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

Electronic Structure Determines Geometry: Bond Length Alternating in Cyclo[2n]carbons

Structure determines the properties. However, whether electronic structure determines geometry or geometry determines electronic structure seems a philosophical question in a chicken and egg situation, which remains unclear. In this work, by applying density functional theory (DFT) and DMRG(4n,4n)-CASSCF methods, theoretical investigation suggested that the dual antiaromaticity in cyclo[2n]carbons with even n should be attributed to the electron correlation effect, instead of decreased geometric symmetry, which actually exists in all cyclo[2n]carbon molecules and does not point out the essence. Such dual antiaromaticity can be conceptualized as electron correlation-stabilized dual antiaromaticity. Results also showed that DFT is reliable for cyclocarbons larger than C14, but we should be careful when applying it to smaller ones. DFT failed to give the correct structure of C6 compared with density matrix renormalization group results.

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.

Exploring Aromaticity Effects on Electronic Transport in Cyclo[n]carbon Single-Molecule Junctions

Cyclo[n]carbon (Cn) is one member of the all-carbon allotrope family with potential applications in next-generation electronic devices. By employing first-principles quantum transport calculations, we have investigated the electronic transport properties of single-molecule junctions of Cn, with n = 14, 16, 18, and 20, connected to two bulk gold electrodes, uncovering notable distinctions arising from the varying aromaticities. For the doubly aromatic C14 and C18 molecules, slightly deformed complexes at the singlet state arise after bonding with one Au atom at each side; in contrast, the reduced energy gaps between the highest occupied and the lowest unoccupied molecular orbitals due to the orbital reordering observed in the doubly anti-aromatic C16 and C20 molecules lead to heavily deformed asymmetric complexes at the triplet state. Consequently, spin-unpolarized transmission functions are obtained for the Au-C14/18-Au junctions, while spin-polarized transmission appears in the Au-C16/20-Au junctions. Furthermore, the asymmetric in-plane π-type hybrid molecular orbitals of the Au-C16/20-Au junctions contribute to two broad but low transmission peaks far away from the Fermi level (Ef), while the out-of-plane π-type hybrid molecular orbitals dominate two sharp transmission peaks that are adjacent to Ef, thus resulting in much lower transmission coefficients at Ef compared to those of the Au-C14/18-Au junctions. Our findings are helpful for the design and application of future cyclo[n]carbon-based molecular electronic devices.

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.

Comparative analysis of absorption resonances between carbynes and cyclo[n]carbons

Two approaches are presented here to analyze the absorption resonances between carbynes and cyclo[n]carbons, namely the analytical tight-binding model to calculate the optical selection rules of cumulenic atomic rings and chains and theab initiotime-dependent density functional theory for the optical investigation of polyynic carbon ring and chains. The optical absorption spectra of the carbon ring match that of the finite chain when their eigen energies align following theNring=2Nchain+2rule, which states that the number of atoms in an atomic ringNringis twice the number of atoms on a finite chainNchainwith two additional atoms. Two representative atomic chains are chosen for our numerical calculations, specifically carbynes withN=7and8carbon atoms as optical resonance spectra match to a recently synthesized carbon ring called cyclo[18]carbon. Despite the mismatch in resonance peaks, molecular orbital transitions of both carbynesN = 7 and 8 and cyclo[18]carbon reveal a wave function symmetry change from inversion to reflection and vice versa for allowed molecular orbital transitions, which results in electron density redistribution along the polyynic carbyne axis or the cyclo[18]carbon circumference. Our investigation of the correlation of optical absorption peaks between carbynes and cyclo[n]carbons is a step towards enhancing the reliability of allotrope identification in advanced molecular device spectroscopy. Moreover, this work could facilitate the non-invasive, rapid and crucial assessment of these sensitive 1D allotropes by providing accurate descriptions of their electronic and optical properties, particularly in controlled synthesis environments.

Investigating the potential of monocyclic B9N9 and C18 rings for the electrochemical sensing, and adsorption of carbazole-based anti-cancer drug derivatives: DFT-based first-principle study

CONTEXT

For the first time, the use of monocyclic rings C18 and B9N9 as sensors for the sensing of carbazole-based anti-cancer drugs, such as tetrahydrocarbazole (THC), mukonal (MKN), murrayanine (MRY), and ellipticine (EPT), is described using DFT simulations and computational characterization. The geometries, electronic properties, stability studies, sensitivity, and adsorption capabilities of C18 and B9N9 counterparts towards the selected compounds confirm that the analytes interact through active cavities of the C18 and B9N9 rings of the complexes.

