Electron correlation in C(4N+2) carbon rings: aromatic versus dimerized structures

On-surface synthesis and characterization of anti-aromatic cyclo[12]carbon and cyclo[20]carbon

Cyclo[n]carbons have recently attracted significant attention owing to their geometric and electronic structures remaining largely unexplored in the condensed phase. In this work, we focus on two anti-aromatic cyclocarbons, namely C12 and C20. By designing two fully halogenated molecular precursors both including 4-numbered rings, we further extend the on-surface retro-Bergman ring-opening reaction, and successfully produce C12 and C20. The polyynic structures of C12 and C20 are unambiguously revealed by bond-resolved atomic force microscopy. More importantly, subtly positioning the C20 molecule into an atomic fence formed by Cl clusters allows us to experimentally probe its frontier molecular orbitals, yielding a transport gap of 3.8 eV measured from scanning tunneling spectroscopy. Our work may advance the field by easier synthesis of a series of cyclocarbons via on-surface retro-Bergman ring-opening strategy.

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.

Computed Gyration Tensors of Knotted Chiral and Achiral Topological Stereoisomers of C60 Cyclocarbons

The electronic origins of the computed optical rotations of the simplest chiral and achiral chemical knots with comparatively simple compositions and large, anticipated magnetoelectric polarizabilities are provided. Linear response theory (LRT) is used to calculate the gyration at 1064 nm of two knotted polyyne chains, topological stereoisomers of cyclo[60]carbon. One isomer is analogous to the trefoil knot with approximate D3 symmetry and the other to the figure eight knot with approximate S4 symmetry. The response in each case can be attributed largely to the magnetic dipole term that arises in a near degenerate E-like excited state. An oriented achiral figure eight knot is as optically active in some directions as the chiral knot in any direction, and its absolute eigenvalues are larger.

Quantum Monte Carlo Simulations of the Vibrational Wavefunction of the Aromatic Cyclo[10]carbon Using a Full Dimensional Permutationally Invariant Potential Energy Surface

New experimental measurements [Sun et al., Nature 2023, 623, 972] of the cyclic C10 reveal a cumulenic pentagon-like D5h structure at ∼5 K. However, the long-standing presumption that a large zero-point vibrational energy combined with an extremely flat D5h ↔ D10h ↔ D5h isomerization pathway washes out the pentagonal D5h structure and yields a symmetric D10h decagon remains at odds with the experiment. We resolve this issue with our fitting approach based on a bond-order charge-density matrix expressed in permutationally invariant polynomials. We train the model on τHCTH/cc-pVQZ data morphed to reproduce a relativistic all-electron CCSDT(Q)/CBS D5h-D10h potential energy barrier (benchmarked previously by others). Large scale diffusion Monte Carlo simulations in full dimensionality show that the vibrational ground state of C10 has compositional character of more than 96% D5h, fully reflecting the experimental imaging data. Quantum mechanical variational calculations in 1-D further suggest persistence of the D5h symmetry structure at higher temperatures.

Using a cyclocarbon additive as a cyclone separator to achieve fast lithiation and delithiation without dendrite growth in lithium-ion batteries

Carbon materials are widely used for reversible lithium uptake in the anode of lithium-ion batteries. Nevertheless, the challenge of uncontrollable dendrite deposition during fast charge-discharge cycles remains a grand hurdle. Various strategies have been explored to prevent detrimental heterogeneous dendrite metal deposits, such as interface engineering and electrolyte modification, but they often compromise the reverse diffusion freedom of Li+ ions during discharging and are incompatible with the most mainstream use of graphite as an anode material. Here, we propose the incorporation of a novel carbon allotrope of cyclocarbon as a potential additive in the anode. In contrast to conventional carbon materials, density functional theory calculations reveal that cyclocarbon has a much higher affinity for Li atoms than Li+ ions, even surpassing the inherent cohesion of Li atoms, due to the charge transfer from the 2s orbital of Li atoms to the unique in-plane π orbital of cyclocarbon. Furthermore, ab initio molecular dynamics simulations show that Li+ ions can shuttle freely back and forth across cyclocarbon, whereas the lithiation process for Li atoms occurs rapidly within picoseconds. The delithiation of Li atoms within cyclocarbon follows a voltage-gated mechanism that is effectively controlled by an external electric field of 3 V nm-1. Remarkably, cyclocarbon exhibits potential compatibility with commercialized graphite electrodes via the π-π interaction and also can be extended to sodium-ion and potassium-ion batteries. These distinct compatibility, scalability and electrochemical properties of cyclocarbon provide a new avenue to realize both safety and ultrafast rechargeable performance of ion batteries.

