Electronic Properties of Möbius Cyclacenes Studied by Thermally-Assisted-Occupation Density Functional Theory

Abstract

It has been extremely difficult for traditional theoretical methods to adequately predict the properties of systems possessing radical character (i.e., multi-reference systems), especially for multi-reference systems at the nanoscale. To circumvent this, we employ thermally-assisted-occupation density functional theory (TAO-DFT) to predict the electronic properties of Möbius cyclacenes, with the number of fused benzene rings ( n ) ranging from 8 to 100. In addition, to investigate the significance of Möbius topology, we also compare these properties with the respective properties of cyclacenes and acenes, containing the same number of fused benzene rings. From our TAO-DFT results, Möbius cyclacenes, cyclacenes, and acenes have singlet ground states for all the cases examined. However, unlike acenes, the electronic properties of Möbius cyclacenes and cyclacenes display clear oscillation patterns when n is small (e.g., n ≤ 10 for Möbius cyclacenes and n ≤ 23 for cyclacenes), and converge to the respective properties of acenes when n greatly exceeds 30. The polyradical character of the ground states of Möbius cyclacenes should increase with the molecular size, intimately correlated with the localization of active orbitals at the edges of molecules.

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

“…(3) , we calculate the symmetrized von Neumann entropy 16,50,51,54,[56][57][58][59][60][61][62]69 using spin-unrestricted TAO-LDA. Here, the occupation number f i,σ of the i th σ-spin orbital (i.e., up-spin orbital or down-spin orbital) obtained with spin-unrestricted TAO-LDA, which ranges from 0 to 1, is closely related to the occupation number of the i th σ-spin natural orbital 49-51 .…”

“…Besides, aiming to improve the accuracy of TAO-DFT for a wide range of applications, a self-consistent scheme determining the fictitious temperature θ in TAO-DFT has been recently proposed 53 . Since TAO-DFT is a computationally efficient electronic structure method, a number of strongly correlated electron systems at the nanoscale have been studied using TAO-DFT in recent years 16,[54][55][56][57][58][59][60][61][62] . Besides, TAO-DFT has been recently shown to be useful in describing the vibrational spectra of molecules with radical nature 63 .…”

TAO-DFT-Based Ab Initio Molecular Dynamics

“…For a GS molecule possessing a nonradical nature, the occupation numbers associated with all orbitals are very close to either 0 or 2, yielding a vanishingly small S vN value. Nonetheless, for a GS molecule with a significant radical nature, the active orbital occupation numbers can deviate significantly from 0 and 2 (for example, 0.2-1.8); hence, the corresponding S vN value can greatly increase as the number of active orbitals increases and/or the active orbital occupation numbers are closer to 1 (Rivero et al, 2013;Chai, 2014Chai, , 2017Wu and Chai, 2015;Seenithurai and Chai, 2016, 2017Wu et al, 2016;Yeh et al, 2018;Chung and Chai, 2019;Deng and Chai, 2019;Huang et al, 2020). On the basis of Equation 8, in a spin-restricted TAO-AIMD simulation, the symmetrized von Neumann entropy of a molecule at time t along a TAO-AIMD trajectory can be defined as…”

“…Owing to its computational efficiency and decent accuracy for exploring the properties of electronic systems at the nanoscale, TAO-DFT has recently been adopted to investigate the electronic properties (Wu and Chai, 2015;Seenithurai and Chai, 2016, 2017, 2020Wu et al, 2016;Yeh and Chai, 2016;Yeh et al, 2018;Chung and Chai, 2019;Deng and Chai, 2019;Huang et al, 2020;Manassir and Pakiari, 2020), hydrogen storage properties (Seenithurai and Chai, 2016, 2017, and vibrational frequencies (Hanson-Heine, 2020) of several electronic systems at the nanoscale, especially for those possessing a radical nature.…”

Emerging DFT Methods and Their Importance for Challenging Molecular Systems with Orbital Degeneracy

“…Finite-Temperature DFT, also called thermally assisted-occupation DFT [22], is a useful tool for systems with a complicated electronic structure [23,24]. Besides its utility to select active orbitals prone to partial occupation, as the first step for more sophisticated multiconfigurational or complete active space self-consistent field (MCSCF/CASSCF) treatments, it has been recently applied to a large set of radical and radicaloid systems [25][26][27][28][29]. It is also conceived as a low-cost tool to explore energy landscapes with varying biradical character, as it may happen in organic chemical reactions, and to discard pathological cases in datasets more effectively than using traditional descriptors [30].…”