Small carbon clusters: spectroscopy, structure, and energetics

Using single and double laser pulses on the molecular Ni4@C48H36 system to design integrated nanospintronic units

The accomplishment of long-distance spin transfer scenarios between several magnetic centers is a big challenge for building and supporting spin-logic units for developing future all-optical magnetic unit operations. Using high-level quantum chemistry theory CCSD and EOM-CCSD, we systematically study the ultrafast laser-induced spin-dynamics process on a carbon-based material, to which four magnetic centers are attached. We show that the CCSD method with the 6-31G basis set calculation is sensitive to the C-Ni bond length. The spin density distribution, which is computed using EOM-CCSD with LanL2DZ+ECP calculations, Mulliken population analysis, including spin-orbit-coupling (SOC) and a magnetic field, fulfills the requirements for achieving spin dynamics processes. Different local spin-flip and spin-transfer processes are accomplished within the subpicosecond regime. The impact of the propagation direction of the laser pulse by switching their polar and the azimuthal angles in spherical coordinates on the spin dynamics processes is analyzed. Double laser pulses with time delay δt ≥ 200 × FWHM yield in a realistic magnetic field gradient selectively a lateral resolution, which corresponds to distances smaller than the CMOS scale (2 nm in 2024) while our system size is comparable to the CMOS scale. Here Λ and V processes with two quasi-degenerate intermediate levels are used. We propose a model of an integrated spin-logic processor created from an array of individual spin-logic blocks, which are realized by four magnetic centers Ni. The findings of this study demonstrate the enormous potential of using laser-induced spin dynamics as the fundamental mechanism for future molecular magnetic technology.

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

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

Gas-phase electronic spectra of HC2n+1H+ (n = 2-6) chains

Highly unsaturated carbon chains are generated in combustion processes and electrical discharges, and are confirmed constituents of the interstellar medium. In hydrogen-rich environments smaller carbon clusters tend to exist as linear chains, capped on each end by hydrogen atoms. Although the HC2nH+ polyacetylene chains have been extensively characterized spectroscopically, the corresponding odd HC2n+1H+ chains have received far less attention. Here we use two-colour resonance enhanced photodissociation spectroscopy to measure electronic spectra for HC2n+1H+ (n = 2-6) chains contained in a cryogenically cooled quadrupole ion trap. The HC2n+1H+ chains are formed either top-down by ionizing and fragmenting pyrene molecules using pulsed 266 nm radiation, or bottom-up by reacting cyclic carbon cluster cations with acetylene. Ion mobility measurements confirm that the HC2n+1H+ species are linear, consistent with predictions from electronic structure calculations. The HC2n+1H+ electronic spectra exhibit three band systems in the visible/near infrared spectral range, which each shifts progressively to longer wavelength by ≈90 nm with the addition of each additional CC subunit. The strongest visible HC11H+ band has a wavelength (λ = 545.1 nm) and width (1.5 nm) that match the strong λ 5450 diffuse interstellar band (DIB). However, other weaker HC11H+ bands do not correspond to catalogued DIBs, casting doubt on the role of HC11H+ as a carrier for the λ 5450 DIB. There are no identifiable correspondences between catalogued DIBs and bands for the other HC2n+1H+ chains, allowing upper limits to be established for their column densities in diffuse interstellar clouds.

Quantum rotational dynamics of l-C4(3Σ-g) by H2 at low temperatures employing a machine learning augmented potential energy surface

A new four dimensional (4D) ab initio potential energy surface (PES) is generated for the collision of C4(3Σg-) with H2(1Σg), considering both molecules as rigid rotors. A supervised neural network model is created to augment the ab initio PES and to get the missing data points. Furthermore, space fixed expansion of the augmented PES is carried out using a least squares fit over two spherical harmonics terms, resulting in radial coefficients (λ1, λ2, and λ). The centre of symmetry in both C4 and H2 forces λ1 and λ2 to have even values, respectively. Moreover, the rotational states of C4 are only populated by odd levels due to its ground state triplet symmetry and the nuclear spin (I = 0) of 12C. The cross-sections and rate coefficients with para and ortho H2 partners are studied for various odd state transitions, where the rate coefficients of the ortho are 10-20% higher than those of the latter. The de-excitation rates obtained by the para H2 collisions are also compared to those of He and are found to be ∼1.7-2.8 times the He rates, across various order transitions. The simple scaling of He rates using a factor of 1.38 proves insufficient to describe para H2 rates. Therefore, these results show the importance of explicitly studying H2 as an important colliding partner, governing the kinetics of various rotational processes in the interstellar space.

