Theoretical Prediction and Comprehensive Characterization of an All-Nitrogenatomic Ring, Cyclo[18]Nitrogen (N18)

The cyclic molecule cyclo[18]carbon composed of 18 carbon atoms has been observed in condensed phase experiment in recent years and has attracted great attention. Through state-of-art quantum chemistry calculation, this study found that 18 nitrogen atoms can also form a macrocyclic system, cyclo[18]nitrogen (N18), though its lifetime is very short at room temperature and can only exist for a relatively long time at very low temperatures. We comprehensively theoretically studied properties of N18, including geometric configurations, thermal decomposition mechanism and rate, molecular dynamics behavior, energetic properties, vibrational and electronic spectra. We also discussed in depth the electronic structure of N18, including nature of the N-N bonds, lone-pairs, charge distribution characteristics, electronic delocalization, and aromaticity. This work is not only the first exploration of the macrocyclic N18 molecule, but also the first time to systematically examine a very long-chain substance fully composed of nitrogen atoms in isolated state.

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 Connected Convolutional Neutral Network Protocol for Design of Two-Dimensional Materials Based on Modified Graphdiyne

In materials science, doping plays a crucial role in manipulating the electronic properties of materials. Conventional screening via a trial-and-error strategy is challenging owing to the enormous chemical space. We proposed a connected convolutional neutral network (CCNN) for quick screening of boron nitrogen (B-N) codoped graphdiyne in terms of band gap. A paired-atomic localized matrix (PALM) descriptor was designed to describe the local chemical environment of materials with the matrix form adapted to a neutral network. An attribution analysis was conducted, and a quantitative relationship between structure and band gap is proposed, which reveals more significant influence of B-N doping at sp2 hybridized sites than at sp hybridized sites on broadening of the band gap of GDY. The accuracy and efficiency of the proposed approach implicate its potential in promoting the design of graphdiyne-based optoelectronic devices and catalysts with expected electronic properties, opening a new avenue for rational design of novel materials.

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.

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.

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.

Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor

Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics. By reformulating the problem of finding the fixed point of Lindblad dynamics as a feasibility semidefinite program, we bypass several well-known issues with variational quantum approaches to solving for steady states. We demonstrate that our hybrid approach allows us to estimate the steady states of higher dimensional open quantum systems and discuss how our method can find multiple steady states for systems with symmetries.

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.

Toward practical quantum embedding simulation of realistic chemical systems on near-term quantum computers

Quantum computing has recently exhibited great potential in predicting chemical properties for various applications in drug discovery, material design, and catalyst optimization. Progress has been made in simulating small molecules, such as LiH and hydrogen chains of up to 12 qubits, by using quantum algorithms such as variational quantum eigensolver (VQE). Yet, originating from the limitations of the size and the fidelity of near-term quantum hardware, the accurate simulation of large realistic molecules remains a challenge. Here, integrating an adaptive energy sorting strategy and a classical computational method-the density matrix embedding theory, which respectively reduces the circuit depth and the problem size, we present a means to circumvent the limitations and demonstrate the potential of near-term quantum computers toward solving real chemical problems. We numerically test the method for the hydrogenation reaction of C6H8 and the equilibrium geometry of the C18 molecule, using basis sets up to cc-pVDZ (at most 144 qubits). The simulation results show accuracies comparable to those of advanced quantum chemistry methods such as coupled-cluster or even full configuration interaction, while the number of qubits required is reduced by an order of magnitude (from 144 qubits to 16 qubits for the C18 molecule) compared to conventional VQE. Our work implies the possibility of solving industrial chemical problems on near-term quantum devices.

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.

Model of B9N9 Response under External Electric Field: Geometry, Electronic Properties, Reaction Activity

In this paper, we performed the ωB97XD/def2-TZVP method with a density functional theory study on the boron–nitrogen (BN) analogues of cyclo[18]carbon. The geometric structure, polarization properties, and excitation effect were calculated in the presence of an external electric field (EEF). Furthermore, the dual descriptor and Fukui function matrices were employed to predict the tendency towards the electrophilic or nucleophilic reactions of B₉N₉ under varying EEF strengths. The results show that the application of an EEF will cause the cyclic structure of B₉N₉ to be considerably distorted towards an elliptical geometry, the polarization to increase, and the reactivity of B₉N₉ to enhance with the increase in the EEF strength. This is of great significance for further experimental exploration into the catalytic properties of BN fullerenes.

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.

Conductance Switching in an Organometallic Single-Electron Transistor Using Current-Constrained Reduced-Density Matrix Theory

We report switching of molecular conductance at finite bias in a binuclear organometallic complex and its cation which were previously experimentally analyzed at low voltages to see the signature of Kondo resonance. The variational reduced density matrix theory is applied to show that the system is strongly multireferenced especially in its charged form. We also study the molecular conductance of both forms using recently developed current-constrained two-electron reduced density matrix theory which is capable of handling strong electronic correlation. We compare the results against an uncorrelated 1-electron reduced density matrix version of conductance calculations using Hartree-Fock molecular orbitals. We observe that despite quantitative disagreements, the qualitative trend in the conductance is correctly predicted to be favorable for the cationic partner by both methods. We explain the results using the inherently high density of states for the low-lying excited states in the cationic partner which is also replicable from uncorrelated electronic structure methods. Our results not only indicate that the low-bias conductance trend is maintained even beyond the Kondo regime and produces quantitative agreement with that of the experiment but also identifies important physical markers that are responsible for the high conductance of the charged species.

Mean-field density matrix decompositions

We introduce new and robust decompositions of mean-field Hartree-Fock and Kohn-Sham density functional theory relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning one-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regard to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure-property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.