Spontaneous Symmetry Breaking in Cyclo[18]Carbon

Chemistry of Cyclo[18]Carbon (C18): A Review

Carbon-based allotropes are propelling a technological revolution in communication, sensing, and computing, concurrently challenging fundamental theories of the previous century. Nevertheless, the demand for advanced carbon-based materials remains substantial. The crux lies in the efficient and reliable engineering of novel carbon allotrope. Although C18 has undergone theoretical and experimental investigation for an extended period, its preparation and direct observation in the condensed phase occurred only recently through STM/AFM techniques. The distinctive cyclic ring structure and the dual 18-center π delocalization character introduce various uncommon properties to C18, rendering it a subject worthy of in-depth exploration. In this context, this review delves into past developments contributing to the state-of-the-art understanding of C18 and provides insights into how future endeavours can expedite practical applications. Encompassing a broad spectrum, this review comprehensively investigates almost all facets of C18, including geometric characteristics, electron delocalization, bonding nature, aromaticity, reactivity, electronic excitation, UV/Vis spectrum, intermolecular interaction, response to external fields, electron affinity, ionization, and other molecular properties. Moreover, the review also outlines representative strategies for the direct synthesis and characterization of C18 using atom manipulation techniques. Following this, C18-based complexes are summarized, and potential applications in catalysis, electrochemical devices, optoelectronics, and sensing are discussed.

Theoretical insight into the doubly antiaromatic carbon allotrope cyclo[16]carbon

A new carbon allotrope, cyclo[16]carbon (C16), has recently been successfully synthesized. It is hypothesized to exhibit double antiaromatic properties owing to the 4n π electrons. Theoretical calculations are a feasible method for systematically studying the structures and properties of unstable antiaromatic molecules. The results show that C16 has a planar structure characterized by alternating long and short bonds with D8h, and a strong antiaromatic characteristic originates from the two perpendicular π systems. We performed an extensive comparative analysis of C16 and the aromatic cyclo[18]carbon, C18. This study offers valuable insight into the structural and electronic characteristics of C16 and could inspire innovative applications and avenues for its utilization in various fields.

Exploring the Aromaticity Differences of Isoelectronic Species of Cyclo[18]carbon (C18), B6C6N6, and B9N9: The Role of Carbon Atoms as Connecting Bridges

The cyclo[18]carbon (C18) has piqued widespread interest in recent years for its geometrical aesthetic and unique electronic structure. Inspired by it, theoretical investigations of its isoelectronic B9N9 have been published occasionally; however, few studies considered their other companion B6C6N6. In this work, we study the geometric structure, charge distribution, bonding characteristic, aromaticity, and electron delocalization of B6C6N6 and B9N9 for the first time and compare the relevant results with those of C18. Based on the comprehensive analysis of aromaticity indicators such as AV1245, nucleus-independent chemical shifts, anisotropy of the induced current density, magnetically induced current density, iso-chemical shielding surface, and induced magnetic field (Bind), we found that B6C6N6 has definitely a double aromatic character similar to C18 and the aromaticities of the two are very close, while B9N9 is a nonaromatic species. In response to this novel finding, we delved into its nature from an electron delocalization perspective through a localized orbital locator, electron localization function, Fermi hole, and atomic remote delocalization index analyses. The C atom between B and N as an interconnecting bridge strengthens the electron delocalization of the conjugate path, which is the essence of the significant enhancement of the molecular aromaticity from B9N9 to B6C6N6. This work elucidates that within the framework of the isoelectronicity of C18, different methods of atomic doping can achieve molecules with completely different properties.

Theoretical design of a dual-motor nanorotator composed of all-carboatomic cyclo[18]carbon and a figure-of-eight carbon hoop

A novel supramolecular complex (2C₁₈@OPP) constructed from two kinds of unique nanorings, all-carboatomic cyclo[18]carbon (C₁₈) and figure-of-eight carbon hoop (OPP), has been studied theoretically from the perspective of an extraordinary dual-motor nanorotator. The rotational barrier of C₁₈ in OPP is extremely small at ambient temperature, implying the possibility of the host-guest complex as an ultrafast nanorotator. The rotational characteristics and thermodynamic stability of the nanorotator at different temperatures were then explored. The rotational behaviors of the two C₁₈ rings in OPP are basically independent of each other. The supramolecule investigated in this work is the first example of a dual-motor nanorotator that promises to be an important building block for constructing complicated molecular machines.