Characterization of Sulfur-Rich Microbial Organic Matter in Jurassic Carbonates Using Laser-Assisted Mass Spectrometry

Laser desorption-ionization mass spectrometry (MS) shows great potential for in situ molecular analysis of planetary surfaces and microanalysis of space-returned samples or (micro)fossils. Coupled with pyrolysis gas chromatography-mass spectrometry (Py-GC-MS) in ESA's ExoMars project, this technique could help assess further the origin of sulfur-bearing organic matter (OM) recently detected on Mars. To unravel this potential, we analyzed sulfurized microbial OM from ca. 150 million year-old carbonates with laser desorption-ionization mass spectrometry (single- and two-step: LDI-MS and L2MS), in comparison with time-of-flight secondary-ion mass spectrometry (ToF-SIMS), gas chromatography-mass spectrometry (GC-MS), and Py-GC-MS. We show that LDI-MS and L2MS readily detect sulfur-bearing moieties such as (alkyl)thiophenes and (alkyl)benzothiophenes. The mineral matrix, however, made the identification of sulfur-bearing molecules challenging in our L2MS experiment. The dominance of small aromatic hydrocarbons (≤14 carbons) in the LDI-MS and L2MS of the extracted soluble and insoluble OM and of the bulk rock is consistent with the low thermal maturity of the sediment and contrasts with the predominance of larger polycyclic aromatic structures commonly observed in meteorites with these techniques. We detected inorganic ions, in particular VO+, in demineralized OM that likely originate from geoporphyrins, which derive from chlorophylls during sediment diagenesis. Finally, insoluble OM yielded distinct compositions compared with extracted soluble OM, with a greater abundance of ions of mass-to-charge ratio (m/z) over 175 and additional N-moieties. This highlights the potential of laser-assisted MS to decipher the composition of macromolecular OM, in particular to investigate the preservation of biomacromolecules in microfossils. Studies comparing diverse biogenic and abiogenic OM are needed to further assess the use of this technique to search for biosignatures.

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.

Laser-induced ultrafast spin-transfer processes in non-linear zigzag carbon chain systems

We combine the high-level quantum chemistry theory CCSD and EOM-CCSD together with local and global Λ processes to investigate the details of the laser-induced ultrafast spin manipulation scenarios in non-linear zigzag carbon chain systems Ni2@C32H32 and Ni2@C36H36. The spin density distribution, which is calculated on each many-body state using a Mulliken population analysis, fulfills the requirements to accomplish the spin dynamics processes. Various spin-flip and spin-transfer scenarios are accomplished. All the spin-dynamics processes can be achieved within subpicosecond times. Under the influence of a magnetic field, we find that the spin-transfer scenarios are preserved, while the local spin-flip scenario on a Ni atom can be significantly inhibited depending on the strength of the magnetic field. The impact of the propagation direction of the laser pulse on the spin dynamics processes by varying their polar and azimuthal angles in spherical coordinates is investigated. Additionally, we find that double laser pulses successfully induce the spin-transfer processes. Our outcomes underline the significant potential of carbon chain systems as building blocks for developing future all-optical integrated logic processing units.

Ultrafast control of laser-induced spin-dynamics scenarios on two-dimensional Ni3@C63H54 magnetic system

The concept of building logically functional networks employing spintronics or magnetic heterostructures is becoming more and more popular today. Incorporating logical segments into a circuit needs physical bonds between the magnetic molecules or clusters involved. In this framework, we systematically study ultrafast laser-induced spin-manipulation scenarios on a closed system of three carbon chains to which three Ni atoms are attached. After the inclusion of spin-orbit coupling and an external magnetic field, different ultrafast spin dynamics scenarios involving spin-flip and long-distance spin-transfer processes are achieved by various appropriately well-tailored time-resolved laser pulses within subpicosecond timescales. We additionally study the various effects of an external magnetic field on spin-flip and spin-transfer processes. Moreover, we obtain spin-dynamics processes induced by a double laser pulse, rather than a single one. We suggest enhancing the spatial addressability of spin-flip and spin-transfer processes. The findings presented in this article will improve our knowledge of the magnetic properties of carbon-based magnetic molecular structures. They also support the relevant experimental realization of spin dynamics and their potential applications in future molecular spintronics devices.

Neural network atomistic potentials for global energy minima search in carbon clusters

The global energy optimization problem is an acute and important problem in chemistry. It is crucial to know the geometry of the lowest energy isomer (global minimum, GM) of a given compound for the evaluation of its chemical and physical properties. This problem is especially relevant for atomic clusters. Due to the exponential growth of the number of local minima geometries with the increase of the number of atoms in the cluster, it is important to find a computationally efficient and reliable method to navigate the energy landscape and locate a true global minima structure. Newly developed neural network (NN) atomistic potentials offer a numerically efficient and relatively accurate approach for molecular structure optimization. An important question that needs to be answered is "Can NN potentials, trained on a given set, represent the potential energy surface (PES) of a neighboring domain?". In this work, we tested the applicability of ANI-1ccx and ANI-nr NN atomistic potentials for the global minima optimization of carbon clusters Cn (n = 3-10). We showed that with the introduction of the cluster connectivity restriction and consequent DFT or ab initio calculations, ANI-1ccx and ANI-nr can be considered as robust PES pre-samplers that can capture the GM structure even for large clusters such as C20.