Cyclo[n]carbons and catenanes from different perspectives: disentangling the molecular thread

All-carbon atomic rings, cyclo[n]carbons, have recently attracted vivid attention of experimentalists and theoreticians. Among them, cyclo[18]carbon is the most studied system. In this paper, we summarize and review various properties of cyclo[n]carbons, emphasising the aspects of their aromaticity/antiaromaticity. In the first part, the trends in bonding patterns and selected aromaticity indices with the increasing size of the rings are discussed. In the second part we explore the properties of catenane models based on interlocked cyclo[18]carbon rings from different perspectives and investigate their behaviour under the action of external force using computational experiments.

On-surface synthesis of aromatic cyclo[10]carbon and cyclo[14]carbon

All-carbon materials based on sp2-hybridized atoms, such as fullerenes1, carbon nanotubes2 and graphene3, have been much explored due to their remarkable physicochemical properties and potential for applications. Another unusual all-carbon allotrope family are the cyclo[n]carbons (Cn) consisting of two-coordinated sp-hybridized atoms. They have been studied in the gas phase since the twentieth century4-6, but their high reactivity has meant that condensed-phase synthesis and real-space characterization have been challenging, leaving their exact molecular structure open to debate7-11. Only in 2019 was an isolated C18 generated on a surface and its polyynic structure revealed by bond-resolved atomic force microscopy12,13, followed by a recent report14 on C16. The C18 work trigged theoretical studies clarifying the structure of cyclo[n]carbons up to C100 (refs. 15-20), although the synthesis and characterization of smaller Cn allotropes remains difficult. Here we modify the earlier on-surface synthesis approach to produce cyclo[10]carbon (C10) and cyclo[14]carbon (C14) via tip-induced dehalogenation and retro-Bergman ring opening of fully chlorinated naphthalene (C10Cl8) and anthracene (C14Cl10) molecules, respectively. We use atomic force microscopy imaging and theoretical calculations to show that, in contrast to C18 and C16, C10 and C14 have a cumulenic and cumulene-like structure, respectively. Our results demonstrate an alternative strategy to generate cyclocarbons on the surface, providing an avenue for characterizing annular carbon allotropes for structure and stability.

[Cs©C18]+ and [Na©C14]+: perfect planar alkaline-metal-centered polyynic cyclo[n]carbon complexes with record coordination numbers

Searching for the maximum coordination number (CN) in planar species with novel bonding patterns has fascinated chemists for many years. Using the experimentally observed polyynic cyclo[18]carbon D9h C18 and theoretically predicted polyynic cyclo[14]carbon D7h C14 as effective ligands and based on extensive first-principles theory calculations, we predict herein their perfect planar alkaline-metal-centered complexes D9h Cs©C18+ (1) and D7h Na©C14+ (4) which as the global minima of the systems possess the record coordination numbers of CN = 18 and 14 in planar polyynic species, respectively. More interestingly, detailed energy decomposition and adaptive natural density partitioning bonding analyses indicate that the hypercoordinate alkaline-metal centers in these complexes exhibit obvious transition metal behaviors, with effective in-plane (π-6s)σ, (π-7p)σ, and (π-5d)σ coordination bonds formed in Cs©C18+ (1) and (π-3s)σ, (π-3p)σ, and (π-3d)σ coordination interactions fabricated in Na©C14+ (4) to dominate the overall attractive interactions between the metal center and its cyclo[n]carbon ligand. Similarly, alkaline-metal-centered planar Cs Cs©C17B (2), C2v Cs©C17- (3), C2v Na©C13B (5), and C2v Na©C13- (6) have also been obtained with CN = 18, 17, 14, and 13, respectively.

