as the early formation of Polycyclic Aromatic Hydrocarbons (PAHs), their self-assembly into large aromatic structures and clusters and finally the coagulation and rearrangement of such clusters to form soot particles. From PAHs to clusters and finally to soot particles, the mass of the formed entities moves from 128-700 Da of the PAH class, to about 1000 - 3000 Da of the PAH clusters (corresponding to an equivalent spherical size of 1 - 3 nm), and finally to masses larger than 3000 Da (corresponding to 4 - 20 nm spherical particle sizes) for soot. During particle nucleation, particularly in correspondence to the early changes of particle size, the spectral light absorption of carbon nanoparticles changes. Molecular PAHs, the building blocks for solid soot particles, comprise a variety of compounds and moieties. As recently visualized by high-resolution atomic force microscopy (HR-AFM), a large fraction of the PAH molecules contains fused six-ring units organized in almost entirely peri-condensed structures with zigzag and free edges. Many molecules exhibit one or two arm-chair edges while only very few present bay-edges. Some others have archipelago-type/cross-linked structures. Several molecules exhibit aliphatic branches and many molecules contain penta-rings on their periphery while a smaller fraction have penta-rings (partially) embedded into the aromatic structure. Some molecules have odd carbon atom numbers (phenalenyl-like) and contains unpaired ?-electrons within the aromatic structure, as well as those with peripheral penta-rings. The presence of unpaired ?-electrons could have importance at the onset of soot formation, when gas-phase molecules and weak clusters convert to a condensed, solid-phase material. Two types of bonding processes might occur- A ?-stacking mechanism (pancake bonding) that forms multi-electron/multi-center delocalized bonds, which are covalent-like, with shorter intermolecular distances and slightly stronger interactions with respect to van der Waals interactions. A second type of bonding is conventional ?-bond formation, with longer distance and weaker strength than regular C-C bond. In this work, we use density functional theory (DFT) with hybrid functional and localized Gaussian basis set (B3LYP/6-31G**) to calculate binding energies and HOMO-LUMO gaps of some PAH molecules and radicals identified by HR-AFM, and their homogeneous clusters. The cluster structure is found to impact the HOMO-LUMO gap with pancake configurations lowering the gap values. We provide theoretical evidence about the morphology of the PAH clusters that may be responsible for particle nucleation.