Increasing Radical Character of Large [n]cyclacenes Unveiled by Wave Function Theory

Enumeration, Nomenclature, and Stability Rules of Carbon Nanobelts

With recent breakthroughs and advances in synthetic chemistry, carbon nanobelts (CNBs) have become an emerging hot topic in chemistry and materials science. Owing to their unique molecular structures, CNBs have intriguing properties with applications in synthetic materials, host-guest chemistry, optoelectronics, and so on. Although a considerable number of CNBs with diverse forms have been synthesized, no systematic nomenclature is available yet for this important family of macrocycles. Moreover, little is known about the detailed isomerism of CNBs, which, in fact, exhibits greater complexity than that of carbon nanotubes. The copious variety of CNB isomers, along with the underlying structure-property relationships, bears fundamental relevance to the ongoing design and synthesis of novel nanobelts. In this paper, we propose an elegant approach to systematically enumerate, classify, and name all possible isomers of CNBs. Besides the simplest, standard CNBs defined by chiral indices (n, m), the nonstandard CNBs (n, m, l) involve an additional winding index l. Based on extensive quantum chemical calculations, we present a comprehensive study of the relative isomer stability of CNBs containing up to 30 rings. A simple Hückel-based model with a high predictive power reveals that the relative stability of standard CNBs is governed by the π stabilization and the strain destabilization induced by the cylindrical carbon framework, and the former effect prevails over the latter. For nonstandard CNBs, a third stability factor, the H···H repulsion in the benzo[c]phenanthrene-like motifs, is also shown to be important and can be incorporated into the simple quantitative model. In general, lower-energy CNB isomers have a larger HOMO-LUMO gap, suggesting that their thermodynamic stability coincides with kinetic stability. The most stable CNB isomers determined can be considered the optimal targets for future synthesis. These results lay an initial foundation and provide a useful theoretical tool for further research on CNBs and related analogues.

On-Surface Synthesis and Determination of the Open-Shell Singlet Ground State of Tridecacene

The character of the electronic structure of acenes has been the subject of longstanding discussion. However, convincing experimental evidence of their open-shell character has so far been missing. Here, we present the on-surface synthesis of tridecacene molecules by thermal annealing of octahydrotridecacene on a Au(111) surface. We characterized the electronic structure of the tridecacene by scanning probe microscopy, which reveals the presence of an inelastic signal at 126 meV. We attribute the inelastic signal to spin excitation from the singlet diradical ground state to the triplet excited state. To rationalize the experimental findings, we carried out many-body ab initio calculations as well as model Hamiltonians to take into account the effect of the metallic substrate. Moreover, we provide a detailed analysis of how the dynamic electron correlation and virtual charge fluctuation between the molecule and metallic surface reduces the singlet-triplet band gap. Thus, this work provides the first experimental confirmation of the magnetic character of tridecacene.

Molecular π-Orbital Construction for Non-Planar Conjugated Systems

We extend the π-orbital space (PiOS) method introduced for planar π-conjugated molecular systems [J. Chem. Theory Comput. 2019, 15, 1679] to also allow constructing efficient π-orbital active spaces for non-planar π-conjugated systems. We demonstrate the performance of this method with multiconfigurational and multireference calculations on prototypical non-planar π-systems: cycloacenes, short carbon nanotubes, various conformations of the 2,2-bipyridine anion, and C20 fullerenes.

Intruder-free cumulant-truncated driven similarity renormalization group second-order multireference perturbation theory

Accurate multireference electronic structure calculations are important for constructing potential energy surfaces. Still, even in the case of low-scaling methods, their routine use is limited by the steep growth of the computational and storage costs as the active space grows. This is primarily due to the occurrence of three- and higher-body density matrices or, equivalently, their cumulants. This work examines the effect of various cumulant truncation schemes on the accuracy of the driven similarity renormalization group second-order multireference perturbation theory. We test four different levels of three-body reduced density cumulant truncations that set different classes of cumulant elements to zero. Our test cases include the singlet-triplet gap of CH2, the potential energy curves of the XΣg+1 and AΣu+3 states of N2, and the singlet-triplet splittings of oligoacenes. Our results show that both relative and absolute errors introduced by these cumulant truncations can be as small as 0.5 kcal mol-1 or less. At the same time, the amount of memory required is reduced from O(NA6) to O(NA5), where NA is the number of active orbitals. No additional regularization is needed to prevent the intruder state problem in the cumulant-truncated second-order driven similarity renormalization group multireference perturbation theory methods.