Tuning the conductance of carbon rings with impurities and electric fields

We explore two mechanisms to tune the electronic conductance of carbon atom rings, namely, substitutional impurities and in-plane external electric fields. First-principles calculations and a tight-binding approach are used to model the systems. Two bond configurations are studied, cumulenic and polyynic, which can be relevant depending on the number of carbon atoms in the ring. We find that both impurity substitution and electric field mechanisms allow for modifying the electronic spectrum and transport characteristics. Interestingly, cumulenic and polyynic carbon rings present a different response to these perturbations, which can also be a way to elucidate the bond nature of these structures.

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.

From Cyclo[18]carbon to the Novel Nanostructures-Theoretical Predictions

In this paper, we present a number of novel pure-carbon structures generated from cyclo[18]carbon. Due to the very high reactivity of cyclo[18]carbon, it is possible to link these molecules together to form bigger molecular systems. In our studies, we generated new structures containing 18, 36 and 72 carbon atoms. They are of different shapes including ribbons, sheets and tubes. All these new structures were obtained in virtual reactions driven by external forces. For every reaction, the energy requirement was evaluated exactly when the corresponding transition state was found or it was estimated through our new approach. A small HOMO-LUMO gap in these nanostructures indicates easy excitations and the multiple bonds network indicates their high reactivity. Both of these factors suggest that some potential applications of the new nanostructures are as components of therapeutically active carbon quantum dots, terminal fragments of graphene or carbon nanotubes obtained after fracture or growing in situ in catalytic reactions leading to the formation of carbonaceous materials.

Transport signatures of few-atom carbon rings

We study the electronic transport through an all-carbon quantum ring side-coupled to a quantum wire. We employ both first-principles calculations and a tight-binding approach; the latter allows for the derivation of analytical expressions for the conductance and density of states, which facilitates the interpretation of the transport characteristics. Two bond models are employed: either all the hoppings are equal (cumulenic ring) or they have alternating bonds (polyynic ring). Assuming cumulenic bonds, if the number of atoms in the carbon ring is a multiple of four, it produces an antiresonant peak in the conductance at the Fermi level. This effect disappears for the polyynic configuration, i.e., when the hoppings in the carbon rings are alternating. Additionally, a gap opens at the Fermi energy in the polyynic rings, yielding distinct transport signatures for the two bond configurations. Comparison to first-principles calculations shows an excellent agreement on the changes of the conductance due to the carbon ring. We propose such transport measurements as a way to elucidate the character of the bonds in these novel carbon nanostructures.

TAO-DFT fictitious temperature made simple

Over the past few years, thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys., 2012, 136, 154104] has been proved to be an efficient electronic structure method for investigating the ground-state properties of large electronic systems with strong static correlation effects. In TAO-DFT, the strength of static correlation in an electronic system at zero temperature is closely related to the so-called fictitious temperature (i.e., the temperature of the corresponding noninteracting reference system). In this work, we propose a simple model to define the optimal system-independent fictitious temperature of a given energy functional in TAO-DFT. Besides, we employ this model to determine the optimal system-independent fictitious temperature of a global hybrid functional in TAO-DFT as a function of the fraction of exact exchange. In addition, we adopt TAO-DFT with various global hybrid functionals and system-independent fictitious temperatures to explore the ground-state properties of several electronic systems with strong static correlation effects, such as the linear acenes and cyclic carbon chains. Furthermore, we discuss the role of exact exchange and an optimal system-independent fictitious temperature in TAO-DFT. Owing to the much reduced self-interaction error, TAO-DFT with exact exchange and an optimal system-independent fictitious temperature can accurately predict the radical character and bond length alternation of cyclic carbon chains (with even number of carbon atoms), which are challenging problems for traditional electronic structure methods.

Optimal system-independent fictitious temperature θ of TAO-GH as a function of the fraction of exact exchange a_x.

From six to eight Π-electron bare rings of group-XIV elements and beyond: can planarity be deciphered from the "quasi-molecules" they embed?