METHODS

Based on the interaction energies, the sensitivity of surfaces towards EPT, MKN, MRY, and THC analytes is observed. The interaction energy of EPT@B9N9, MKN@B9N9, MRY@B9N9, and THC@B9N9 complexes are observed - 20.40, - 19.49, - 20.07, and - 18.27 kcal/mol respectively which is more exothermic than EPT@C18, MKN@C18, MRY@C18, and THC@C18 complexes are - 16.37, - 13.97, - 13.96, and - 11.39 kcal/mol respectively. According to findings from the quantum theory of atoms in molecules (QTAIM) and the reduced density gradient (RDG), dispersion forces play a significant role in maintaining the stability of these complexes. The electronic properties including FMOs, density of states (DOS), natural bond orbitals (NBO), charge transfer, and absorption studies are carried out. In comparison of B9N9 and C18, the analyte recovery time for C18 is much shorter (9.91 × 10-11 for THC@C18) than that for B9N9 shorter recovery time value of 3.75 × 10-9 for EPT@B9N9. These results suggest that our reported sensors B9N9 and C18 make it faster to detect adsorbed molecules at room temperature. The sensor response is more prominent in B9N9 due to its fine energy gap and high adsorption energy. Consequently, it is possible to think of these monocyclic systems as a potential material for sensor applications.

Genesis of Polynitrogen Compounds Employing Silicon Substituted cyclo[18]carbon: A DFT Investigation

Activation of molecular N2 and its catalytic ability to form NH3 using C17Si has been already reported. This current study reports the formation of exclusive polynitrogen clusters (N4 and N5) on the C17Si ring. The clusters are generated using N2 and N3 respectively. Physical and chemical property analyses of the clusters show that the N5 cluster exhibits greater stability than N4. The former is seen to experience reduced molecular strain compared to the latter owing to its co-planar geometry. The thermodynamic calculations of the systems further show that the formation of the N5 cluster is spontaneous compared to N4 on the C17Si ring.

Facilitating Electron Transfer by Resizing Cyclocarbon Acceptor from C18 to C16

Recent advances in synthetic methods, combined with tip-induced on-surface chemistry, have enabled the formation of numerous cyclocarbon molecules. Here, we investigate computationally the experimentally studied C16 and C18 molecules as well as their van der Waals (vdW) complexes with several typical donor and acceptor molecules. Our results demonstrate a remarkable electron-withdrawing ability of cyclocarbon molecules. The vdW complexes of C16 and C18 exhibit a thermodynamically favorable photoinduced electron transfer (ET) from the donor partner to the cyclocarbons that occurs on a picosecond time scale. The lower reorganization energy of C16 compared to C18 leads to a significant acceleration of the ET reactions.

Mechanistic Inquisition on the Reduction of C17Si(NH2)2 to NH3: A DFT Study

Activation of molecular nitrogen by silicon-substituted cyclo[18]carbon and its ability to produce the C17Si-(NH2)2 derivative, as the precursor of NH3, has been recently reported. This specific acquisition has piqued an interest to investigate the possibility of NH3 formation with further addition of H2 molecules in the gaseous reaction media. The current investigations reported in this article show that two moles of molecular H2 generate two molecules of NH3 and a C17Si-H2 byproduct from its precursor. The catalyst gets restored by an in situ reaction between some unreacted C17Si-N2 and the byproduct in the media. This reaction also produces the next C17Si-(NH)2 adduct, which restarts the catalytic cycle for NH3 production again.