Solid state-like high harmonic generation from cluster molecules with rotational periodicities

High harmonic generation (HHG) from solid-state crystals in strong laser fields has been understood by the band structure of the solids, which is based on the periodic boundary condition (PBC) due to translational invariance. For the systems with PBC due to rotational invariance, an analogous Bloch theorem can be applied. Considering a ring-type cluster of cyclo[18]carbon as an example, we develop a quasi-band model and predict the solid state-like HHG in this system. Under the irradiation of linearly polarized laser field, cyclo[18]carbon exhibits solid state-like HHG originated from intraband oscillations and interband transitions, which, in turn, is promising to optically detect the symmetry and geometry of molecular or material structures. Our results based on the Liouville-von Neumann equations are well reproduced by the time-dependent density functional theory calculations and are foundational in providing a connection linking the HHG physics of gases and solids.

Probing Colossal Carbon Rings

Carbon aggregates containing between 10 and 30 atoms preferentially arrange themselves as planar rings. To learn more about this exotic allotrope of carbon, electronic spectra are measured for even cyclo[n]carbon radical cations (C14+-C36+) using two-color photodissociation action spectroscopy. To eliminate spectral contributions from other isomers, the target cyclo[n]carbon radical cations are isomer-selected using a drift tube ion mobility spectrometer prior to spectroscopic interrogation. The electronic spectra exhibit sharp transitions spanning the visible and near-infrared spectral regions with the main absorption band shifting progressively to longer wavelength by ≈100 nm for every additional two carbon atoms. This behavior is rationalized with a Hückel theory model describing the energies of the in-plane and out-of-plane π orbitals. Photoexcitation of smaller carbon rings leads preferentially to neutral C₃ and C₅ loss, whereas rings larger than C24+ tend to also decompose into two smaller rings, which, when possible, have aromatic stability. Generally, the observed charged photofragments correspond to low energy fragment pairs, as predicted by density functional theory calculations (CAM-B3LYP-D3(BJ)/cc-pVDZ). Using action spectroscopy it is confirmed that C14+ and C18+ photofragments from C28+ rings have cyclic structures.

Odd-Number Cyclo[n]Carbons Sustaining Alternating Aromaticity

Cyclo[n]carbons (n = 5, 7, 9, ..., 29) composed from an odd number of carbon atoms are studied computationally at density functional theory (DFT) and ab initio complete active space self-consistent field (CASSCF) levels of theory to get insight into their electronic structure and aromaticity. DFT calculations predict a strongly delocalized carbene structure of the cyclo[n]carbons and an aromatic character for all of them. In contrast, calculations at the CASSCF level yield geometrically bent and electronically localized carbene structures leading to an alternating double aromaticity of the odd-number cyclo[n]carbons. CASSCF calculations yield a singlet electronic ground state for the studied cyclo[n]carbons except for C₂₅, whereas at the DFT level the energy difference between the lowest singlet and triplet states depends on the employed functional. The BHandHLYP functional predicts a triplet ground state of the larger odd-number cyclo[n]carbons starting from n = 13. Current-density calculations at the BHandHLYP level using the CASSCF-optimized molecular structures show that there is a through-space delocalization in the cyclo[n]carbons. The current density avoids the carbene carbon atom, leading to an alternating double aromaticity of the odd-number cyclo[n]carbons satisfying the antiaromatic [4k+1] and aromatic [4k+3] rules. C₁₁, C₁₅, and C₁₉ are aromatic and can be prioritized in future synthesis. We predict a bond-shift phenomenon for the triplet state of the cyclo[n]carbons leading to resonance structures that have different reactivity toward dimerization.

Cyclo[18]carbon including zero-point motion: ground state, first singlet and triplet excitations, and hole transfer

Recent synthesis of cyclo[18]carbon has spurred increasing interest in carbon rings. We focus on a comparative inspection of ground and excited states, as well as of hole transfer properties of cumulenic and polyynic cyclo[18]carbon via Density Functional Theory (DFT), time-dependent DFT (TD-DFT) and real-time time-dependent DFT (RT-TDDFT). Zero-point vibrations are also accounted for, using a Monte Carlo sampling technique and a less exact, yet mode-resolved, quadratic approximation. The inclusion of zero-point vibrations leads to a red-shift on the HOMO-LUMO gap and the first singlet and triplet excitation energies of both conformations, correcting the values of the 'static' configurations by 9% to 24%. Next, we oxidize the molecule, creating a hole at one carbon atom. Hole transfer along polyynic cyclo[18]carbon is decreased in magnitude compared to its cumulenic counterpart and lacks the symmetric features the latter displays. Contributions by each mode to energy changes and hole transfer between diametrically opposed atoms vary, with specific bond-stretching modes being dominant.