Ab initio molecular orbital theory is used to study the structures of six and eight π-electron bare rings of group-XIV elements, and even larger [n]annulenes up to C₁₈H₁₈, including some of their mono-, di-, tri-, and tetra-anions. While some of the above rings are planar, others are nonplanar. A much spotlighted case is cyclo-octatetraene (C₈H₈), which is predicted to be nonplanar together with its heavier group-XIV analogues Si₈H₈ and Ge₈H₈, with the solely planar members of its family having the stoichiometric formulas C₄Si₄H₈ and C₄Ge₄H₈. A similar situation arises with the six π-electron bare rings, where benzene and substituted ones up to C₃Si₃H₆ or so are planar, while others are not. However, the explanations encountered in the literature find support in ab initio calculations for such species, often rationalized from distinct calculated features. Using second-order Møller-Plesset perturbation theory and, when affordable (particularly tetratomics, which may allow even higher levels), the coupled-cluster method including single, double, and perturbative triple excitations, a common rationale is suggested based on a novel concept of quasi-molecules or the (3+4)-atom partition scheme. Any criticism of tautology is therefore avoided. The same analysis has also been successfully applied to even larger [n]annulenes, to their mixed family members involving silicon and germanium atoms, and to the C₁₈ carbon ring. Furthermore, it has been extended to annulene anions to check the criteria of the popular Hückel rule for planarity and aromaticity. Exploratory work on cycloarenes is also reported. Besides a partial study of the involved potential energy surfaces, equilibrium geometries and harmonic vibrational frequencies have been calculated anew, for both the parent and the actual prototypes of the quasi-molecules.

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.

Carbyne Ring Activated Using ZnCl2 for Hydrogen Adsorption: DFT Study

We have studied the feasibility of activated carbyne as a good hydrogen storage material. Density functional theory (DFT) simulations through van der Waals interactions have been applied to investigate calcium sorption on activating carbyne with zinc dichloride (ZnCl₂) and also interactions of molecular hydrogen with pristine carbyne and Ca functionalized on an activated carbyne C₁₂-ring. The obtained results showed that (i) the chemical activation of the C₁₂-ring with ZnCl₂ increases its area by 5.17% with respect to pristine carbyne. (ii) Ca atoms at small concentrations tend to get atomically sparse on carbyne, donating +0.94e and +1.05e to the ring, according to Mulliken population analysis and the electrostatic potential fitting charges, respectively. Furthermore, in the presence of calcium, hydrogen sorption increases by 21.8% in comparison with Ca-decorated pure carbyne. (iii) Seven hydrogen molecules per Ca atom have adsorption energy close to the range of ∼0.3-0.5 eV per H₂, which is necessary for effective charge/discharge cycles. (iv) Theoretical uptake (7.11 wt %) with a single Ca atom is higher than the U.S. Department of Energy target (5.5 wt %). Therefore, an activated C₁₂-ring can bind three Ca atoms with its seven H₂ molecules reaching 13.8 wt %. (v) Equilibrium pressure for CaC₁₂-7H₂ and Ca₃C₁₂-21H₂ systems (5-15 MPa) by means of adsorption isotherm calculations. The calculated van't Hoff desorption temperatures exceed considerably the boiling point of liquid nitrogen. In addition, we also performed DFT-based molecular dynamics simulations for the C₁₂, CaC₁₂, CaC₁₂-7H₂, and Ca₃C₁₂-21H₂ systems to study thermal stability. Our results confirm the potential of Ca-decorated carbyne for hydrogen storage.

Stability of the polyynic form of C18, C22, C26, and C30 nanorings: a challenge tackled by range-separated double-hybrid density functionals

We calculate the relative energy between the cumulene and polyyne structures of a set of C_4k+2 (k = 4-7) rings (C₁₈, C₂₂, C₂₆, and C₃₀ prompted by the recent synthesis of the cyclo[18]carbon (or simply C₁₈) compounds. Reference results were obtained by a costly Quantum Monte-Carlo (QMC) approach, providing thus very accurate values allowing to systematically compare the performance of a variety of wavefunction methods [(i.e., MP2, SCS-MP2, SOS-MP2, DLPNO-CCSD, and DLPNO-CCSD(T)] as well as DFT approaches, applying for the latter a diversity of density functionals covering global and range-separated hybrid and double-hybrid models. The influence of the use of a range-separation scheme for density functionals, for both hybrid and double-hybrid expressions, is discussed according to its key role. Overall, range-separated double-hybrid functionals (e.g., RSX-QIDH) behave very accurately and provide competitive results compared with DLPNO-CCSD(T), at a more reasonable computational cost.