Sr-centered monocyclic carbon ring Sr@C14: A new stable cluster

The study of stable neutral metal endohedral cyclo[n]carbon is helpful for discovering single-molecule devices. Extensive structural search and density functional theory calculations performed here indicate that the perfect planar alkaline metal-doped complexes Sr@C14 possess the well-defined global minima of the system with the metal atom located exactly at the center of the carbon ring. The configuration and bonding properties of C14 are different from those of pristine cyclo [14]carbon. The significant stabilization when forming Sr@C14 predominantly originates from the electrostatic interaction between Sr2+ and C142-. The detailed molecular orbital, nucleus-independent chemical shift (NICS), and ring current analyses indicate that Sr@C14 is aromatic in nature. The NICS values of Sr@C14 are considerably larger than those of benzene. Ab initio molecular dynamics simulations at different temperatures reveal that this system exhibits certain stability at low or moderate temperatures. The findings of this study effectively enrich the chemical structures and bonding patterns of metal-doped cyclo[n]carbon and provide the knowledge required to obtain novel structures of Sr@C14 in future experiments.

Impact of Halogen Termination and Chain Length on π-Electron Conjugation and Vibrational Properties of Halogen-Terminated Polyynes

We explored the optoelectronic and vibrational properties of a new class of halogen-terminated carbon atomic wires in the form of polyynes using UV-vis, infrared absorption, Raman spectroscopy, X-ray single-crystal diffraction, and DFT calculations. These polyynes terminate on one side with a cyanophenyl group and on the other side, with a halogen atom X (X = Cl, Br, I). We focus on the effect of different halogen terminations and increasing lengths (i.e., 4, 6, and 8 sp-carbon atoms) on the π-electron conjugation and the electronic structure of these systems. The variation in the sp-carbon chain length is more effective in tuning these features than changing the halogen end group, which instead leads to a variety of solid-state architectures. Shifts between the vibrational frequencies of samples in crystalline powders and in solution reflect intermolecular interactions. In particular, the presence of head-to-tail dimers in the crystals is responsible for the modulation of the charge density associated with the π-electron system, and this phenomenon is particularly important when strong I··· N halogen bonds occur.

Electron transfer-mediated synergistic nonlinear optical response in the Agn@C18 (n = 4-6) complexes: A DFT study on the electronic structures and optical characteristics

Seeking highly efficient and stable non-linear optical (NLO) materials is crucial yet challenging, given their promising applications in laser diodes and photovoltaics. In this study, we employ the excess electron and charge transfer strategies to theoretically design three novel complexes, namely Agn@C18 (n = 4-6), by adsorbing silver clusters onto the cyclo[18]carbon ring (C18). Our aim is to investigate the NLO characteristics of these complexes using density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations. The results reveal that the adsorption of Ag clusters onto C18 leads to a decrease in excitation energy and an increase in dipole moment and oscillator strengths, thereby significantly enhancing the hyperpolarizability of the complexes. Strikingly, among all these complexes, Ag6@C18 exhibits the highest first hyperpolarizability value of approximately 109496.2620 au calculated at the B3LYP/cc-PVDZ-pp level of theory, which is about 1.3 × 106 times higher than that of pure C18. This finding validates the effectiveness of the proposed strategies in enhancing the NLO response of the species. Moreover, the calculated UV-Vis absorption spectrum demonstrates that the Agn@C18 complexes with excess electrons exhibit absorption at longer wavelengths (ranging from 385 to 731 nm) compared to C18. In addition, the stability, chemical bonding, and charge transfer characteristics of the Agn@C18 (n = 4-6) complexes were also discussed. These findings highlight the potential of these complexes for the development of highly efficient NLO devices.

Electronic Structure of Metalloporphenes, Antiaromatic Analogues of Graphene

Zinc porphene is a two-dimensional material made of fully fused zinc porphyrins in a tetragonal lattice. It has a fully conjugated π-system, making it similar to graphene. Zinc porphene has recently been synthesized, and a combination of rough conductivity measurements and infrared and Raman spectroscopies all suggested that it is a semiconductor (Magnera, T.F. et al. Porphene and Porphite as Porphyrin Analogs of Graphene and Graphite, Nat. Commun.2023, 14, 6308). This is in contrast with all previous predictions of its electronic structure, which indicated metallic conductivity. We show that the gap-opening in zinc porphene is caused by a Peierls distortion of its unit cell from square to rectangular, thus giving the first account of its electronic structure in agreement with the experiment. Accounting for this distortion requires proper treatment of electron delocalization, which can be done using hybrid functionals with a substantial amount of exact exchange. Such a functional, PBE38, is then applied to predict the properties of many first transition row metalloporphenes, some of which have already been prepared. We find that changing the metal strongly affects the electronic structure of metalloporphenes, resulting in a rich variety of both metallic conductors and semiconductors, which may be of great interest to molecular electronics and spintronics. Properties of these materials are mostly governed by the extent of the Peierls distortion and the number of electrons in their π-system, analogous to changes in aromaticity observed in cyclic conjugated molecules upon oxidation or reduction. These results give an account of how the concept of antiaromaticity can be extended to periodic systems.