Bonding Character, Electron Delocalization, and Aromaticity of Cyclo[18]Carbon (C18 ) Precursors, C18 -(CO)n (n=6, 4, and 2): Focusing on the Effect of Carbonyl (-CO) Groups

The bonding character, electron delocalization, and aromaticity of the cyclo[18]carbon (C₁₈ ) precursors, C₁₈ -(CO)_n (n=6, 4, and 2), have been studied by combining quantum chemical calculations and various electronic wavefunction analyses with different physical bases. It was found that C₁₈ -(CO)_n (n=6, 4, and 2) molecules exhibit alternating long and short C-C bonds, and have out-of-plane and in-plane dual π systems (π^out and πⁱⁿ ) perpendicular to each other, which are consistent with the relevant characteristics of C₁₈ . However, the presence of carbonyl (-CO) groups significantly reduced the global electron conjugation of C₁₈ -(CO)_n (n=6, 4, and 2) compared to C₁₈ . Specifically, the -CO group largely breaks the extensive delocalization of πⁱⁿ system, and the π^out system is also affected by it but to a much lesser extent; as a consequence, C₁₈ -(CO)_n (n=6, 4, and 2) with larger n shows weaker overall aromaticity. Mostly because of the decreased but still apparent π^out electron delocalization in the C₁₈ -(CO)_n (n=6, 4, and 2), a notable diatropic induced ring current under the action of external magnetic field is observed, demonstrating the clear aromatic characteristic in the molecules. The correlation between C₁₈ -(CO)_n (n=6, 4, and 2) and C₁₈ in terms of the gradual elimination of -CO from the precursors showed that the direct elimination of two CO molecules in C₁₈ -(CO)_n (n=6, 4, and 2) has a synergistic mechanism, but it is kinetically infeasible under normal conditions due to the high energy barrier.

Electronic spectra of positively charged carbon clusters-C2n + (n = 6-14)

Electronic spectra are measured for mass-selected C_2n ⁺(n = 6-14) clusters over the visible and near-infrared spectral range through resonance enhanced photodissociation of clusters tagged with N₂ molecules in a cryogenic ion trap. The carbon cluster cations are generated through laser ablation of a graphite disk and can be selected according to their collision cross section with He buffer gas and their mass prior to being trapped and spectroscopically probed. The data suggest that the C_2n ⁺(n = 6-14) clusters have monocyclic structures with bicyclic structures becoming more prevalent for C₂₂ ⁺ and larger clusters. The C_2n ⁺ electronic spectra are dominated by an origin transition that shifts linearly to a longer wavelength with the number of carbon atoms and associated progressions involving excitation of ring deformation vibrational modes. Bands for C₁₂ ⁺, C₁₆ ⁺, C₂₀ ⁺, C₂₄ ⁺, and C₂₈ ⁺ are relatively broad, possibly due to rapid non-radiative decay from the excited state, whereas bands for C₁₄ ⁺, C₁₈ ⁺, C₂₂ ⁺, and C₂₆ ⁺ are narrower, consistent with slower non-radiative deactivation.

Remarkable Size Effect on Photophysical and Nonlinear Optical Properties of All-Carboatomic Rings, Cyclo[18]carbon and Its Analogues

Inspired by recent experimental observation of molecular morphology and theoretical predictions of multiple properties of cyclo[18]carbon, we systematically studied the photophysical and nonlinear optical properties of cyclo[2N]carbons (N=3-15) allotropes through density functional theory. This work unveils the unusual optical properties of the sp-hybridized carbon rings with different sizes. The remarkable size dependence of the optical properties of these systems and their underlying nature are profoundly explored, and the relevance between aromaticity and optical properties are highlighted. The extrapolation curves fitted for energy level of frontier molecular orbitals, maximum absorption wavelength, and (hyper)polarizability of considered carbon rings are presented, which can be used to reliably predict corresponding properties for arbitrarily large carbon rings. The findings in this study will facilitate the exploration of potential application of cyclocarbons in the field of optical materials.

