it has been challenging to adequately investigate the properties of nanosystems with radical nature using conventional electronic structure methods. We address this challenge by calculating the electronic properties of linear carbon chains (l-cc[n]) and cyclic carbon chains (c-cc[n]) with n = 10-100 carbon atoms, using thermally-assisted-occupation density functional theory (TAO-DFT). For all the cases investigated, l-cc[n]/c-cc[n] are ground-state singlets, and c-cc[n] are energetically more stable than l-cc[n]. the electronic properties of l-cc[n]/c-cc[n] reveal certain oscillation patterns for smaller n, followed by monotonic changes for larger n. For the smaller carbon chains, odd-numbered l-cc[n] are more stable than the adjacent even-numbered ones; c-cc[4m + 2]/c-CC[4m] are more/less stable than the adjacent odd-numbered ones, where m are positive integers. As n increases, l-cc[n]/c-cc[n] possess increasing polyradical nature in their ground states, where the active orbitals are delocalized over the entire length of l-cc[n] or the whole circumference of c-cc[n]. Carbon is the most versatile element in forming various structures. In bulk phase, graphite and diamond, which are well-known materials, have been used for centuries. In nanoforms, fullerenes and graphene have been studied in detail for decades. In general, nanostructures can be classified into three categories: zero-dimensional (0D), one-dimensional (1D), and two-dimensional (2D) nanomaterials. Carbon forms all these nanostructures with unique shapes and properties. Over the past few decades, carbon nanomaterials have been widely studied, and applied in diverse industries 1-3. A number of carbon nanostructures have been synthesized and applied in different fields. The 0D carbon nanomaterials include clusters, quantum dots, nanoflakes, and buckyballs 3. Among them, the C 60 fullerene molecule (containing 12 pentagons and 20 hexagons), where the carbon atoms are sp 2-sp 3-hybridized, has been a popular carbon nanomaterial 1. The discovery of C 60 has led to the flourishment of carbon nanomaterials in various ways. Graphite is a bulk layered material, where the sp 2-hybridized carbon atoms in each layer are arranged in a hexagonal lattice. The 2D carbon nanomaterial, graphene, can be obtained by mechanically exfoliating a single layer of carbon atoms from graphite 2. Thus, graphene, which is a perfect arrangement of hexagons made up of sp 2-hybridized carbon atoms in a 2D planar surface, can be the thinnest (i.e., single-atom-thick) material synthesized ever. Graphene is a zero-gap semiconductor or semimetal with massless Dirac fermions with linear dispersion at low energy. Because of the Dirac-cone feature, graphene has huge potential in electronics applications 2. The discovery of graphene has also led to the discovery of other 2D materials. Besides, if a graphene sheet can be rolled up to form a seamless cylinder, one obtains a carbon nanotube (CNT), which belongs to the class of 1D nanostructures. Note that CNTs were first observed by Iijima in 19...

Recently, AIMD (ab initio molecular dynamics) has been extensively employed to explore the dynamical information of electronic systems. However, it remains extremely challenging to reliably predict the properties of nanosystems with a radical nature using conventional electronic structure methods (e.g., Kohn-Sham density functional theory) due to the presence of static correlation. To address this challenge, we combine the recently formulated TAO-DFT (thermally-assisted-occupation density functional theory) with AIMD. The resulting TAO-AIMD method is employed to investigate the instantaneous/average radical nature and infrared spectra of n-acenes containing n linearly fused benzene rings (n = 2-8) at 300 K. According to the TAO-AIMD simulations, on average, the smaller n-acenes (up to n = 5) possess a nonradical nature, and the larger n-acenes (n = 6-8) possess an increasing radical nature, showing remarkable similarities to the ground-state counterparts at 0 K. Besides, the infrared spectra of n-acenes obtained with the TAO-AIMD simulations are in qualitative agreement with the existing experimental data.

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