Aromaticity Reversal Induced by Vibrations in Cyclo[16]carbon

Aromaticity is typically regarded as an intrinsic property of a molecule, correlated with electron delocalization, stability, and other properties. Small variations in the molecular geometry usually result in small changes in aromaticity, in line with Hammond's postulate. For example, introducing bond-length alternation in benzene and square cyclobutadiene by modulating the geometry along the Kekulé vibration gradually decreases the magnitude of their ring currents, making them less aromatic and less antiaromatic, respectively. A sign change in the ring current, corresponding to a reversal of aromaticity, typically requires a gross perturbation such as electronic excitation, addition or removal of two electrons, or a dramatic change in the molecular geometry. Here, we use multireference calculations to show how movement along the Kekulé vibration, which controls bond-length alternation, induces a sudden reversal in the ring current of cyclo[16]carbon, C16. This reversal occurs when the two orthogonal π systems of C16 sustain opposing currents. These results are rationalized by a Hückel model which includes bond-length alternation, and which is combined with a minimal model accounting for orbital contributions to the ring current. Finally, we successfully describe the electronic structure of C16 with a "divide-and-conquer" approach suitable for execution on a quantum computer.

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.

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.

Comparative rotatory power of bent and twisted polyynes

Linear polyynes of the formula C18 H2 (symmetry D∞h ) were bent in silico by progressively introducing CCC angles less than 180°. The bent structures (symmetry C2v ) were then twisted by introducing torsion angles across the CCCC segments by as much as 60°. The gyration tensors of these 19 structures (linear, bent, and twisted) were computed by linear response methods. Bending is massively generative of optical activity in oriented structures, even achiral structures, whereas twisting in conjunction with bending, serves to linearize the molecules and diminish maximally observable optical activity. This computational exercise is intended to unbind the infelicitous linkage of optical activity and chirality, which is only meaningful in isotropic media. Although bent structures are not optically active in solution-the spatial average of the optical activity is necessarily zero-solution measurements that deliver the spatial averages are a special class of measurements, albeit the overwhelmingly most common chiroptical measurements, that prejudice our common understanding of how π-conjugated structures generate gyration. Bending is far more effective than twisting at generating optical activity along some directions for oriented structures. The respective contributions from the transition electric dipole-magnetic dipole polarizability and the transition electric dipole-electric quadrupole polarizability are compared.

Size dependence of optical nonlinearity for H-capped carbon chains, H-(CC)n-H (n = 3-15): analysis of its nature and prediction for long chains

Based on a computational approach that can accurately describe their geometric structures and electronic spectra, we have theoretically studied the nonlinear optical (NLO) properties of H-capped carbon chains, H-(CC)n-H (n = 3-15), for the first time. Special attention was paid to the size dependence of the molecular (hyper)polarizability of these species through the nonlinear fitting of the data, which formed two power-law formulas of αiso(∞) = -0.206 + 0.264n1.498 and γ‖(∞) = -0.624 + 0.006n3.368 and was thoroughly discussed at the electronic structure level by in-depth wavefunction analyses. The fundamental gap (ΔE) between vertical ionization energy (VIE) and vertical electron affinity (VEA) is found to be related to the molecular (hyper)polarizability. The calculated (hyper)polarizability of the carbon chains H-(CC)n-H (n = 3-15) is more sensitive to the density functional theory (DFT) applied than to the basis set selected. The results are expected to provide theoretical guidance for the property prediction of arbitrarily long carbon chains not yet synthesized.