Probing Colossal Carbon Rings

Carbon aggregates containing between 10 and 30 atoms preferentially arrange themselves as planar rings. To learn more about this exotic allotrope of carbon, electronic spectra are measured for even cyclo[n]carbon radical cations (C14+-C36+) using two-color photodissociation action spectroscopy. To eliminate spectral contributions from other isomers, the target cyclo[n]carbon radical cations are isomer-selected using a drift tube ion mobility spectrometer prior to spectroscopic interrogation. The electronic spectra exhibit sharp transitions spanning the visible and near-infrared spectral regions with the main absorption band shifting progressively to longer wavelength by ≈100 nm for every additional two carbon atoms. This behavior is rationalized with a Hückel theory model describing the energies of the in-plane and out-of-plane π orbitals. Photoexcitation of smaller carbon rings leads preferentially to neutral C₃ and C₅ loss, whereas rings larger than C24+ tend to also decompose into two smaller rings, which, when possible, have aromatic stability. Generally, the observed charged photofragments correspond to low energy fragment pairs, as predicted by density functional theory calculations (CAM-B3LYP-D3(BJ)/cc-pVDZ). Using action spectroscopy it is confirmed that C14+ and C18+ photofragments from C28+ rings have cyclic structures.

Electronic Transition of the l-C6+ Cation at 417 nm

A new electronic transition is reported for the linear C6+ cation with an origin at 416.8 nm. This spectrum can be compared to the matrix isolation spectra at lower energies reported previously by Fulara et al. (J. Chem. Phys. 123, 044305 (2005)), which assigned linear and cyclic isomers, and to the gas phase spectrum reported previously by Campbell and Dunk (Rev. Sci. Instrum. 90, 103101 (2019)), which detected the same cyclic-isomer spectrum reported by Fulara. Comparisons to electronically excited states and vibrations predicted by various forms of theory allow assignment of the spectrum to a new electronic state of linear C6+. The spectrum consists of a strong origin band, two vibronic progression members at higher energy and four hotbands at lower energies. The hotbands provide the first gas phase information on ground state vibrational frequencies. The vibronic structure of this excited state of C6+ provides a severe challenge to computational chemistry.

Photofragment Imaging of Carbon Cluster Cations: Explosive Ring Rupture

Carbon cluster cations (C_n⁺) produced by laser vaporization are mass selected and photodissociated at 355 nm. Multiphoton dissociation of smaller ions leads to the elimination of neutral C₃, as in previous work, whereas larger clusters exhibit more varied fragmentation channels. Photofragment velocity-map imaging detects significant kinetic energy release (KER) in the various n - 3 cation fragments. Small cations (n = 6 or 7) with linear structures produce moderate KER, whereas larger cations (n = 10, 11, 12, 15, or 20) having monocyclic ring structures produce much higher KER values. Such high KER values are unanticipated, as optical excitation should produce a wide distribution of internal energies. These carbon clusters have a surprising ability to absorb multiple photons of ultraviolet radiation, achieving a state of extreme excitation prior to dissociation. The remarkable nonstatistical distribution of energy is apparently influenced by the significant ring strain that can be released upon photodissociation.

Symmetry collapse due to the presence of multiple local aromaticity in Ge244

Understanding the structural changes taking place during the assembly of single atoms leading to the formation of atomic clusters and bulk materials remains challenging. The isolation and theoretical characterization of medium-sized clusters can shed light on the processes that occur during the transition to a solid-state structure. In this work, we synthesize and isolate a continuous 24-atom cluster Ge₂₄⁴⁻, which is characterized by X-ray diffraction analysis and Energy-dispersive X-ray spectroscopy, showing an elongated structural characteristic. Theoretical analysis reveals that electron delocalization plays a vital role in the formation and stabilization of the prolate cluster. In contrast with carbon atoms, 4 s orbitals of Ge-atoms do not easily hybridize with 4p orbitals and s-type lone-pairs can be localized with high occupancy. Thus, there are not enough electrons to form a stable symmetrical fullerene-like structure such as C₂₄ fullerene. Three aromatic units with two [Ge₉] and one [Ge₆] species, connected by classical 2c-2e Ge-Ge σ-bonds, are aligned together forming three independent shielding cones and eventually causing a collapse of the global symmetry of the Ge₂₄⁴⁻ cluster.

Gaining insight on the structural transformations from atomic clusters to bulk materials is challenging. Here the authors synthesize a continuous cluster of germanium Ge₂₄⁴⁻, which can be viewed as two terminal Ge₉ units bridged via a Ge₆ central fragment, and characterize it by several techniques including X-ray diffraction; theoretical analysis indicates the presence of three aligned independent aromatic fragments.

Radiative relaxation in isolated large carbon clusters: Vibrational emission versus recurrent fluorescence

Recurrent fluorescence (RF) from isolated carbon clusters containing between 24 and 60 atoms is theoretically investigated as a function of internal energy, cluster size, and structural features. The vibrational relaxation kinetics and the associated IR emission spectra are determined by means of a Monte Carlo approach with vibrational density of states computed in the harmonic approximation. RF is generally found to be highly competitive with vibrational emission. The behaviors predicted for clusters of various sizes and archetypal structures indicate that the IR emission spectra are strongly influenced by RF, an energy gap law being obtained for the evolution of the RF rate constant depending on the electronic excitation state. The present results are relevant to the photophysics of the interstellar medium and could contribute to elucidating the carriers of the extended red emission bands and the continuum emission lying below the aromatic infrared bands believed to originate from mixed aromatic–aliphatic compounds.

