Möbius and Hückel Cyclacenes with Dewar and Ladenburg Defects

Orbital magnetic susceptibility of zigzag carbon nanobelts: a tight-binding study

The magnetic properties of a circular graphene nanoribbon (carbon belt) in a magnetic field parallel to its central axis is studied using a tight-binding model. Orbital magnetic susceptibility is calculated using an analytical expression of the energy eigenvalues as a function of the magnetic flux density for any size, and its temperature dependence is considered. In the absence of electron hopping parallel to the magnetic field, the orbital magnetic susceptibility diverges at absolute zero if the chemical potential is zero and the number of atoms is a multiple of four. As the temperature increases, the magnitude of susceptibility decreases according to the power law, whose exponent depends on the size. In the presence of electron hopping parallel to the magnetic field, the divergence of the susceptibility near absolute zero disappears, and the sign changes with the transfer integral parallel to the magnetic field and the temperature.

Tuning optical properties of π-conjugated double nanohoops under external electric field stimuli-responsiveness

Carbon nanorings have attracted substantial interest from synthetic chemists due to their unique topological structures and distinct physical properties. An intriguing π-conjugated double-nanoring structure, denoted as [8]CPP-[10]cyclacene, was constructed via the integration of [8]cycloparaphenylene ([8]CPP) into [10]cyclacene. Using the external electric field stimuli-responsiveness of [8]CPP-[10]cyclacene, directional charge transfer can be induced, resulting in the emergence of intriguing properties. The effects of the external electric field in three specific directions were explored, vertically in the [8]CPP unit (Fy), vertically in the [10]cyclacene unit (Fz), and horizontally along the double nanorings diameter (Fx). Interestingly, the external electric field vertically to the [10]cyclacene unit significantly enhanced the first hyperpolarizability (βtot) compared to that vertically to the [8]CPP unit. Notably, [8]CPP-[10]cyclacene under Fx exhibited significantly larger the βtot values (1.48 × 105 a.u.) than those of vertical Fy and Fz. This work opens up a wide range of nonlinear optics, making it a compelling area to explore in the field of carbon nanomaterials.

Static Electron Correlation in Anharmonic Molecular Vibrations: A Hybrid TAO-DFT Study

Hybrid thermally-assisted-occupation density functional theory is used to examine the effects of static electron correlation on the prediction of a benchmark set of experimentally observed molecular vibrational frequencies. The B3LYP and B97-1 thermally-assisted-occupation measure of static electron correlation is important for describing the vibrations of many of the molecules that make up several popular test sets of experimental data. Shifts are seen for known multireference systems and for many molecules containing atoms from the second row of the periodic table of elements. Several molecules only show significant shifts in select vibrational modes, and significant improvements are seen for the prediction of hydrogen stretching frequencies throughout the test set.

Disclosure of Ground-State Zimmerman-Möbius Aromaticity in the Radical Anion of [6]Helicene and Evidence for 4π Periodic Aromatic Ring Currents in a Molecular "Metallic" Möbius Strip

In 1966, Zimmerman proposed a type of Möbius aromaticity that involves through-space electron delocalization; it has since been widely applied to explain reactivity in pericyclic reactions, but is considered to be limited to transition-state structures. Although the easily accessible hexahelicene radical anion has been known for more than half a century, it was overlooked that it exhibits a ground-state minimum and robust Zimmerman-Möbius aromaticity in its central noose-like opening, becoming, hence, the oldest existing Möbius aromatic system and with smallest Möbius cycle known. Despite its overall aromatic stabilization energy of 13.6 kcal mol-1 (at B3LYP/6-311+G**), the radical also features a strong, globally induced paramagnetic ring current along its outer edge. Exclusive global paramagnetic currents can also be found in other fully delocalized radical anions of 4N+2 π-electron aromatic polycyclic benzenoid hydrocarbons (PAH), thus questioning the established magnetic criterion of antiaromaticity. As an example of a PAH with nontrivial topology, we studied a novel Möbius[16]cyclacene that has a non-orientable surface manifold and a stable closed-shell singlet ground state at several density functional theory levels. Its metallic monoanion radical (0.0095 eV band gap at HSE06/6-31G* level) is also wave-function stable and displays an unusual 4π-periodic, magnetically induced ring current (reminiscent of the transformation behaviour of spinors under spatial rotation), thus indicating the existence of a new, Hückel-rule-evading type of aromaticity.

Electronic Properties of Carbon Nanobelts Predicted by Thermally-Assisted-Occupation DFT

Accurate prediction of properties of large-scale multi-reference (MR) electronic systems remains difficult for traditional computational methods (e.g., the Hartree-Fock theory and Kohn-Sham density functional theory (DFT)). Recently, thermally-assisted-occupation (TAO)-DFT has been demonstrated to offer reliable description of electronic properties of various large-scale MR electronic systems. Consequently, in this work, TAO-DFT is used to unlock the electronic properties associated with C-Belt[n] (i.e., the carbon nanobelts containing n fused 12-membered carbon rings). Our calculations show that for all the system sizes reported (n = 4-24), C-Belt[n] have singlet ground states. In general, the larger the size of C-Belt[n], the more pronounced the MR character of ground-state C-Belt[n], as evident from the symmetrized von Neumann entropy and the occupation numbers of active TAO-orbitals. Furthermore, the active TAO-orbitals are delocalized along the circumference of C-Belt[n], as evident from the visualization of active TAO-orbitals.

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

The carriers of the diffuse interstellar bands (DIBs) are still largely unknown although polycyclic aromatic hydrocarbons, carbon chains, and fullerenes are likely candidates. A recent analysis of the properties of n-acenes of general formula C4n+2 H2n+4 suggested that these could be potential carriers of some DIBs. Dehydrogenation reactions of n-acenes after absorption of an interstellar UV photon may result in dehydroacenes. Here the reaction energies and barriers for formation of n-cyclacenes from 2,3-didehydroacenes (n-DDA) by intramolecular Diels-Alder reaction to dihydro-etheno-cyclacenes (n-DEC) followed by ejection of ethyne by retro-Diels-Alder reactions are analyzed using thermally assisted occupation density functional theory (TAO-DFT) for n=10-20. It is found that the barriers for each of the steps depend on the ring strain of the underlying n-cyclacene, and that the ring strain of n-DEC is about 75 % of that of the corresponding n-cyclacene. In each case, ethyne extrusion is the step with the highest energy barrier, but these barriers are smaller than CH bond dissociation energies, suggesting that formation of cyclacenes is an energetically conceivable fate of n-acenes after multiple absorption of UV photons.

TAO-DFT-Based Ab Initio Molecular Dynamics

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.