On-surface synthesis of a doubly anti-aromatic carbon allotrope

Synthetic carbon allotropes such as graphene1, carbon nanotubes2 and fullerenes3 have revolutionized materials science and led to new technologies. Many hypothetical carbon allotropes have been discussed4, but few have been studied experimentally. Recently, unconventional synthetic strategies such as dynamic covalent chemistry5 and on-surface synthesis6 have been used to create new forms of carbon, including γ-graphyne7, fullerene polymers8, biphenylene networks9 and cyclocarbons10,11. Cyclo[N]carbons are molecular rings consisting of N carbon atoms12,13; the three that have been reported to date (N = 10, 14 and 18)10,11 are doubly aromatic, which prompts the question: is it possible to prepare doubly anti-aromatic versions? Here we report the synthesis and characterization of an anti-aromatic carbon allotrope, cyclo[16]carbon, by using tip-induced on-surface chemistry6. In addition to structural information from atomic force microscopy, we probed its electronic structure by recording orbital density maps14 with scanning tunnelling microscopy. The observation of bond-length alternation in cyclo[16]carbon confirms its double anti-aromaticity, in concordance with theory. The simple structure of C16 renders it an interesting model system for studying the limits of aromaticity, and its high reactivity makes it a promising precursor to novel carbon allotropes15.

Synergy of semiempirical models and machine learning in computational chemistry

Catalyzed by enormous success in the industrial sector, many research programs have been exploring data-driven, machine learning approaches. Performance can be poor when the model is extrapolated to new regions of chemical space, e.g., new bonding types, new many-body interactions. Another important limitation is the spatial locality assumption in model architecture, and this limitation cannot be overcome with larger or more diverse datasets. The outlined challenges are primarily associated with the lack of electronic structure information in surrogate models such as interatomic potentials. Given the fast development of machine learning and computational chemistry methods, we expect some limitations of surrogate models to be addressed in the near future; nevertheless spatial locality assumption will likely remain a limiting factor for their transferability. Here, we suggest focusing on an equally important effort-design of physics-informed models that leverage the domain knowledge and employ machine learning only as a corrective tool. In the context of material science, we will focus on semi-empirical quantum mechanics, using machine learning to predict corrections to the reduced-order Hamiltonian model parameters. The resulting models are broadly applicable, retain the speed of semiempirical chemistry, and frequently achieve accuracy on par with much more expensive ab initio calculations. These early results indicate that future work, in which machine learning and quantum chemistry methods are developed jointly, may provide the best of all worlds for chemistry applications that demand both high accuracy and high numerical efficiency.

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.

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.

Origin of structure and stability of M@C18 (M = Cu, Ag, and Au) complexes with D9h point group

Theoretical predictions and recent experimental studies lead to the discovery of an exciting new member of the carbon allotrope family polyynic cyclo[18]carbon (C₁₈ ). Present investigation aims to probe the structure, stability, and properties of coinage metal (M)@C₁₈ complexes using density functional theory (DFT) calculations. The DFT results unequivocally show that even Cu@C₁₈ , Ag@C₁₈ , and Au@C₁₈ complexes substantially preserve the ground state polyynic structure of C₁₈ . It is also worth to mention that only Au@C₁₈ is a stable D_9h structure, however the symmetry is distorted in the case of Cu@C₁₈ and Ag@C₁₈ . Due to computational limitations, in this investigation the M@C₁₈ complexes were scrutinized using the C_2v sub abelian group of D_9h . The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of D_9h conformers are a singlet a₁ and two same value singlets a₁  ⊕ b₁ generated from doublet e, respectively. The non-covalent interaction index (NCI), quantum theory of atoms in molecule (QTAIM), and energy decomposition analysis (EDA) vividly explains the interaction between a coinage metal atom and C₁₈ ring. It is found from the results that the stability of Cu@C₁₈ Ag@C₁₈ , and Au@C₁₈ is governed by the attractive electrostatic, orbital and dispersion interaction.

Trapping of Small Molecules within Single or Double Cyclo[18]carbon Rings

The encapsulation of a set of small molecules, H₂, CO, CO₂, SO₂, and SO₃, by a circular C₁₈ ring is investigated by quantum calculations. These ligands lie near the center of the ring but, with the exception of H₂, are disposed roughly perpendicular to the ring plane. Their binding energies with the C₁₈ vary from 1.5 kcal/mol for H₂ up to 5.7 kcal/mol for SO₂, and the bonding is dominated by dispersive interactions spread over the entire ring. The binding of these ligands on the outside of the ring is weaker but allows the opportunity for each to bond covalently with the ring. A pair of C₁₈ units lie parallel to one another. This pair can bind each of these ligands in the area between them with only small perturbations of the double ring geometry. The binding energies of these ligands to this double ring configuration are amplified by some 50% compared to the single ring systems. The presented data concerning the trapping of small molecules may have larger implications regarding hydrogen storage or air pollution reduction.

