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.

A wide-bandgap graphene-like structure C6BN with ultra-low dielectric constant

This study introduces a new wide-bandgap graphene-like structure, denoted as C6BN, achieved by incorporating an eight-electron BN pair, substantially modifying its electronic properties. Utilizing extensive density functional calculations, we comprehensively analyzed the stability, electronic structure, mechanical properties, and optical-electrical characteristics of C6BN. Our investigations reveal the material's exceptional thermodynamic, mechanical, and dynamic stability. Notably, the calculated wide bandgap of 2.81 eV in C6BN, supported by analyses of energy levels, band structures, and density of states, positions it as a promising two-dimensional wide-bandgap semiconductor. Additionally, C6BN exhibits isotropic mechanical features, highlighting its inherent flexibility. Remarkably, our calculations indicate an ultra-low dielectric constant (k = 1.67) for C6BN, surpassing that of well-established third-generation semiconductors. Further exploration into the thermoelectric properties of C6BN demonstrates its promising performance, as evidenced by calculations of thermal conductivity (κ), power factor (P), and Seebeck coefficient (S). In summary, our findings underscore the significant potential of the proposed C6BN structure as a flexible two-dimensional material poised to drive future advancements in electronic and energy-related technologies.

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.

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

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

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.

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.

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.

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.

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.

Intermolecular interactions between cyclo[18]carbon and XCN (X = H, F, Cl, Br, I): a theoretical study

In this article, the intermolecular interactions of cyclo[18]carbon with XCN (X = H, F, Cl, Br, I) were investigated in detail by quantum chemistry calculations and wavefunction analyses. The electrostatic potential and van der Waals potential of cyclo[18]carbon were examined, then the structures of the complexes, the interaction energies of the intermolecular interactions were studied. Quantum theory of atoms in molecules analysis was performed to help understand the specific interactions. The XCN molecules can insert into the cyclo[18]carbon ring, and ClCN, BrCN, and ICN could also bind with cyclo[18]carbon from outside. Charge transfer in the inner complex is more prominent than that of the outer complex. Plots of electron density difference revealed that electron density shift was significantly different when the X atom changed. The main driving force for molecular binding is dispersion attraction, which is disclosed by interaction region indicator analysis and energy decomposition calculations.

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.

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.

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.

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.

Encapsulation of monocyclic carbon clusters into carbon nanotubes: A continuum modeling approach

Carbon clusters are challenging to produce and isolate due to their highly reactive nature. One of the strategies for their isolation is to encapsulate the clusters into carbon nanotubes (CNTs) of appropriate radii. Herein, we have investigated the energetics for the encapsulation of the monocyclic carbon rings, [Formula: see text] ([Formula: see text], and [Formula: see text]) into CNTs of various radii using the continuum approximation. The encapsulation is driven by the non-covalent interactions between the carbon rings and the CNTs. The analyzes of the axial forces and the interaction energies at various orientations and positions of centers of mass of the rings with respect to the CNT axes clearly suggested the role of the tube radius in governing the energetics of encapsulation. Estimation of the acceptance and the suction energies as a function of CNT radius led to the prediction that the CNTs with radii of 5.38 Å, 5.83 Å, 6.25 Å, 6.68 Å, 7.07 Å, 7.51 Å, and 7.90 Å can efficiently encapsulate C10, C12, C14, C16, C18, C20, and C22 rings, respectively. In the limit of large tube radii, the numerical results lead to those obtained for carbon ring adsorption on graphene. Furthermore, the continuum approach enabled us to explore the potential energy surfaces thereby arriving at the equilibrium configurations of the rings inside the CNTs. Such an analysis is invaluable because of the enormous computational cost associated with quantum chemical calculations.

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

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

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

It has been challenging to adequately investigate the properties of nanosystems with radical nature using conventional electronic structure methods. We address this challenge by calculating the electronic properties of linear carbon chains (l-CC[n]) and cyclic carbon chains (c-CC[n]) with n = 10-100 carbon atoms, using thermally-assisted-occupation density functional theory (TAO-DFT). For all the cases investigated, l-CC[n]/c-CC[n] are ground-state singlets, and c-CC[n] are energetically more stable than l-CC[n]. The electronic properties of l-CC[n]/c-CC[n] reveal certain oscillation patterns for smaller n, followed by monotonic changes for larger n. For the smaller carbon chains, odd-numbered l-CC[n] are more stable than the adjacent even-numbered ones; c-CC[[Formula: see text]]/c-CC[4m] are more/less stable than the adjacent odd-numbered ones, where m are positive integers. As n increases, l-CC[n]/c-CC[n] possess increasing polyradical nature in their ground states, where the active orbitals are delocalized over the entire length of l-CC[n] or the whole circumference of c-CC[n].

Si2C5H2 isomers - search algorithms versus chemical intuition

The pros and cons of using search algorithms alone in identifying new geometries have been discussed by using the Si₂C₅H₂ elemental composition as an example. Within 30 kcal mol^-1 at the CCSD(T)/def2-TZVP//PBE0/def2-TZVP level of theory, the coalescence kick and cuckoo methods postulate merely four isomers (1, 3, 6, and 7) for Si₂C₅H₂ (O. Yañez et. al., Chem. Commun., 2017, 53, 12112). On the contrary, chemical intuition yields fourteen (2, 4, 5, and 8-18) new isomers within the same energy range at the B3LYP/6-311++G(2d,2p) level of theory. Based on the relative energies of the first eleven isomers of Si₂C₅H₂ (1, C_2v, 0.00; 2, C_s, 21.39; 3, C_s, 21.95; 4, C_s, 22.76; 5, C_s, 24.74; 6, C_s, 25.34; 7, C_s, 25.64; 8, C_s, 25.79; 9, C_s, 27.20; 10, C_2v, 28.59; and 11, C_2v, 29.16 kcal mol^-1) calculated at the CCSD(T)/cc-pVTZ level of theory, it is evident that the search algorithms had missed at least seven isomers in the same energy range. The relative energy gaps of isomers 12-18 fall in the range of 30-40 kcal mol^-1 at the latter level of theory. Consequentially, this scenario triggers a speculation going forward with search algorithms alone in the search of all new isomers. While one cannot underestimate the power of these algorithms, the role of chemical intuition may not be completely neglected. Retrospectively, the fourteen new isomers found by chemical intuition may help in writing better search algorithms. All eighteen isomers - including the most stable isomer with a planar tetracoordinate carbon atom 1- remain elusive in the laboratory to date. Thus, structural and spectroscopic parameters have been presented here, which may possibly aid the future experimental studies.