Electronic Spectroscopy of Monocyclic Carbon Ring Cations for Astrochemical Consideration

Gas phase electronic spectra of pure carbon cations generated by laser vaporization of graphite in a supersonic jet and cooled to below 10 K and tagged with helium atoms in a cryogenic trap are presented. The measured C_2n⁺–He with n from 6 to 14, are believed to be monocyclic ring structures and possess an origin band wavelength that shifts linearly with the number of carbon atoms, as recently demonstrated through N₂ tagging by Buntine et al. (J. Chem. Phys.2021, 155, 21430234879679). The set of data presented here further constrains the spectral characteristics inferred for the bare C_2n⁺ ions to facilitate astronomical searches for them in diffuse clouds by absorption spectroscopy.

Electronic spectra of positively charged carbon clusters-C2n + (n = 6-14)

Electronic spectra are measured for mass-selected C_2n ⁺(n = 6-14) clusters over the visible and near-infrared spectral range through resonance enhanced photodissociation of clusters tagged with N₂ molecules in a cryogenic ion trap. The carbon cluster cations are generated through laser ablation of a graphite disk and can be selected according to their collision cross section with He buffer gas and their mass prior to being trapped and spectroscopically probed. The data suggest that the C_2n ⁺(n = 6-14) clusters have monocyclic structures with bicyclic structures becoming more prevalent for C₂₂ ⁺ and larger clusters. The C_2n ⁺ electronic spectra are dominated by an origin transition that shifts linearly to a longer wavelength with the number of carbon atoms and associated progressions involving excitation of ring deformation vibrational modes. Bands for C₁₂ ⁺, C₁₆ ⁺, C₂₀ ⁺, C₂₄ ⁺, and C₂₈ ⁺ are relatively broad, possibly due to rapid non-radiative decay from the excited state, whereas bands for C₁₄ ⁺, C₁₈ ⁺, C₂₂ ⁺, and C₂₆ ⁺ are narrower, consistent with slower non-radiative deactivation.

Association Reaction of Gaseous C2H4 in Femtosecond Laser Filaments Studied by Time-of-Flight Mass Spectrometry

Association reactions by femtosecond laser filamentation in gaseous C2H4 were studied by time-of-flight mass spectrometry of neutral reaction products. Direct sampling from the reaction cell to a mass spectrometer via a differential pumping stage allowed the identification of various hydrocarbon molecules C n H m with n = 3-7 and m = 4-7, which includes species not observed in the previous studies. It was found that products containing three and four carbon atoms dominate the mass spectrum with smaller yields for higher-mass species, suggesting that carbon chain growth proceeds through the reaction with C2H4 in the reaction cell. The product distribution showed a clear dependence on the laser pulse energy for filamentation.

Experimental determination of the interaction potential between a helium atom and the interior surface of a C60 fullerene molecule

The interactions between atoms and molecules may be described by a potential energy function of the nuclear coordinates. Nonbonded interactions between neutral atoms or molecules are dominated by repulsive forces at a short range and attractive dispersion forces at a medium range. Experimental data on the detailed interaction potentials for nonbonded interatomic and intermolecular forces are scarce. Here, we use terahertz spectroscopy and inelastic neutron scattering to determine the potential energy function for the nonbonded interaction between single He atoms and encapsulating C₆₀ fullerene cages in the helium endofullerenes ³He@C₆₀ and ⁴He@C₆₀, synthesized by molecular surgery techniques. The experimentally derived potential is compared to estimates from quantum chemistry calculations and from sums of empirical two-body potentials.

Boron nitride nanotube precursor formation during high-temperature synthesis: kinetic and thermodynamic modelling

We performed integrated modelling of the chemical pathways of formation for boron nitride nanotube (BNNT) precursors during high-temperature synthesis in a B/N₂mixture. Integrated modelling includes quantum chemistry, Quantum-classical molecular dynamics, thermodynamic modelling, and kinetic approaches. We demonstrate that BN compounds are formed via the interaction of molecular nitrogen with small boron clusters, rather than through interactions with less reactive liquid boron. (This process can also be described as N₂molecule fixation.) Liquid boron evaporates to produce these boron clusters (B_mwithm≤ 5), which are subsequently converted into B_mN_nchains. The production of such chains is crucial to the growth of BNNTs because these chains form the building blocks of bigger and longer BN chains and rings, which are in turn the building blocks of fullborenes and BNNTs. Additionally, kinetic modelling revealed that B₄N₄and B₅N₄species in particular play a major role in the N₂molecule fixation process. The formation of these species via reactions with B₄and B₅clusters is not adequately described under the assumption of thermodynamic equilibrium, as is demonstrated in our kinetic modelling. Thus, the accumulation of both B₄N₄and B₅N₄depends on the background gas pressure and the gas cooling rate. Long BN chains and rings, which are precursors of the fullborene and BNNT growth, form via self-assembly of components B₄N₄and B₅N₄. Our modelling results-particularly the increased densities of B₄N₄and B₅N₄species at higher gas pressures-explain the experimentally observed effect of gas pressure on the yield of high-quality BNNTs. The catalytic role of hydrogen was also studied; it is shown that HBNH molecules can be the main precursor of BNNT synthesis in the presence of hydrogen.

