Huang H.-J.Seenithurai S.Chai J.-D.JENG-DA CHAI2021-07-282021-07-28202020794991https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087115036&doi=10.3390%2fnano10061236&partnerID=40&md5=7f2b7091a3173d032182bfbd548951cbhttps://scholars.lib.ntu.edu.tw/handle/123456789/573481At 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 n = 2–15 benzenoid rings fused together at each side, designated as n-pyrenes (as they could be expanded from pyrene). For all the n values considered, n-pyrenes are ground-state singlets. With increasing the size of n-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 n increases, there is a smooth transition from the nonradical character of the smaller n-pyrenes to the increasing polyradical nature of the larger n-pyrenes. Furthermore, the latter is shown to be related to the increasing concentration of active orbitals on the zigzag edges of the larger n-pyrenes. ? 2020 by the authors. Licensee MDPI, Basel, Switzerland.journal article10.3390/nano100612362-s2.0-85087115036