HOMO–LUMO Gaps of Homogeneous Polycyclic Aromatic Hydrocarbon Clusters

Recent UV–visible absorption spectral analyses of a series of flame-formed carbon nanoparticles show that these particles exhibit behaviors that can be closely described by the quantum confinement effect (Liu, C.; et al. Proc. Natl. Acad. Sci. 2019, 116, 12692–12697). To further interpret these results, we carried out molecular dynamics/density functional theory calculations for homogeneous clusters of polycyclic aromatic hydrocarbons (PAHs) including naphthalene, pyrene, coronene, and ovalene over a range of cluster sizes and configurational sampling. PAH clusters were built using molecular dynamics followed by a calculation of its HOMO–LUMO gap as the energy difference between the HOMO and LUMO Kohn–Sham orbitals at the B3LYP/6-31G(d) level of theory. It was found that for all PAHs studied the gap size follows a m–2/3 dependence, where m is the number of molecules in the cluster, and that such a dependence is qualitatively consistent with the quantum confinement behavior observed for flame-formed carbon nanoparticles. The detailed cluster structure is found to impact the HOMO–LUMO gap to an extent with T-shaped configurations producing lowered gap values. As it is important, we provided additional theoretical evidence to illustrate that PAH clusters behave like an indirect band gap material, in agreement with the experimental observations made earlier.