Atomic Clusters: Structure, Reactivity, Bonding, and Dynamics

Atomic clusters lie somewhere in between isolated atoms and extended solids with distinctly different reactivity patterns. They are known to be useful as catalysts facilitating several reactions of industrial importance. Various machine learning based techniques have been adopted in generating their global minimum energy structures. Bond-stretch isomerism, aromatic stabilization, Rener-Teller effect, improved superhalogen/superalkali properties, and electride characteristics are some of the hallmarks of these clusters. Different all-metal and nonmetal clusters exhibit a variety of aromatic characteristics. Some of these clusters are dynamically stable as exemplified through their fluxional behavior. Several of these cluster cavitands are found to be agents for effective confinement. The confined media cause drastic changes in bonding, reactivity, and other properties, for example, bonding between two noble gas atoms, and remarkable acceleration in the rate of a chemical reaction under confinement. They have potential to be good hydrogen storage materials and also to activate small molecules for various purposes. Many atomic clusters show exceptional opto-electronic, magnetic, and nonlinear optical properties. In this Review article, we intend to highlight all these aspects.

Carbon Clusters: Thermochemistry and Electronic Structure at High Temperatures

This paper studies the thermochemistry and electronic structure of small carbon clusters and hydrocarbons, which are major constituents of pyrolysis gases released into the boundary layer of ablating heat shields. Our focus lies on clusters of up to four carbon atoms. Among other molecules, thermochemistry data for molecules such as C₃H and C₄H have been determined using the Weizmann-1 (W1) method. These molecules have very limited thermochemistry data recorded in the literature, thereby necessitating new and accurate computations of required properties such as electronic energies of low-lying states, heats of formation, harmonic frequencies, and rotational constants. A study of electronically excited states of these molecules computed using the equations of motion coupled cluster singles doubles method revealed C₄ and C₄H to be potential sources of radiation absorption in the boundary layer. The excited electronic states of interest are studied further to obtain their optimum geometries, rotational constants, and vibrational frequencies. Moreover, we also study the effect of low-lying excited electronic states on the partition function to assess their effect on the thermodynamics of these pyrolysis gases in the high-temperature regime. Neglecting the excited electronic states records a maximum difference of 12% in the computed specific heat capacity values, C_p values. Finally, comparisons of the equilibrium mole fractions obtained using the thermodynamics computed in this paper with the existing state-of-the-art tables used for hypersonic applications (e.g., JANAF and Gurvich Tables) show an order of magnitude difference in the mixture compositions. It is shown that the rhombic isomer of C₄ (¹A_g), which is energetically close to the ground state (³Σ_g^-) and usually neglected in composition calculations, contributes to a 28% increase in the equilibrium mole fraction of the C₄ molecule.

Endocircular Li Carbon Rings

By employing accurate state-of-the-art many-electron quantum-chemistry methods, we establish that monocyclic carbon rings can accommodate Li guest atoms. The low-lying electronic states of these endocircular systems are analyzed and found to include both charge-separated states where the guest Li atom appears as a cation and the ring as an anion and encircled-electron states where Li and the ring are neutral. The electron binding energies of the encircled-electron states increase drastically at their highly symmetric equilibrium geometries with increasing size of the ring, and in Li@C24 , this state becomes the ground state. Li is very weakly bound vertical to the rings in the low-lying encircled-electron states, hinting to van-der-Waals binding. Applcations are mentioned.

An unbiased confirmation of the participating isomers of C2B5- in the formation of its photo-detachment spectra: a theoretical study

The primary goal of the present article is to provide an unbiased structural confirmation of C2B5-, relying on its available experimental photo-detachment spectra. The study is performed from scratch by optimizing the lowest energy isomers of C2B5- and later, suitable molecular vibronic Hamiltonians are constructed by analyzing the normal modes of these optimized isomers. The Hamiltonians' parameters are evaluated from the fits of the calculated ab initio single point energies using a state of the art multireference configuration (MRCI) level of theory employing a correlation consistent polarized triple zeta (cc-pVTZ) basis set. The state-averaged variant of the MRCI level of theory is also applied to deal with the highly interactive electronic states of both of the isomers. A detailed analysis of the potential energy curves along the totally symmetric vibrational modes is performed to understand the energy modulation between the different electronic states and also to find the energetic locations of the conical intersections. The introduction of the non-symmetric vibrational modes in the Hamiltonians help to understand the impact of non-adiabaticity during energy modulation in the coupled surfaces. Later, both adiabatic and non-adiabatic nuclear dynamics are performed on the electronic states of both of the isomers using the constructed reduced and full-dimensional Hamiltonians. The results of the adiabatic dynamics are used to assign the positions of the simulated photo-detachment bands, while the non-adiabatic dynamics improve the shape of those bands. Finally, we compare our theoretical findings with the available experimental photo-detachment spectra of C2B5- to provide an unbiased structural confirmation of the participating isomers of C2B5- in its photo-detachment spectra.