Infinitenes as the Most Stable Form of Cycloarenes: The Interplay among π Delocalization, Strain, and π-π Stacking

The recent successful preparation of infinitene has sparked widespread attention due to its aesthetic appeal and synthetic challenge. Spectroscopic measurements and follow-up computational investigations suggest that infinitene holds fundamental significance and potential applications in chiroptics, optoelectronics, asymmetric synthesis, and supramolecular chemistry. However, unlike other looped polyarenes enriched with sizes and shapes, the infinitene molecule seems, so far, the only known example of this fascinating new form of nanocarbons, whose further exploitation would be considerably limited because of the lack of molecular diversity. Here, we introduce a whole new family of generalized infinitenes with different sizes and topologies. Three types of infinitene structures are rationally designed by joining two units of coronene, kekulene, or their extended analogs. The constructed molecules of varying sizes, each with a large number of possible topoisomers, are systematically studied by DFT calculations. Comprehensive analysis using a simple energy decomposition model uncovers that the stability of infinitenes is governed by the interplay among π delocalization, steric strain, and π-π stacking. While the first two factors are crucial to the stability of smaller infinitenes, the latter is the primary stabilizing interaction for larger infinitenes. Most importantly, we show that larger-sized infinitenes are actually the energetically most favorable form among all known looped polyarenes; their substantial thermodynamic stability surpassing that of circulenes, various carbon nanobelts, and kekulene-like macrocycles renders them promising targets for synthesis. The simulated ¹H NMR, UV-vis, and circular dichroism spectra along with optical rotations for the most stable infinitene species may help their identification in future synthetic efforts.

Impact of Di- and Poly-Radical Characters on the Relative Energy of the Doubly Excited and La States of Linear Acenes and Cyclacenes

Linear and cyclic acenes are polycyclic aromatic hydrocarbons that can be viewed as building blocks of graphene nanoribbons and carbon nanotubes, respectively. While short linear acenes demonstrated remarkable efficiency in several optoelectronic applications, the longer members are unstable and difficult to synthesize as their cyclic counterparts. Recent progress in on-surface synthesis, a powerful tool to prepare highly reactive species, opens promising perspectives and motivates the computational investigations of these potentially functional molecules. Owing to their di- and poly-radical character, low-lying excited states dominated by doubly excited configurations are expected to become more important for longer members of both linear and cyclic molecules. In this work, we investigate the lowest-lying La and the doubly excited (DE) state of linear acenes and cyclacenes, with different computational approaches, to assess the influence of the di-/poly-radical characters (increasing with the molecular dimensions) on their relative order. We show that DFT/MRCI calculations correctly reproduce the crossing of the two states for longer linear acenes, while TDUDFT calculations fail to predict the correct excitation energy trend of the DE state. The study suggests a similarity in the excited electronic state pattern of long linear and cyclic acenes leading ultimately to a lowest lying dark DE state for both.

Excitation energies of polycylic aromatic hydrocarbons by double-hybrid functionals: Assessing the PBE0-DH and PBE-QIDH models and their range-separated versions

A family of non-empirical double-hybrid (DH) density functionals, such as Perdew-Burke-Ernzerhof (PBE)0-DH, PBE-QIDH, and their range-separated exchange (RSX) versions RSX-0DH and RSX-QIDH, all using Perdew-Burke-Ernzerhof(PBE) exchange and correlationfunctionals, is applied here to calculate the excitation energies for increasingly longer linear and cyclic acenes as part of their intense benchmarking for excited states of all types. The energies for the two lowest-lying singlet ¹L_a and ¹L_b states of linear oligoacenes as well as the triplet ³L_a and ³L_b states, are calculated and compared with experimental results. These functionals clearly outperform the results obtained from hybrid functionals and favorably compare with other double-hybrid expressions also tested here, such as B2-PLYP, B2GP-PLYP, ωB2-PLYP, and ωB2GP-PLYP. The study is complemented by the computation of adiabatic S₀-T₁ singlet-triplet energy difference for linear acenes as well as the extension of the study to strained cyclic oligomers, showing how the family of non-empirical expressions robustly leads to competitive results.

