Number Of Hexagonal Rings Research Articles

Harmonic oscillator model of aromaticity (HOMA) in conjugated radicals and cations

We propose the extension of Harmonic Oscillator Model of Aromaticity (HOMA), reparametrizing it for radicals and cations. The application is based on a series of experimental structures based on phenalenyl core, found in both radical and cationic forms. Phenalenyl is the first member of the topological spin molecules named triangulenes, looking like triangular graphene flakes, the series being indexed by the number of hexagonal rings at the edge. We discussed the series of triangulenes with n = 2,3 and 4 sizes. In this view, a HOMA parameterization based on computed structures is devised. We found that phenalenyl systems (the n = 2 triangulene) are relatively high aromatic in both radical and cationic forms, with the experimental structures having HOMA indices comprised between 0.89 and 0.99. Along the n-triangulene series, the global aromaticity of radicals decreases, having HOMA = 0.965, 0.932 and 0.925, for computed structures of n = 2, 3 and 4 congeners, respectively, tending to a plateau estimated at HOMA = 0.914 for hypothetical larger systems. The HOMA indices are approximately correlated with the aromatic stabilization estimated in a spin-coupling phenomenology.

The evolution of the principle of circumscribing

Circumscribing benzenoid polycyclic aromatic hydrocarbons was first introduced in 1982 under the topic of a periodic table for benzenoid hydrocarbons and isomer enumeration. This circumscribing process was rendered on benzene to successively generate coronene, circumcoronene, dicircumcornene, and so on as the first constant-isomer series. Subsequently, numerous benzenoid constant-isomer series were uncovered because of the coupling of the benzenoid periodic table (Table PAH6) and circumscribing. Circumscribing even carbon monocyclic polyenes produced [n]cyclacenes (n = number of hexagonal rings) which are monotier nanotubes. Starting with [n]cyclacenes and successive circumscribing generates (n,0) Zigzag nanotubes of increasing length. Successive circumscribing cycloparaphenylenes leads to (n,n) Armchair nanotubes of increasing length. Successive supercircumscribing cycloparaphenylenes leads to total-resonant-sextet Armchair nanotubes of maximum stability. Circumscribing polycyclic conjugated systems was subsequently introduced for other ring sizes. Circumscribing polycyclic hydrocarbons with a combination of pentagonal and hexagonal rings leads to fullerenes when 12 pentagonal ring is reached. Generation of altans is a specialised type of circumscribing in which the encircling annulene is attached via its alternate degree-2 vertices to the degree-2 vertices of the core structure. We show that monocapped nanotubes are circumscribed altans.

Magnetism in curved VSe2 monolayers.

Our extensive first-principles calculations on magnetic VSe2 monolayers reveal the curvature-induced periodic fluctuation in the magnetic moments of V atoms and the occurrence of charge density waves for curved VSe2 monolayers. The bending energies of curved 2H-VSe2 monolayers increase with increasing curvature but that of curved 1T-VSe2 monolayers with curvature is not monotonic. The significant periodic magnetic orders in curved VSe2 monolayers can be attributed to the curvature-induced modification of V-Se bond structure and periodic length variations in V-Se bonds. A phenomenological model is established to describe the relation of the total magnetic moment in one period of a curved VSe2 monolayer with its curvature radius and the number of hexagonal rings that forms one period. These results unveil the effect of bending deformation on magnetic van der Waals monolayers and provide a possible way to develop functional magnetic devices by mechanical design.

{X,Y}-Cyclacene Graphs with Next Nearest Neighbor Interactions

ABSTRACTEigensolutions of {X( = C,B,N),Y( = C,B,N)}-cyclacene graphs with next nearest neighbor (nnn) interactions have been obtained in analytical forms by adapting n-fold rotational symmetry followed by two-fold rotational symmetry (or a plane of symmetry). Expressions of eigensolution indicate the subspectral relationship among such cyclacenes with an even number of hexagonal rings e.g., eigenvalues of {X,Y}-di-cyclacene are found in the eigenspectra of all such even cyclacenes. Total π-electron energies and highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) gaps are calculated using the analytical expressions obtained and are found to vary negligibly with the variation of nnn interactions in such cyclacenes. Total π-electron energy is found to increase due to increase in restriction intensity of nnn interactions, whereas the HOMO–LUMO gap of polyacenecs having the even number of hexagonal rings and with one electron at each site (atom) decreases with increase in the restriction intensity since such systems contain degenerate half-filled HOMO (bonding or nonbonding) that are much more vulnerable for perturbations imposed through nnn interactions.

Bond-order potential for transition metal carbide cluster for the growth simulation of a single-walled carbon nanotube

A classical many-body potential for transition metal carbide cluster is developed in the form of the bond-order type potential function. The parameter sets between carbon atoms and several transition metal atoms (Fe, Co and Ni) are constructed by fitting binding energies from Density Functional Theory (DFT) calculations. Using the potential function, clustering process of carbon atoms to a small metal cluster is studied by classical molecular dynamics (MD) simulation. The number of hexagonal rings in the Co cluster increases about twice as fast as in the Fe cluster. This implies that the graphitic lattice interacts more strongly with Co atoms than with Fe atoms. A Co cluster has a crystal structure where metal atoms are regularly allocated and embedded in the hexagonal carbon network in the simulation. In contrast, carbon atoms cover the entire surface in case of the Fe cluster. Additionally, the potential energy surface that a carbon atom feels from a 2D closed-packed facet is examined using a hypothetical FCC(111) facet of several transition metals. The potential energy minima are distributed on the hexagonal network showing the 2D closed-packed facet can be a template where a graphene is formed.

Structural and electronic properties of single-wall GaN nanotubes: semi-empirical SCF-MO calculations

The structural and electronic properties of armchair and zigzag models of single-wall GaN nanotubes have been investigated by performing semi-empirical molecular orbital self-consistent field calculations at the level of PM3 method within the RHF formulation. It has been found that these structures are stable and endothermic. The armchair model has zero net dipole moment, whereas the zigzag model has nonzero net dipole moment. It has been found that GaN armchair tube with even number of hexagonal rings on the circumference has more excess charge on it and thus this tube may have better conducting properties, they may be candidates to be used as good conducting nanowires.

Predicting bond lengths in planar benzenoid polycyclic aromatic hydrocarbons: a chemometric approach.

Two hundred and twenty-three aromatic carbon-carbon bond lengths in high precision crystal structures containing 22 planar condensed benzenoid polycyclic aromatic hydrocarbons (PB-PAHs) were related to the Pauling pi-bond order, its analogue corrected to crystal packing effects, the number of hexagonal rings around the bond, and the numbers of carbons atoms around the bond at topological distance one and two. Principal Component Analysis (PCA) showed that the bond lengths in PB-PAHs are at least two-dimensional phenomenon, with well pronounced classification into 12 types of bonds, as confirmed with Hierachical Cluster Analysis (HCA). Consequently, Multiple Linear Regression (MLR) and Partial Least Squares (PLS) models were superior to univariate models, reducing the degeneration of the data set and improving the estimation of Julg's structural aromaticity index. The approximate regression models based on topological descriptors only were built for fast and easy prediction of bond lengths and bond orders in PB-PAHs.