On-Surface Synthesis of sp-Carbon Nanostructures

The on-surface synthesis of carbon nanostructures has attracted tremendous attention owing to their unique properties and numerous applications in various fields. With the extensive development of scanning tunneling microscope (STM) and noncontact atomic force microscope (nc-AFM), the on-surface fabricated nanostructures so far can be characterized on atomic and even single-bond level. Therefore, various novel low-dimensional carbon nanostructures, challenging to traditional solution chemistry, have been widely studied on surfaces, such as polycyclic aromatic hydrocarbons, graphene nanoribbons, nanoporous graphene, and graphyne/graphdiyne-like nanostructures. In particular, nanostructures containing sp-hybridized carbons are of great advantage for their structural linearity and small steric demands as well as intriguing electronic and mechanical properties. Herein, the recent developments of low-dimensional sp-carbon nanostructures fabricated on surfaces will be summarized and discussed.

Cyclo[n]carbons Form Strong N → C Dative/Covalent Bonds with Piperidine

The newly synthesized C₁₈ ring is demonstrated as the smallest all-carbon acceptor that exhibits strong electron acceptance. This study provides a quantum-chemical investigation of the electron-acceptance behavior of monocyclic carbon rings with a particular emphasis on C₁₈ through the formation of a dative bond with piperidine. The results show that C_n rings form strong dative bonds with piperidine, whereas the respective van der Waals (vdW) complexes are higher in energy. The main driving force is the release of angle strain of cyclo[n]carbons caused by the change in hybridization from sp to sp² associated with the formation of the dative bond. On the contrary, other sp allotropes, diynes, favorably form vdW complexes. Molecular dynamics (MD) simulations support the stability of the dative bond throughout a simulation of 20 ps. This opens up the possibility of stabilizing highly reactive C₁₈ through dative/covalent functionalization.

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.

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.

Theoretical investigation on bond and spectrum of cyclo[18] carbon (C18) with sp-hybridized

In an experiment, cyclo[18]carbon (C₁₈), prepared with low-temperature STM-AFM (scanning tunneling microscopy-atomic force microscopy) from C₂₄O₆, C₂₂O₄, and C₂₀O₂ molecules, have been confirmed being alternating single and triple bonds structure. Nevertheless, the stability of C₁₈ is weak at room temperature in gas. Thus, it is difficult to study the spectrum, orbital, and bonds characters of the C₁₈ molecule in the experiment. In this paper, we have obtained absorption spectrum, orbital, and bonding characters of the C₁₈ molecule in theory. Besides, bonds and spectra of C₂₄O₆, C₂₂O₄, C₂₀O₂, B₉N₉, C₆, C₁₂, C₁₆, and C₂₀ molecules have been investigated to further confirm the structure and the characters of the C₁₈ molecule. The results show that carbon-carbon bonds of C₂₄O₆, C₂₂O₄, and C₂₀O₂ molecules in ring are alternating single and triple bonds except those connected with CO group. B₉N₉ molecule as the isoelectronic structure of C₁₈ has a larger bandgap and shorter wavelength of absorption spectra than those of the C₁₈ molecule. Moreover, all bonds between boron and nitrogen in B₉N₉ molecule are single one. Study bonding characters for C₆, C₁₂, C₁₆, and C₂₀ molecules have confirmed that carbon-carbon bonds of cyclo[n]carbon changed gradually from double bonds to alternating single and triple bonds with increasing n value. The data from theory would give help for future research on C₁₈ and B₉N₉ molecules in experiment. Graphical abstract Theoretical investigation for bond and spectra characters of cyclo[18]carbon (C₁₈), prepared with low-temperature STM-AFM (scanning tunneling microscopy-atomic force microscopy) from C₂₄O₆, C₂₂O₄, and C₂₀O₂ molecules, which have been confirmed being alternating single and triple bonds structure.