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.

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

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[[Formula: see text]]/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].

TAO-DFT Study on the Electronic Properties of Diamond-Shaped Graphene Nanoflakes

At 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.

Möbius and Hückel Cyclacenes with Dewar and Ladenburg Defects

Cyclacene nanobelts have not been synthesized in over 60 years and remain one of the last unsynthesized building blocks of carbon nanotubes. Recent work has predicted that Hückel-cyclacenes containing Dewar benzenoid ring isomers are the most stable isomeric forms for several of the smaller sizes of cyclacene belts. Here, we give a more complete picture of the isomers that are possible within these nanobelt systems by simulating embedded Ladenburg (prismane) benzenoid rings in Hückel-[n]cyclacenes (n = 5-14) and embedded Dewar benzenoid rings in twisted Möbius-[n]cyclacenes (n = 9-14). The Möbius-[9]cyclacene isomer containing one Dewar benzenoid defect and the Hückel-[5]cyclacene isomer containing two maximally spaced Ladenburg benzenoid defects are found to be more stable than their conventional Kekulé benzenoid ring counterparts. The isomers that contain Dewar and Ladenburg benzenoid rings have larger electronic singlet-triplet energy gaps and lower polyradical character when compared with the conventional isomers.

Dewar Benzenoids Discovered In Carbon Nanobelts

The synthesis of cyclacene nanobelts remains an elusive goal dating back over 60 years. These molecules represent the last unsynthesized building block of carbon nanotubes and may be useful both as seed molecules for the preparation of structurally well-defined carbon nanotubes and for understanding the behavior and formation of zigzag nanotubes more broadly. Here we report the discovery that isomers containing two Dewar benzenoid rings are the preferred form for several sizes of cyclacene. The predicted lower polyradical character and higher singlet-triplet stability that these isomers possess compared with their pure benzenoid counterparts suggest that they may be more stable synthetic targets than the structures that have previously been identified. Our findings should facilitate the exploration of new routes to cyclacene synthesis through Dewar benzene chemistry.

Toward the Synthesis of a Highly Strained Hydrocarbon Belt

Hydrocarbon belts including fully conjugated beltarenes and their (partially) saturated analogs have fascinated chemists for decades due to their aesthetic structures, tantalizing properties, and potential applications in supramolecular chemistry and carbon nanoscience and nanotechnology. However, synthesis of hydrocarbon belts still remains a formidable challenge. We report in this communication a general approach to hydrocarbon belts and their derivatives. Closing up all four fjords of resorcin[4]arene derivatives through multiple intramolecular Friedel-Crafts alkylation reactions in an operationally simple one-pot reaction manner enabled efficient construction of octohydrobelt[8]arenes. Synthesis of belt[8]arene from DDQ-oxidized aromatization of octohydrobelt[8]arene under different conditions resulted in aromatization and simultaneous [4 + 2] cycloaddition reactions with DDQ or TCNE to produce selectively tetrahydrobelt[8]arene-DDQ₂, tetrahydrobelt[8]arene-TCNE₂, and belt[8]arene-DDQ₄ adducts. Formation of belt[8]arene, a fully conjugated hydrocarbon belt, was observed from retro-Diels-Alder reaction of a belt[8]arene-DDQ₄ adduct with laser irradiation under MALDI conditions. The new and practical synthetic method established would open an avenue to create belt-shaped molecules from easily available starting materials.