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.

Activation and Conversion of Molecular Nitrogen to the Precursor of Ammonia on Silicon Substituted Cyclo[18]Carbon: a DFT Design

Recent synthesis of sp-hybridized cyclo[18]carbon allotrope has attracted immense curiosity. Since then, a generous amount of theoretical studies concerning aromaticity, adsorption, and spectra of the molecule have been performed. However, very few stuides have been carried out concerning its reactivities and catalytic behaviour. In this article, a DFT-based inquisition has been reported regarding the reactivity of Si substituted cyclo[18]carbon molecule towards molecular N₂ . Results show that the Si substituted derivative is effective in producing adducts with molecular nitrogen. Charge calculations and IRC trapping methods indicate that only the Si center of C₁₇ Si and its (HOMO-1) level participate in N₂ addition. The N-adduct so formed, is then found to spontaneously react with molecular H₂ . The addition of two H₂ molecules to the activated nitrogen molecule to give respective amine derivatives have also been studied. The successful generation of the precursor of NH₃ by C₁₇ Si lays a clear emphasis on its potentiality.

Parallel-Self-Assembling Stack, Center-Capture Effect, and Reactivity-Enhancing Effect of N-Layer (N = 1, 2, 3) Cyclo[18]carbon

Cyclo[18]carbon (C₁₈) is an captivating allotrope of carbon synthesized recently, which has drawn the attention among scientists. There are still few studies on the dynamic behaviors of C₁₈. To gain knowledge in this area, we systematically explored the stacking behaviors and the oxidation kinetics of C₁₈, as well the electronic transport behaviors of C₁₈ oxides, by density functional theory and nonequilibrium Green's function calculations combined with reactive force field molecular dynamics simulations. The parallel-self-assembling behaviors were observed in the stack of two- or three-layer C₁₈. During the oxidation process of C₁₈, we found an evident center-capture effect in which the hollow rings would preferentially attract an O₂ molecule into their centers. Moreover, the adsorption of O₂ on the O₂-doped rings was dramatically enhanced by the O₂ at the center of the ring, showing the reactivity-enhancing effect. The excellent electron transport property of central-O₂-doped C₁₈ among 13 types of C₁₈ oxides demonstrates the potential of C₁₈ oxides as promising molecular devices for various applications. This study reveals the dynamic behaviors of C₁₈ and provides theoretical guidance for use of C₁₈ and C₁₈ oxides in molecular devices.

Cyclo[18]carbon Formation from C18Br6 and C18(CO)6 Precursors

Although cyclo[18]carbon has been isolated experimentally from two precursors, C₁₈Br₆ and C₁₈(CO)₆, no reaction mechanisms have yet been explored. Herein, we provide insight into the mechanism behind debromination and decarbonylation. Both neutral precursors demonstrate high activation barriers of ∼2.3 eV, while the application of an electric field can lower the barriers by 0.1-0.2 eV. The barrier energy of the anion-radicals is found to be significantly lower for C₁₈Br₆ compared to C₁₈(CO)₆, confirming a considerably higher yield of cylco[18]carbon when the C₁₈Br₆ precursor is used. Elongation of the C-Br bond in the anion-radical confirms its predissociation condition. Natural bonding orbital analysis shows that the stability of C-Br and C-CO bonds in the anion-radicals is lower compared to their neutral species, indicating a possible higher yield. The applied analysis provides crucial details regarding the reaction yield of cyclo[18]carbon and can serve as a general scheme for tuning reaction conditions for other organic precursors.

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.

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.

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.