Systematic description of molecular deformations with Cremer-Pople puckering and deformation coordinates utilizing analytic derivatives: Applied to cycloheptane, cyclooctane, and cyclo[18]carbon

The conformational properties of ring compounds such as cycloalkanes determine to a large extent their stability and reactivity. Therefore, the investigation of conformational processes such as ring inversion and/or ring pseudorotation has attracted a lot of attention over the past decades. An in-depth conformational analysis of ring compounds requires mapping the relevant parts of the conformational energy surface at stationary and also at non-stationary points. However, the latter is not feasible by a description of the ring with Cartesian or internal coordinates. We provide in this work, a solution to this problem by introducing a new coordinate system based on the Cremer-Pople puckering and deformation coordinates. Furthermore, analytic first- and second-order derivatives of puckering and deformation coordinates, i.e., B-matrices and D-tensors, were developed simplifying geometry optimization and frequency calculations. The new coordinate system is applied to map the potential energy surfaces and reaction paths of cycloheptane (C₇H₁₄), cyclooctane (C₈H₁₆), and cyclo[18]carbon (C₁₈) at the quantum chemical level and to determine for the first time all stationary points of these ring compounds in a systematic way.

Spontaneous Symmetry Breaking in Cyclo[18]Carbon

After the experimental evidence of polyynic as the stable form of cyclo[18]carbon, in the present paper, using ab initio electronic structure calculations, we show that this result is a symmetry breaking event, a consequence of the second-order Jahn-Teller effect. We show that the eigenfunctions associated with lowest unoccupied molecular orbitals (LUMO) and LUMO + 1, the excited states of this ring molecule, interact with the eigenfunctions associated with the ground state (occupied states), and this interaction stabilizes the less symmetric polyynic form of cyclo[18]carbon with D_9h symmetry, instead of the cumulenic form. The frontier state interactions are responsible for the distortions in the symmetry in the electronic structures, lowering the energy and making the polyynic form the stable one with alternating triple and single bonds.

Potential molecular semiconductor devices: cyclo-Cn (n = 10 and 14) with higher stabilities and aromaticities than acknowledged cyclo-C18

Theoretical calculations reveal that the zero-dimensional allotropes of carbon atoms, cyclo-C_n (n = 10 and 14), have higher thermodynamic, kinetic, optical, and dynamic stabilities and aromaticity than the acknowledged cyclo-C₁₈.

Cyclo[18]carbon: the smallest all-carbon electron acceptor

The recently synthesized C₁₈ molecule demonstrates strong electron acceptor properties similar to C₆₀.

Theoretical design of an ultrafast supramolecular rotor composed of carbon nano-rings

A new type of supramolecular rotor composed of C₁₈ and cycloparaphenylenes exhibits ultrahigh rotation speeds as temperature increases.

Non-equilibrium steady state conductivity in cyclo[18]carbon and its boron nitride analogue

A ring-shaped carbon allotrope was recently synthesized for the first time, reinvigorating theoretical interest in this class of molecules.

Induced magnetic field in sp-hybridized carbon rings: analysis of double aromaticity and antiaromaticity in cyclo[2N]carbon allotropes

The induced magnetic field of C2N (N = 3-14) carbon rings was dissected to contributions from out-of-plane and in-plane π orbitals revealing two concurrent long range shielding or deshielding cones as a manifestation of the dual aromatic and antiaromatic character of C4n+2 and of C4n rings respectively. Aromaticity based on the magnetic criterion was evaluated with regard to the bonding pattern and geometrical characteristics that elucidate the influence of bond length and bond angle alteration on out-of-plane and in-plane magnetic responses. Ground state polyynic geometries of C4n+2 rings exhibit comparable shielding cones to annulenes, decreasing the magnetic response with regard to the ring size and similar πout and πin diatropicity. Transition state cumulenic rings display increased aromaticity expressed by a very strong constant magnetic response and augmented πout diatropicity with regard to πin. The variations of the induced magnetic field are explained on the basis of frontier orbital interactions through rotational excitations, which enable further rationalization of the aromatic/antiaromatic behavior.

Carbon Tunneling in the Automerization of Cyclo[18]carbon

Cyclo[18]carbon (C₁₈ ), a recently synthesized carbon allotrope, was found to have a polyynic ground-state structure with D_9h symmetry and formally alternating single and triple bonds. Yet, under less influencing experimental conditions this molecule might undergo an automerization reaction between its two degenerate geometries through a cumulenic (non-alternating, adjacent double bonds) D_18h transition state. Herein, we discuss the role of quantum mechanical tunneling (QMT) in this degenerate reaction. Our computations predict that at the experimental temperature (5 K) the reaction in the gas phase is completely driven by an extremely rapid heavy atom tunneling (k=2.1×10⁸  s^-1 ). Even when approaching room temperature, the QMT rate is still an order of magnitude faster than the semi-classical one. We propose an experimental test to support our prediction, by measuring a characteristic tunneling energy splitting within the radio wave region. Additionally, we examine the role of QMT in other hypothetical C_4n+2 carbon clusters.