Anchoring a bow-shaped boron single chain in binary Be6B7- cluster: hybrid octagonal ring, multifold π/σ aromaticity, and dual electronic transmutation

Elemental boron clusters do not form linear chain or monocyclic ring structures, which is in contrast to carbon. Based on computer global searches and quantum chemical calculations, we report on the viability of a curved boron single chain in binary Be6B7- cluster. The boron motif assumes a bow shape, being anchored on a Be6 prism. Such a motif, which appears to be highly strained in its free-standing form, is exotic in boron-based clusters and nanostructures. Chemically, the cluster is analogous to a "clam-and-pearl-chain" system at the nanoscale (about 1 nm in size), in which a Be6 clam moderately opens its mouth, except that a B7 pearl chain is too large to be encapsulated inside. The picture differs from a three-layered sandwich. This cluster features a hybrid Be2B7 monocyclic ring, which is octagonal in nature and supports double 10π/6σ aromaticity. The number of π bonds substantially surpasses that in bare boron clusters of similar sizes. Two Be3 rings in the prism are also σ aromatic, albeit with effective 1σ/1σ electron-counting only. The unique multifold 1σ/10π/6σ/1σ aromaticity governs the geometry of the Be6B7- cluster, which can also be rationalized using the concept of dual electronic transmutation.

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].

Bound states and symmetry breaking of the ring C20 - anion

Determining the geometry of carbon rings is an ongoing challenge. Based on our calculations at a state-of-the-art level, we found that the C₂₀ ^- ring possesses five bound electronic states, including a superatomic state, which is the first superatomic state found for a ring. The nature of these electronic states is discussed. Our calculation reveals a symmetry breaking of the C₂₀ ^- ring anion ground electronic structure occurring upon attaching an electron to the neutral ring. The discussion of the possible symmetry breaking mechanisms indicates that the shrinking and distortion of the ring upon electron attachment, leading to the symmetry breaking, is a result of the interplay between the symmetry breaking and the totally symmetric modes. The discussion enriches the palette of possible symmetry breaking phenomena in carbon clusters.

Boron-Based Chiral Helix Be6 B10 2- and Be6 B11 - Clusters: Structures, Chemical Bonding, and Formation Mechanism

Boron forms a rich variety of low-dimensional nanosystems, including the newly discovered helix Be₆ B₁₀ ^2- (1) and Be₆ B₁₁ ^- (2) clusters. We report herein on the elucidation of chemical bonding in clusters 1/2, using the modern quantum chemistry tools of canonical molecular orbital analyses and adaptive natural density partitioning (AdNDP). It is shown that clusters 1/2 contain a chiral helix Be₂ B₁₀ Be₂ or Be₂ B₁₁ Be₂ skeleton with a total of 11 and 12 segments, respectively, which effectively curve into "helical pseudo rings" and chemically consist of two "quasicircles" as defined by their anchoring Be centers. The helix skeleton is connected via Lewis-type B-B and Be-B-Be σ bonds, being further stabilized by island π/σ bonds and a loose π bond at the junction. The Be₆ component in 1/2 assumes a distorted prism shape only physically, and it is fragmented into four parts: two terminal Be₂ dimers and two isolated Be centers. A Be₂ dimer at the far end manages to bend over and cap a quasicircle from one side of B plane. Consequently, each quasicircle of a helical pseudo ring is capped from opposite sides by two Be₂ /Be units, facilitating intramolecular charge-transfers of 5 electrons from Be to B. Overall, the folding of B helix involves as many as 10 electrons. The enormous electrostatics offers the ultimate driving forces for B helix formation.

Vibrational spectra and chemical imaging of cyclo[18]carbon by tip enhanced Raman spectroscopy

Vibrational modes and tip enhanced Raman spectroscopy (TERS) of a new carbon allotrope, cyclo[18]carbon (C18), were studied by density functional theory. A silver cluster tip was used to probe the interaction with C18, which is dependent on the distance and the atomically resolved positions. The TERS images show the position of the C[triple bond, length as m-dash]C bonds, as observed in a recent experimental report.

Prevalence of non-aromatic carbonaceous molecules in the inner regions of circumstellar envelopes

Evolved stars are a foundry of chemical complexity, gas and dust that provides the building blocks of planets and life, and dust nucleation first occurs in their photosphere. Despite their importance, the circumstellar regions enveloping these stars remain hidden to many observations, thus dust formation processes are still poorly understood. Laboratory astrophysics provides complementary routes to unveil these chemical processes, but most experiments rely on combustion or plasma decomposition of molecular precursors under physical conditions far removed from those in space. We have built an ultra-high vacuum machine combining atomic gas aggregation with advanced in-situ characterization techniques to reproduce and characterize the bottom-up dust formation process. We show that carbonaceous dust analogues formed from low-pressure gas-phase condensation of C atoms in a hydrogen atmosphere, in a C/H2 ratio similar to that reported for evolved stars, leads to the formation of amorphous C nanograins and aliphatic C-clusters. Aromatic species or fullerenes do not form effectively under these conditions, raising implications for the revision of the chemical mechanisms taking place in circumstellar envelopes.

