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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.

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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.

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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.

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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.

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We introduce a fermionic potential, v f , as a comprehensive measure of electron (de)localization in atomic-molecular systems. Unlike other common descriptors as ELF, LOL, etc., it characterizes all physical effects responsible for (de)localization of electrons, namely: an exchange hole depth, its tendency to change, a sensitivity of an exchange correlation hidden in a pair density and kinetic potential to local variations in electron density. Wells in the v f distribution correspond to the domains of maximum electron localization, while the potential's barriers prevent delocalization of electrons through them. It also estimates bond orders and successfully reveals the impact of chemical modifications or environmental effects on the delocalization of electrons in molecules and crystals. The v f components provide a unique opportunity to compare the influence of the mentioned physical effects on electron (de)localization. This merges physical and chemical views of electron delocalization using functions appearing in density functional theory.

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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 D9h 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 C2v sub abelian group of D9h . The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of D9h 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.

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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.

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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.

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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.

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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.

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Planarity is a very important structural character of molecules, which is closely related to many molecular properties. Unfortunately, there is currently no simple, universal, and robust way to measure molecular planarity. In order to fill this evident gap, we propose two metrics of molecular planarity, namely molecular planarity parameter (MPP) and span of deviation from plane (SDP), to quantitatively characterize planarity of molecules. MPP reflects the overall degree of deviation of the structure from a plane, while SDP represents the span of the structural deviation relative to the fitting plane; respectively, they are complementary to each other. The examples in this article demonstrate that these metrics have strong rationality and practicality. They can not only be used to investigate the planarity of the entire molecule, but also measure the planarity of local structures, and they can even be employed to study variation of molecular planarity during a dynamic process. In addition, we also propose a new representation, namely coloring atoms according to their signed deviation distance to the fitting plane. This kind of map allows researchers to intuitively and quickly recognize position of the atoms in the system relative to the fitting plane. It can be seen from the examples that this representation is very useful in graphically exhibiting molecular planarity. The methods proposed in this work have been implemented in our open-source analysis code Multiwfn, which can be freely obtained via http://sobereva.com/multiwfn . The use is very simple and rich file formats are supported as input file.

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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.

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Recently, Shuhong Xu et al. reported theoretical calculation of molecular structure, bonding, aromaticity, electron delocalization, and electronic spectrum of cyclo[18]carbon in J. Mol. Model., 26, 111 (2020). Due to inappropriate consideration of calculation strategy, misunderstanding of some analysis methods and concepts, and some errors in the data, there are misleading statements and unconvincing conclusions in their paper. Here, we will point out inadequacies of Shuhong Xu's paper and put forward our own views. The contents of this comment will also help those who are studying cyclo[18]carbon to better understand this system and its analogues.

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The vibrational spectra of cyclo[18]carbon and its analogues, cyclo[2n]carbon (n=3 to 15), were carefully simulated and characterized. The in-plane C-C stretching vibrations shows strong rigidity, while out-of-plane motions seem to be extremely flexible. The solvation effect can enhance signal strengths of the vibrational spectra, but does not evidently change the shape of the spectral curves. The infrared and Raman spectra of cyclo[2n]carbons are quite sensitive to ring size in the range of n=3 to 7, while the size only modestly affects peak positions and strengths for larger rings. Molecular dynamic trajectories show that the fluctuation period of the skeleton of cyclo[18]carbon is basically constant at different temperatures, and they are all about 300 fs. With increase of simulation temperature, the ring distortion due to thermal motion is notable and becomes much stronger. However, neither ring breaking nor isomerization in cyclo[18]carbon is observed during the simulations untill 298.15 K.

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Cyclo[18]carbon has a very unique geometry and electronic structure. We found that an external electric field (EEF) has an ultrastrong regulation effect on various aspects of the cyclo[18]carbon: (1) The EEF makes the shape of the cyclo[18]carbon change from a circle to an oval, the elongation is particularly striking at a large EEF magnitude. (2) The EEF causes a huge polarization of distribution of in-plane π electrons, and strong EEF can even make some of the electrons detached from the carbon ring (3) EEF significantly lowers LUMO energy and reduces HOMO-LUMO gap (4) Large EEF leads to absorption band in the visible light range and thus makes the cyclo[18]carbon display color (5) Strong EEF causes a large number of new absorption peaks in IR spectrum. We also carefully analyzed how EEF deforms structure of the cyclo[18]carbon from the perspective of atomic forces and decomposition of energy variation, and the reason why the in-plane π electrons are much more polarizable by EEF than the out-of-plane π electrons is discussed. Moreover, we demonstrated that it is feasible to equivalently apply a strong EEF on the cyclo[18]carbon via a purely chemical and thus a more easily achieve way, namely introducing divalent alkaline earth metal cation.

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Electrostatics and van der Waals (vdW) interactions are two major components of intermolecular weak interactions. Electrostatic potential has been a very popular function in revealing electrostatic interaction between the system under study and other species, while the role of vdW potential was less recognized and has long been ignored. In this paper, we explicitly present definition of vdW potential, describe its implementation details, and demonstrate its important practical values by several examples. We hope this work can arouse researchers' attention to the vdW potential and promote its application in the studies of weak interactions. Calculation, visualization, and quantitative analysis of the vdW potential have been supported by our freely available code Multiwfn ( http://sobereva.com/multiwfn ).

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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.

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The anisotropy of the optical activity of cyclo[18]carbon (C18 ), fully hydrogenated C18 (C18 H36 ), and 26 hydrogenated compounds of intermediate composition, C18 H2n , n = 1,2…17, were computed. These compounds were selected because they resemble loops of wire. The maximum gyration for acetylenic and cumulenic subgroups of compounds was linearly proportional to the product of the geometric area over which the charge can circulate, multiplied by the largest separation between carbon atoms on opposing sides of the loops. These geometric quantities can be likened to transition magnetic dipole moments and transition electric dipole moments, respectively, that can be generated in electronic excitations and which contribute in the main to nonresonant optical activity. The correlation between a computed geometric product of distance and area, and a quantum chemical property, establishes that chiroptical structure-activity relationships can be well established for judiciously chosen series of comparatively large compounds.