Mapping the optoelectronic property space of small aromatic molecules

Small aromatic molecules and their quinone derivatives find use in organic transistors, solar-cells, thermoelectrics, batteries and photocatalysts. These applications exploit the optoelectronic properties of these molecules and the ease by which such properties can be tuned by the introduction of heteroatoms and/or the addition of functional groups. We perform a high-throughput virtual screening using the xTB family of density functional tight-binding methods to map the optoelectronic property space of ~250,000 molecules. The large volume of data generated allows for a broad understanding of how the presence of heteroatoms and functional groups affect the ionisation potential, electron affinity and optical gap values of these molecular semiconductors, and how the structural features - on their own or in combination with one another - allow access to particular regions of the optoelectronic property space. Finally, we identify the apparent boundaries of the optoelectronic property space for these molecules: regions of property space that appear off limits for any small aromatic molecule.

Interplay between Aromaticity and Radicaloid Character in Nitrogen-Doped Oligoacenes Revealed by High-Level Multireference Methods

Aromaticity is a multivariable concept in organic chemistry that plays a central role for understanding the structure, stability, and reactivity of polycyclic aromatic hydrocarbons (PAHs). Several types of PAHs are characterized as singlet biradicaloid species and their chemical stability is intimately linked to the degree of aromatic character. In this study, theoretically designed routes to tune the biradical character (and thereby its chemical stability) of nitrogen-substituted octacenes have been investigated on the basis of the high-level multireference averaged quadratic coupled-cluster MR-AQCC method necessary for the appropriate description of polyradicaloid systems. The influence of nitrogen centers on the aromaticity of octacene is probed through structural (HOMA) and electron localization (ELF) indices by comparing the N- against NH-doping cases. These analyses reveal that the aromaticity and biradical character of octacene is only slightly affected by replacing one pair of CH groups with N atoms, i.e., by N-doping. However, a significant aromatic stabilization can be obtained when NH-doping is applied at the inner octacene rings; this is also accompanied by an overall decrease of the open-shell character, as evidenced by the gradual quenching of the unpaired electrons and increase in the singlet-triplet splittings when the NH doping groups are moved toward the center of the octacene molecule. Our findings aid in the rational design of new PAH compounds with balanced biradicaloid character and chemical stability which is important, e.g., for practical applications in organic solar cells based on the singlet-fission mechanism.

Exploring the novel donor-nanotube archetype as an efficient third-order nonlinear optical material: asymmetric open-shell carbon nanotubes

Contrary to the enormous number of previous studies on carbon nanotubes (CNTs), herein, we realized the origin of the intrinsic open-shell diradical character and second hyperpolarizability γ using a broken symmetry approach. This study was inspired by our recent findings (S. Muhammad, et al., Nanoscale, 2016, 8, 17998 and Nakano, et al., J. Phys. Chem. C, 2016, 120, 1193). We performed structural modifications through a unique asymmetric donor-nanotube framework, which led to a novel paradigm of modified CNTs with tunable open-shell diradical character and remarkably superior NLO response properties. Interestingly, asymmetry and diradical character were found to be the crucial factors to modulate the second hyperpolarizability γ. We initially performed a comparative analysis of the diradical characters and γ amplitudes of boron nitride nanotubes (BNNTs) and CNTs possessing significant ionic characters and covalent characters, respectively. The basic findings for these simple configurations were further extended to the donor-acceptor CNT paradigm, which finally led to excellent asymmetric donor-CNT configurations with remarkably larger γ amplitudes. Furthermore, among the CNTs, finite length zigzag CNT(6,0)3 were modified with different donor-acceptor configurations. Interestingly, for the first time, unique donor-nanotube configurations [1,4-(NH2)2CNT-(6,0)3 and 1,4-(NH2)2CNT-(6,0)5] were found; they showed significantly robust γ amplitudes as large as 2519 × 103 and 4090 × 103 a.u. at the LC-UBLYP(μ = 0.33)/6-31G* level of theory. Additionally, several molecular level insights have been obtained for these novel donor-nanotube configurations using their odd electron densities, molecular electrostatic maps, densities of states and γ density analyses to highlight the realization of these novel materials for highly efficient optical and NLO applications.

The role of topology in organic molecules: origin and comparison of the radical character in linear and cyclic oligoacenes and related oligomers

We discuss the nature of electron-correlation effects in carbon nanorings and nanobelts by a combined approach based on FT-DFT and RAS-SF methods.