▎ 摘　　要

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 withn= 2-15 benzenoid rings fused together at each side, designated asn-pyrenes (as they could be expanded from pyrene). For all thenvalues considered,n-pyrenes are ground-state singlets. With increasing the size ofn-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. Whennincreases, there is a smooth transition from the nonradical character of the smallern-pyrenes to the increasing polyradical nature of the largern-pyrenes. Furthermore, the latter is shown to be related to the increasing concentration of active orbitals on the zigzag edges of the largern-pyrenes.