Antiaromaticity-aromaticity transition of cyclo[16]carbon upon metal encapsulation

In contrast to aromatic compounds with particular stability, antiaromatic compounds are usually less stable due to their high reactivity and unfavorable formation energies. Cyclo[16]carbon (C₁₆) is a carbon ring molecule with a dual antiaromatic character. In this study, we demonstrate that C₁₆ can be transformed into highly aromatic molecules upon metal encapsulation. The geometrical characteristics, electronic properties and thermodynamic stability of MC₁₆ compounds (M = Ca, Sc, Ti, V, Ce, U) are fully investigated from a theoretical perspective. Based on natural population analysis, atom-in-molecules theory and localized molecular orbital analysis, the nature of the metal-carbon interaction in the MC₁₆ compounds is investigated. It has been proved that the bonding between Ca and C₁₆ corresponds to a typical ionic interaction, while other metal atoms form polar covalent bonds with C₁₆. By analyzing the frontier molecular orbitals and magnetic response of MC₁₆, we have found that all the encapsulated metal atoms donate two electrons to the in-plane π orbitals via either electron transfer or orbital hybridization, which makes the in-plane π orbitals completely satisfy the 4n + 2 (n = 4) Hückel aromaticity rule. The U atom formally transfers four electrons to the carbon ring in total, two to the in-plane π orbitals and two to the out-of-plane π orbitals, which results in the remarkable dual aromaticity feature of UC₁₆. The transformation of aromaticity can be utilized to develop new strategies for the synthesis of novel carbon ring molecules.

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

The recently synthesized cyclo[18]carbon molecule has been characterized in a number of studies by calculating electronic, spectroscopic, and mechanical properties. However, cyclo[18]carbon is only one member of the class of cyclo[n]carbons—standalone carbon allotrope representatives. Many of the larger members of this class of molecules have not been thoroughly investigated. In this work, we calculate the magnetically induced current density of cyclo[n]carbons in order to elucidate how electron delocalization and aromatic properties change with the size of the molecular ring (n), where n is an even number between 6 and 100. We find that the Hückel rules for aromaticity (4k + 2) and antiaromaticity (4k) become degenerate for large C_n rings (n > 50), which can be understood as a transition from a delocalized electronic structure to a nonaromatic structure with localized current density fluxes in the triple bonds. Actually, the calculations suggest that cyclo[n]carbons with n > 50 are nonaromatic cyclic polyalkynes. The influence of the amount of nonlocal exchange and the asymptotic behavior of the exchange–correlation potential of the employed density functionals on the strength of the magnetically induced ring current and the aromatic character of the large cyclo[n]carbons is also discussed.

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].

Synthesis of Cyclo[18]carbon via Debromination of C18Br6

Cyclo[18]carbon (C₁₈, a molecular carbon allotrope) can be synthesized by dehalogenation of a bromocyclocarbon precursor, C₁₈Br₆, in 64% yield, by atomic manipulation on a sodium chloride bilayer on Cu(111) at 5 K, and imaged by high-resolution atomic force microscopy. This method of generating C₁₈ gives a higher yield than that reported previously from the cyclocarbon oxide C₂₄O₆. The experimental images of C₁₈ were compared with simulated images for four theoretical model geometries, including possible bond-angle alternation: D_18h cumulene, D_9h polyyne, D_9h cumulene, and C_9h polyyne. Cumulenic structures, with (D_9h) and without (D_18h) bond-angle alternation, can be excluded. Polyynic structures, with (C_9h) and without (D_9h) bond-angle alternation, both show a good agreement with the experiment and are challenging to differentiate.

Achieving Adaptive Aromaticity in Cyclo[10]carbon by Screening Cyclo[n]carbon (n=8-24)

Discovery of species with adaptive aromaticity (being aromatic in both the lowest singlet and triplet states) is particularly challenging as cyclic species are generally aromatic either in the ground state or in the excited state only, according to Hückel's and Baird's rules. Inspired by the recent realization of cyclo[18]carbon, here we demonstrate that cyclo[10]carbon possesses adaptive aromaticity by screening cyclo[n]carbon (n=8-24), which is supported by nucleus-independent chemical shift (NICS), anisotropy of the current-induced density (ACID), π contribution of electron localization function (ELF_π ) and electron density of delocalized bonds (EDDB) analyses. Further study reveals that the lowest triplet state of cyclo[10]carbon is formed by in-plane ππ* excitation. Thus, the major contribution to the aromaticity from out-of-plane π molecular orbitals does not change significantly in the lowest singlet state. Our findings highlight a crucial role of out-of-plane π orbitals in maintaining aromaticity for both the lowest singlet and triplet states as well as the aromaticity dependence on the number of the carbon in cyclo[n]carbon.