Electron structure, geometry and thermochemistry of the cyclic carbon clusters Cn (n=8, 10, 12)

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.

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.

Magnetically induced current density in triple-layered beryllium–boron clusters

Magnetically induced current densities reveal the double aromatic character of the examined Be–B clusters.

Use of density functional theory method to calculate structures of neutral carbon clusters Cn (3 ≤ n ≤ 24) and study their variability of structural forms

In this work, we present modifications to the well-known basin hopping (BH) optimization algorithm [D. J. Wales and J. P. Doye, J. Phys. Chem. A 101, 5111 (1997)] by incorporating in it the unique and specific nature of interactions among valence electrons and ions in carbon atoms through calculating the cluster's total energy by the density functional tight-binding (DFTB) theory, using it to find the lowest energy structures of carbon clusters and, from these optimized atomic and electronic structures, studying their varied forms of topological transitions, which include a linear chain, a monocyclic to a polycyclic ring, and a fullerene/cage-like geometry. In this modified BH (MBH) algorithm, we define a spatial volume within which the cluster's lowest energy structure is to be searched, and introduce in addition a cut-and-splice genetic operator to increase the searching performance of the energy minimum than the original BH technique. The present MBH/DFTB algorithm is, therefore, characteristically distinguishable from the original BH technique commonly applied to nonmetallic and metallic clusters, technically more thorough and natural in describing the intricate couplings between valence electrons and ions in a carbon cluster, and thus theoretically sound in putting these two charged components on an equal footing. The proposed modified minimization algorithm should be more appropriate, accurate, and precise in the description of a carbon cluster. We evaluate the present algorithm, its energy-minimum searching in particular, by its optimization robustness. Specifically, we first check the MBH/DFTB technique for two representative carbon clusters of larger size, i.e., C60 and C72 against the popular cut-and-splice approach [D. M. Deaven and K. M. Ho, Phys. Rev. Lett. 75, 288 (1995)] that normally is combined with the genetic algorithm method for finding the cluster's energy minimum, before employing it to investigate carbon clusters in the size range C3-C24 studying their topological transitions. An effort was also made to compare our MBH/DFTB and its re-optimized results carried out by full density functional theory (DFT) calculations with some early DFT-based studies.

Cubic C8 : An Observable Allotrope of Carbon?

Ab initio and DFT calculations are used to investigate the structure, electronic properties, spectra and reactivity of cubic C8 , which is predicted to be aromatic according to Hirsch's rule. Although highly strained and with a small amount of diradical character, the carbon cube represents a surprisingly deep minimum and should therefore be observable as an isolated molecule. It is, however, predicted to be very reactive, both with itself and triplet oxygen. Calculated IR, Raman, and UV/Vis spectra are provided to aid identification of cubic C8 should it be synthesized.

A threshold-based approach to calorimetry in helium droplets: measurement of binding energies of water clusters

Helium droplet beam methods have emerged as a versatile technique that can be used to assemble a wide variety of atomic and molecular clusters. We have developed a method to measure the binding energies of clusters assembled in helium droplets by determining the minimum droplet sizes required to assemble and detect selected clusters in the spectrum of the doped droplet beam. The differences in the droplet sizes required between the various multimers are then used to estimate the incremental binding energies. We have applied this method to measure the binding energies of cyclic water clusters from the dimer to the tetramer. We obtain measured values of D(0) that are in agreement with theoretical estimates to within ∼20%. Our results suggest that this threshold-based approach should be generally applicable using either mass spectrometry or optical spectroscopy techniques for detection, provided that the clusters selected for study are at least as strongly bound as those of water, and that a peak in the overall spectrum of the beam corresponding only to the cluster chosen (at least in the vicinity of the threshold) can be located.

Self-consistent field tight-binding model for neutral and (multi-) charged carbon clusters

A semiempirical model for carbon clusters modeling is presented, along with structural and dynamical applications. The model is a tight-binding scheme with additional one- and two-center distance-dependent electrostatic interactions treated self-consistently. This approach, which explicitly accounts for charge relaxation, allows us to treat neutral and (multi-) charged clusters not only at equilibrium but also in dissociative regions. The equilibrium properties, geometries, harmonic spectra, and relative stabilities of the stable isomers of neutral and singly charged clusters in the range n=1-14, for C(20) and C(60), are found to reproduce the results of ab initio calculations. The model is also shown to be successful in describing the stability and fragmentation energies of dictations in the range n=2-10 and allows the determination of their Coulomb barriers, as examplified for the smallest sizes (C(2) (2+),C(3) (2+),C(4) (2+)). We also present time-dependent mean-field and linear response optical spectra for the C(8) and C(60) clusters and discuss their relevance with respect to existing calculations.

Ionization Thresholds of Small Carbon Clusters: Tunable VUV Experiments and Theory

Small carbon clusters (Cn, n = 2-15) are produced in a molecular beam by pulsed laser vaporization and studied with vacuum ultraviolet (VUV) photoionization mass spectrometry. The required VUV radiation in the 8-12 eV range is provided by the Advanced Light Source (ALS) at the Lawrence Berkeley National Laboratory. Mass spectra at various ionization energies reveal the qualitative relative abundances of the neutral carbon clusters produced. By far the most abundant species is C3. Using the tunability of the ALS, ionization threshold spectra are recorded for the clusters up to 15 atoms in size. The ionization thresholds are compared to those measured previously with charge-transfer bracketing methods. To interpret the ionization thresholds for different cluster sizes, new ab initio calculations are carried out on the clusters for n = 4-10. Geometric structures are optimized at the CCSD(T) level with cc-pVTZ (or cc-pVDZ) basis sets, and focal point extrapolations are applied to both neutral and cation species to determine adiabatic and vertical ionization potentials. The comparison of computed and measured ionization potentials makes it possible to investigate the isomeric structures of the neutral clusters produced in this experiment. The measurements are inconclusive for the n = 4-6 species because of unquenched excited electronic states. However, the data provide evidence for the prominence of linear structures for the n = 7, 9, 11, 13 species and the presence of cyclic C10.

Double Aromaticity in Monocyclic Carbon, Boron, and Borocarbon Rings Based on Magnetic Criteria

The double-aromatic character of selected monocyclic carbon, boron, and borocarbon rings is demonstrated by refined nucleus-independent chemical shift (NICS) analyses involving the contributions of individual canonical MOs and their out-of-plane NICS tensor component (CMO-NICS(zz)). The double aromaticity considered results from two mutually orthogonal Hückel p AO frameworks in a single molecule. The familiar pi orbitals are augmented by the in-plane delocalization of electrons occupying sets of radial (rad) p orbitals. Such double aromaticity is present in B(3) (-), C(6)H(3) (+), C(6) (4+), C(4)B(4) (4+), C(6), C(5)B(2), C(4)B(4), C(2)B(8), B(10) (2-), B(12), C(10), C(9)B(2), C(8)B(4), C(7)B(6), C(6)B(8), and C(14). Monocyclic C(8) and C(12) are doubly antiaromatic, as both the orthogonal pi and radial Hückel sets are paratropic. Planar C(7) and C(9) monocycles have mixed aromatic (pi) and antiaromatic (radial) systems.