sp-hybridized carbon allotrope molecular structures: An ongoing challenge for density-functional approximations

The recent synthesis of a C₁₈ monocyclic ring constitutes a major breakthrough as a new all-carbon disclosed form. However, modern density functional theory approaches do not lead to the correct experimental polyynic structure and favor the cumulenic one instead. We demonstrate here that this serious drawback can be solved by recently developed range-separated nonempirical schemes, independently of which kind of functional is being applied (i.e., semilocal, hybrid, or double-hybrid).

Cyclo[18]carbon: Insight into Electronic Structure, Aromaticity, and Surface Coupling

Cyclo[18]carbon (C₁₈) is studied computationally at the density functional theory (DFT) and ab initio levels to obtain insight into its electronic structure, aromaticity, and adsorption properties on a NaCl surface. DFT functionals with a small amount of Hartree-Fock exchange fail to determine the experimentally observed polyyne molecular structure, revealing a cumulene-type geometry. Exchange-correlation functionals with a large amount of Hartree-Fock exchange as well as ab initio CASSCF calculations yield the polyyne structure as the ground state and the cumulene structure as a transition state between the two inverted polyyne structures through a Kekule distortion. The polyyne and the cumulene structures are found to be doubly Hückel aromatic. The calculated adsorption energy of cyclo[18]carbon on the NaCl surface is small (37 meV/C) and almost the same for both structures, implying that the surface does not stabilize a particular geometry.

An sp-hybridized molecular carbon allotrope, cyclo[18]carbon

Carbon allotropes built from rings of two-coordinate atoms, known as cyclo[n]carbons, have fascinated chemists for many years, but until now they could not be isolated or structurally characterized because of their high reactivity. We generated cyclo[18]carbon (C18) using atom manipulation on bilayer NaCl on Cu(111) at 5 kelvin by eliminating carbon monoxide from a cyclocarbon oxide molecule, C24O6. Characterization of cyclo[18]carbon by high-resolution atomic force microscopy revealed a polyynic structure with defined positions of alternating triple and single bonds. The high reactivity of cyclocarbon and cyclocarbon oxides allows covalent coupling between molecules to be induced by atom manipulation, opening an avenue for the synthesis of other carbon allotropes and carbon-rich materials from the coalescence of cyclocarbon molecules.

Adsorption of Monocyclic Carbon Rings on Graphene: Energetics Revealed via Continuum Modeling

Gas-phase spectroscopic detection of tiny carbon clusters is a recent success story in the area of carbon cluster research. However, experimental production and isolation of these clusters are extremely difficult because of their high reactivity. One possibility to isolate the generated clusters would be to deposit them on graphene and to desorb them for subsequent use. One of the pertinent questions toward realizing this would be the energetics of the adsorption process. Therefore, in this work, the energetics for the adsorption of the monocyclic carbon rings (C _n with n = 10, 12, 14, 16, 18, 20, and 22) on a graphene sheet are investigated using the analytical approaches, developed earlier by Hill and co-workers. The adsorption process here is driven by the noncovalent interactions between the carbon rings and the graphene sheet. The analyses of the interaction energies as a function of both the vertical distance Z and the rotational angle ϕ are performed in order to determine the preferred orientations, equilibrium positions, and binding energies for the adsorption of various carbon rings on graphene. We find that the preferred orientation of the rings with respect to the graphene sheet is the parallel orientation. The results from continuum, discrete-continuum, and discrete models are in good agreement. Further, computations using density functional theory and quantum mechanics/molecular mechanics approaches are performed, and comparisons of the computed energetics with the data from the models are reported. Finally, we highlight the scope and the limitations of the analytical models.

Carbon-atom wires: 1-D systems with tunable properties

This review provides a discussion of the current state of research on linear carbon structures and related materials based on sp-hybridization of carbon atoms (polyynes and cumulenes). We show that such systems have widely tunable properties and thus represent an intriguing and mostly unexplored field for both fundamental and applied sciences. We discuss the rich interplay between the structural, vibrational, and electronic properties focusing on recent advances and the future perspectives of carbon-atom wires and novel hybrid sp-sp(2)-carbon architectures.

