| Summary: | At the nanoscale, it has been rather troublesome to properly explore the properties associated with electronic systems exhibiting a radical nature using traditional electronic structure methods. Graphene nanoflakes, which are graphene nanostructures of different shapes and sizes, are typical examples. Recently, TAO-DFT (i.e., thermally-assisted-occupation density functional theory) has been formulated to tackle such challenging problems. As a result, we adopt TAO-DFT to explore the electronic properties associated with diamond-shaped graphene nanoflakes with <i>n</i> = 2–15 benzenoid rings fused together at each side, designated as <i>n</i>-pyrenes (as they could be expanded from pyrene). For all the <i>n</i> values considered, <i>n</i>-pyrenes are ground-state singlets. With increasing the size of <i>n</i>-pyrene, the singlet-triplet energy gap, vertical ionization potential, and fundamental gap monotonically decrease, while the vertical electron affinity and symmetrized von Neumann entropy (which is a quantitative measure of radical nature) monotonically increase. When <i>n</i> increases, there is a smooth transition from the nonradical character of the smaller <i>n</i>-pyrenes to the increasing polyradical nature of the larger <i>n</i>-pyrenes. Furthermore, the latter is shown to be related to the increasing concentration of active orbitals on the zigzag edges of the larger <i>n</i>-pyrenes.
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