Photophysical properties and optical nonlinearity of cyclo[18]carbon (C18) precursors, C18-(CO)n (n = 2, 4, and 6): focusing on the effect of the carbonyl groups

The electronic spectra and (hyper)polarizability of C₁₈-(CO)_n (n = 2, 4, and 6) are studied using theoretical calculations to reveal the effect of introducing carbonyl (-CO) groups on the molecular optical properties. Successive introduction of -CO groups is observed to cause a red-shift in the absorption spectrum, but maximum absorption of all molecules is mainly due to the charge redistribution within the C₁₈ moiety. The (hyper)polarizabilities of the cyclocarbon oxides present an ascending trend with the -CO groups in the molecule, and the higher-order response properties are more sensitive. With (hyper)polarizability density analysis and (hyper)polarizability contribution decomposition, the fundamental reasons for the difference of (hyper)polarizability of different molecules are systematically discussed from the perspective of physical and structural origins, respectively. Significant optical resonances under the frequency-dependent fields are found for the (hyper)polarizabilities of the cyclocarbon oxides, which is in contrast to the insignificant influence on their polarizability.

Heavy-Atom Tunneling in the Covalent/Dative Bond Complexation of Cyclo[18]carbon-Piperidine

Recent quantum chemical computations demonstrated the electron-acceptance behavior of this highly reactive cyclo[18]carbon (C₁₈) ring with piperidine (pip). The C₁₈–pip complexation exhibited a double-well potential along the N–C reaction coordinate, forming a van der Waals (vdW) adduct and a more stable, strong covalent/dative bond (DB) complex by overcoming a low activation barrier. By means of direct dynamical computations using canonical variational transition state theory (CVT), including the small-curvature tunneling (SCT), we show the conspicuous role of heavy atom quantum mechanical tunneling (QMT) in the transformation of vdW to DB complex in the solvent phase near absolute zero. Below 50 K, the reaction is entirely driven by QMT, while at 30 K, the QMT rate is too rapid (k_T ∼ 0.02 s^–1), corresponding to a half-life time of 38 s, indicating that the vdW adduct will have a fleeting existence. We also explored the QMT rates of other cyclo[n]carbon–pip systems. This study sheds light on the decisive role of QMT in the covalent/DB formation of the C₁₈–pip complex at cryogenic temperatures.

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 the Endocircular Li@C16 System

The endocircular Li@C₁₆ is a promising system as it can form both a charge-separated donor-acceptor complex and a non-charge-separated van der waals complex. By employing the state-of-the-art equation-of-motion coupled-cluster method, our study shows that the carbon ring of this system possesses high flexibility and may undertake large distortions. Due to the intricate interaction between the guest Li⁺ cation and the negatively charged ring, this system can form several isomers possessing different ground states. The interesting electronic structure properties indicate its applicability as a catalyst candidate in the future.

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.

On the Stabilization of Carbynes Encapsulated in Penta-Graphene Nanotubes: a DFT Study

We carried out density functional theory calculations to investigate the electronic and structural properties of linear carbon chains (carbynes) encapsulated in armchair and zigzag penta-graphene (PGNT) nanotubes. Results showed that PGNTs-wrapped carbyne can present negative formation energies that tend to stabilize that encapsulated carbon chains. These chains were stabilized in their cumulene and polyyne forms, with slight dependence on tube diameter. As a general trend, the PGNT band structures are kept almost unchanged upon carbyne encapsulation. This finding indicates weak orbital interactions between the PGNT and the carbyne. No net charge was found in chains encapsulated on zigzag PGNTs. Schematic representation of a carbyne encapsulated in a pentagraphene nanotube.

Reaction mechanisms of cyclo[18]carbon and triplet oxygen

Recently, a new carbon allotrope, cyclo[18]carbon, of alternating short and long carbon-carbon bonds has been synthesized and characterized in the condensed phase. Inspired by experiments, a lot of theoretical studies involving adsorption, aromaticity, catalysis and spectra have been performed. Although cyclo[18]carbon is generally regarded as an unstable molecule, the theoretical explanation of its instability is still inadequate. In this work, we studied the intermediate process of reactions between cyclo[18]carbon and triplet oxygen by density functional theory calculations. The reaction is expected to happen easily because the maximal reaction energy barrier is less than 1 eV, and cyclo[16]carbon, cyclo[17]carbon and straight-chain C₁₈O₂ molecules have been considered as possible products. Infrared and Raman spectra were calculated to help in differentiating the final products. The thermal stability of cyclo[17]carbon is rather weak according to ab initio molecular dynamics simulations. This work sheds light on the synthesis of other cyclo[n]carbons and cumulenes by utilizing cyclo[18]carbon.

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.

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.

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.