Carbon rings: a DFT study on geometry, aromaticity, intermolecular carbon–carbon interactions and stability

Strong complimentary electrostatic interactions lead to large number of C⋯C interactions in doubly antiaromatic C_4N dimers while the delocalized system of π electrons in doubly aromatic C_4N+2 dimers suggest very few intermolecular C⋯C interactions.

Even-odd product variation of the C(n)(+) + D(2) (n = 4-9) reaction: complexity of the linear carbon cation electronic states

We have studied reactions between linear Cn(+) (n = 4-9) and D2, using ion mobility mass spectrometry techniques and quantum chemical calculations in order to understand the complex reactivity of the linear cluster cations. Only linear CnD(+) products were observed for the odd (n = 5, 7, 9) linear clusters, while CnD2(+) was the main product for the even clusters. For the reaction rate constants determined for these two channels, we obtained the following two features: (1) the rate constant decreases with the size n, and (2) even-sized clusters have lower rate constants than neighboring odd-sized clusters. In the theoretical calculations using the CCSD(T) and B3LYP methods with the cc-pVTZ basis, we found that a low lying (2)Σ state in odd clusters may play an important role in these reactions. This opposes the previous interpretation that the (2)Πg/u state is the dominant electronic state for linear Cn(+) (n = 4-9) clusters. We showed that a barrierless radical abstraction forming CnD(+) occurs through a direct head on approach for the (2)Σ state Cn(+). In contrast, a carbene-like insertion forming CnD2(+) occurs through a sideways approach for the (2)Πg/u state Cn(+). We have concluded that the higher rate constants for the odd clusters come from the existence of symmetry broken (2)Σ states which are absent in even linear clusters.

Confinement and controlling the effective compressive stiffness of carbyne

Carbyne is a one-dimensional chain of carbon atoms, consisting of repeating sp-hybridized groups, thereby representing a minimalist molecular rod or chain. While exhibiting exemplary mechanical properties in tension (a 1D modulus on the order of 313 nN and a strength on the order of 11 nN), its use as a structural component at the molecular scale is limited due to its relative weakness in compression and the immediate onset of buckling under load. To circumvent this effect, here, we probe the effect of confinement to enhance the mechanical behavior of carbyne chains in compression. Through full atomistic molecular dynamics, we characterize the mechanical properties of a free (unconfined chain) and explore the effect of confinement radius (R), free chain length (L) and temperature (T) on the effective compressive stiffness of carbyne chains and demonstrate that the stiffness can be tuned over an order of magnitude (from approximately 0.54 kcal mol(-1) Å(2) to 46 kcal mol(-1) Å(2)) by geometric control. Confinement may inherently stabilize the chains, potentially providing a platform for the synthesis of extraordinarily long chains (tens of nanometers) with variable compressive response.

Carbyne from first principles: chain of C atoms, a nanorod or a nanorope

We report an extensive study of the properties of carbyne using first-principles calculations. We investigate carbyne's mechanical response to tension, bending, and torsion deformations. Under tension, carbyne is about twice as stiff as the stiffest known materials and has an unrivaled specific strength of up to 7.5 × 10(7) N·m/kg, requiring a force of ∼10 nN to break a single atomic chain. Carbyne has a fairly large room-temperature persistence length of about 14 nm. Surprisingly, the torsional stiffness of carbyne can be zero but can be "switched on" by appropriate functional groups at the ends. Further, under appropriate termination, carbyne can be switched into a magnetic semiconductor state by mechanical twisting. We reconstruct the equivalent continuum elasticity representation, providing the full set of elastic moduli for carbyne, showing its extreme mechanical performance (e.g., a nominal Young's modulus of 32.7 TPa with an effective mechanical thickness of 0.772 Å). We also find an interesting coupling between strain and band gap of carbyne, which is strongly increased under tension, from 2.6 to 4.7 eV under a 10% strain. Finally, we study the performance of carbyne as a nanoscale electrical cable and estimate its chemical stability against self-aggregation, finding an activation barrier of 0.6 eV for the carbyne-carbyne cross-linking reaction and an equilibrium cross-link density for two parallel carbyne chains of 1 cross-link per 17 C atoms (2.2 nm).