Searching for double σ- and π-aromaticity in borazine derivatives

Inspired by the double-aromatic (σ and π) C₆H₃⁺, C₆I₆²⁺, and C₆(SePh)₆²⁺ ring-shaped compounds, herein we theoretically study their borazine derivative analogues. The systems studied are the cation and dications with formulas B₃N₃H₃⁺, B₃N₃Br₆²⁺, B₃N₃I₆²⁺, B₃N₃(SeH)₆²⁺, and B₃N₃(TeH)₆²⁺. Our DFT calculations indicate that the ring-shaped planar structures of B₃N₃H₃⁺, B₃N₃I₆²⁺, and B₃N₃(TeH)₆²⁺ are more stable in the singlet state, while those of B₃N₃Br₆²⁺ and B₃N₃(SeH)₆²⁺ prefer the triplet state. Besides, exploration of the potential energy surface shows that the ring-shaped structure is the putative global minimum only for B₃N₃I₆²⁺. According to chemical bonding analysis, B₃N₃H₃⁺, B₃N₃I₆²⁺, and B₃N₃(TeH)₆²⁺ have σ and π delocalized bonds. The number of delocalized σ/π electrons is 2/6 for the first, and 10/6 for the second and third, similar to what their carbon analogs exhibit. Finally, the analysis of the magnetically induced current density allows B₃N₃H₃⁺, B₃N₃I₆²⁺, and B₃N₃(TeH)₆²⁺ to be classified as strongly σ aromatic, and poorly π aromatic compounds.

Evolutionary algorithms, Born–Oppenheimer molecular dynamics and the magnetic criteria of aromaticity have been used to evaluate the stability and σ–π aromaticity of borazine derivatives in order to expand the family of double aromatics systems.

Accurate CHIPR Potential Energy Surface for the Lowest Triplet State of C3

We report the first global ab initio-based potential energy surface (PES) for ground-state triplet C₃(³A') based on accurate energies extrapolated to the complete basis set (CBS) limit, and using the combined-hyperbolic-inverse-power-representation method for the analytical modeling. By relying on a cost-effective CBS(D,T) protocol, we ensure that the final form reproduces all topographical features of the PES, including its cyclic-linear isomerization barrier, with CBS(5,6)-quality. To partially account for the incompleteness of the N-electron basis and other minor effects, the available accurate experimental data on the relevant diatomics were used to obtain direct-fit curves that replace the theoretical ones in the many-body expansion. Besides describing properly long-range interactions at all asymptotic channels and permutational symmetry by built-in construction, the PES reported here reproduces the proper exothermicities at dissociation regions as well as the spectroscopy of the diatomic fragments. Bound vibrational state calculations in both linear and cyclic isomers have also been carried out, unveiling a good match of the available data on C₃(ã ³Π_u), while assisting with IR band positions for C₃(³A₂^') that may serve as a guide for its laboratory and astronomical detection.

Generation and structural characterization of Ge carbides GeCn (n = 4, 5, 6) by laser ablation, broadband rotational spectroscopy, and quantum chemistry

Following the recent discovery of T-shaped GeC₂, rotational spectra of three larger Ge carbides, linear GeC₄, GeC₅, and GeC₆ have been observed using chirped pulse and cavity Fourier transform microwave spectroscopy and a laser ablation molecule source, guided by new high-level quantum chemical calculations of their molecular structure. Like their isovalent Si-bearing counterparts, Ge carbides with an even number of carbon atoms beyond GeC₂ are predicted to possess ¹Σ ground electronic states, while odd-numbered carbon chains are generally ³Σ; all are predicted to be highly polar. For the three new molecules detected in this work, rotational lines of four of the five naturally occurring Ge isotopic variants have been observed between 6 and 22 GHz. Combining these measurements with ab initio force fields, the Ge-C bond lengths have been determined to high precision: the derived values of 1.776 Å for GeC₄, 1.818 Å for GeC₅, and 1.782 Å for GeC₆ indicate a double bond between these two atoms. Somewhat surprisingly, the spectrum of GeC₅ very closely resembles that of a ¹Σ molecule, implying a spin-spin coupling constant λ in excess of 770 GHz for this radical, a likely consequence of the large spin-orbit constant of atomic Ge (∼1000 cm^-1). A systematic comparison between the production of SiC_n and GeC_n chains by laser ablation has also been undertaken. The present work suggests that other large metal-bearing molecules may be amenable to detection by similar means.

Quantum Scattering Calculations for Rotational Excitations of by Hydrogen Atom: Potential Energy Surfaces and Rate Coefficients

Ab initio calculations are performed to determine new potential energy surfaces for the ground state and low-lying excited states of C₃ induced by collision with atomic hydrogen. The calculations are performed using the multireference configuration interaction method including Davidson's correction using aug-cc-pVQZ (augmented correlation consistent polarized valence quadruple zeta) basis sets. Nonadiabatic effects leading to avoided crossings are observed between ground and excited states. The computed points of the ground-state surface are fitted to an analytical form suitable for time-independent quantum scattering calculations of the state-to-state collisional cross sections. The close-coupling calculations are performed up to 1000 cm^-1. Resonances are observed at very low energies. Among all the rotational transitions, Δj = 2 is found to be predominant for excitation. After Boltzmann thermal averaging collisional cross sections, rate coefficients for rotational levels j = 0, 2, ..., 8 are obtained and discussed covering the temperature up to 100 K. The magnitude of the state-to-state excitation rate obtained is maximum for j = 0 → 2 transition and decrease for other higher excitations. The results computed in this work will be crucially required to accurately model the abundance of carbon trimer and its hydrocarbon form in space.

