TAO-DFT investigation of electronic properties of linear and cyclic carbon chains

Abstract

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...

Aromaticity of Even-Number Cyclo[n]carbons (n = 6–100)

“…Based on the GIMIC calculations, they and the larger cyclo[ n ]carbons are nonaromatic polyalkynes, which perfectly explains the previously observed saturation of electronic descriptors such as the ionization potential, electron affinity, singlet–triplet splitting, singlet–quintet splitting, and so forth of the larger cyclo[ n ]carbons. 8 , 28 , 29 …”

“…Seenithurai and Chai 29 recently reported a systematic density functional theory (DFT) study of the energy differences between the lowest singlet and triplet states and between the lowest singlet and quintet states of cyclo[ n ]carbons ( n = 8–100). They also reported ionization potentials, electron affinities, fundamental gaps, occupation numbers of the frontier orbitals, and the relative energy with respect to the linear isomers.…”

Giant Switching Effect and Spintronic Transport Properties in Cyclo[18]carbon‐Based Molecular Devices

“…The successful preparation of C 18 has garnered significant interest in the study of its potential properties. [ 9–17 ] Currently, C 18 composed of 18 carbon atoms by sp‐hybridization has been demonstrated to exhibit ohmic and quasi Schottky features, as well as current limiting ability in molecular devices. [ 18 ] Furthermore, C 18 may display excellent conductivity in molecular devices owing to its extensive π electron delocalization.…”

Energetics of Formation of Cyclacenes from 2,3‐Didehydroacenes and Implications for Astrochemistry

“…To overcome the computational expense of high‐level ab initio multi‐reference methods, thermally assisted‐occupation density functional theory (TAO‐DFT) was recently developed, [57, 58] and shows to be a very efficient electronic structure method for studying the properties of large ground‐state systems (e.g., containing up to a few thousand electrons) with strong static correlation effects [52, 68, 69] . TAO‐DFT is a density functional theory with fractional orbital occupations, wherein strong static correlation is explicitly described by the entropy contribution, [57] with a function of the fictitious temperature and orbital occupation numbers.…”

“…Accordingly, TAO‐DFT reduces to KS‐DFT for SR systems, and outperforms KS‐DFT for MR systems. TAO‐DFT has been widely applied to study the electronic properties of various MR systems at the nanoscale level including acenes and cyclacenes [52–54, 68–70] due to its computational efficiency that is similar to KS‐DFT. Therefore, we adopt TAO‐DFT to investigate the possibility of n ‐cyclacene ( n =10–20) formation from the corresponding n ‐didehydroacene.…”