Boron-based inorganic heterocyclic clusters: electronic structure, chemical bonding, aromaticity, and analogy to hydrocarbons

This Perspective article deals with recent computational and experimental findings in boron-based heterocyclic clusters, which focuses on binary B-O and B-S clusters, as well as relevant ternary B-X-H (X = O, S, N) species. Boron is electron-deficient and boron clusters do not form monocyclic rings or linear chains. Boron-based heterocyclic clusters are intuitively even more electron-deficient and feature exotic chemical bonding, which make use of O 2p, S 3p, or N 2p lone-pairs for π delocalization over heterocyclic rings, facilitating new cluster structures and new types of bonding. Rhombic, pentagonal, hexagonal, and polycyclic clusters are discussed herein. Rhombic species are stabilized by four-center four-electron (4c-4e) π bonding, that is, the o-bond. An o-bond cluster differs from a typical 4π antiaromatic system, because it has 4π electrons in an unusual bonding/nonbonding combination, which takes advantage of the empty 2p_z atomic orbitals from electron-deficient boron centers. A variety of examples (notably including boronyl boroxine) possess a hexagonal ring, as well as magic 6π electron-counting, making them new members of the inorganic benzene family. Pentagonal clusters bridge rhombic o-bond systems and inorganic benzenes, but they do not necessarily favor 6π electron-counting as in cyclopentadienide anion. In contrast, pentagonal 4π clusters are stable, leading to the concept of pentagonal o-bond. One electron can overturn the potential energy landscape of a system, enabling rhombic-to-hexagonal structural transition, which further reinforces the idea that 4π electron-counting is favorable for rhombic systems and 6π is magic for hexagonal rings. The bonding analogy between heterocyclic clusters and hydrocarbons goes beyond monocyclic species, which allows rational design of boron-based inorganic analogs of polycyclic aromatic hydrocarbons, including s-indacene as a puzzling aromatic/antiaromatic system. Selected linear B-O clusters are also briefly discussed, featuring dual 3c-4e π bonds, that is, ω-hyperbonds. Dual ω-hyperbonds, rhombic or pentagonal o-bond, and inorganic benzenes share a common chemical origin. The field of boron-based heterocyclic clusters is still in its infant stage, and much new chemistry remains to be discovered in forthcoming experimental and theoretical studies.

Modified Particle Swarm Optimization Algorithms for the Generation of Stable Structures of Carbon Clusters, Cn (n = 3-6, 10)

Particle Swarm Optimization (PSO), a population based technique for stochastic search in a multidimensional space, has so far been employed successfully for solving a variety of optimization problems including many multifaceted problems, where other popular methods like steepest descent, gradient descent, conjugate gradient, Newton method, etc. do not give satisfactory results. Herein, we propose a modified PSO algorithm for unbiased global minima search by integrating with density functional theory which turns out to be superior to the other evolutionary methods such as simulated annealing, basin hopping and genetic algorithm. The present PSO code combines evolutionary algorithm with a variational optimization technique through interfacing of PSO with the Gaussian software, where the latter is used for single point energy calculation in each iteration step of PSO. Pure carbon and carbon containing systems have been of great interest for several decades due to their important role in the evolution of life as well as wide applications in various research fields. Our study shows how arbitrary and randomly generated small Cn clusters (n = 3-6, 10) can be transformed into the corresponding global minimum structure. The detailed results signify that the proposed technique is quite promising in finding the best global solution for small population size clusters.

Optical Spectroscopy of Small Carbon Clusters from Electron-Impact Fragmentation and Ionization of Fullerene-C60

A series of cationic molecular fragments (C _n⁺, n = 11, 12, 15, 16, 18, and 21), produced by electron-impact ionization of C₆₀ in the gas phase, were each mass-selected and accumulated in cryogenic Ne matrices. Optical absorption measurements in the UV-vis and IR spectral ranges reveal linear carbon chain structures. In particular, we have observed the known electronic transitions of linear C₁₁, C₁₅, and C₂₁. The NIR transitions of linear C₁₅^-, C₁₆^-, and C₁₈^- have also been detected, indicating that soft-landing of the corresponding cations can also involve charge-changing. Newly observed electronic absorptions at 410.3 and 429.9 nm have been assigned to linear C₁₈ absorptions at 438.2, 443.5, 422.3, and 433.7 nm, to linear C₁₅⁺, and absorption at 395.5 nm, to linear C₁₆. Increasing deposition energy leads to fragmentation upon impact. This is indicated by absorptions of C₁₀ (313, 316.3 nm), when depositing C _n⁺ ( n = 11, 15, 16) as well as C₁₂ (332 nm) or C₁₄ (347.4, 356.6 nm), when depositing C₁₅⁺ or C₁₆⁺, respectively. These were previously assigned to cyclic isomers. We reassign them to linear isomers here on the basis of plausibility arguments. The observations have been supported by time-dependent density functional theory calculations for ring and chain isomers of C _n^+/-/0, 10 ≤ n ≤ 20 up to the vacuum-UV range. The electronic absorptions of carbon chains are at least 1 order of magnitude stronger than all NIR electronic absorptions of C₆₀⁺, which have recently been attributed to several of the diffuse interstellar bands. Considering that fullerene multifragmentation yields long carbon chains that have very strong absorptions both in the UV-vis and IR spectral regions, these systems appear to be good candidates to be observed in regions of space containing fullerenes.