Search Results (30)

Carbon is one of nature’s basic elements, hosting a tremendous number of allotropes benefiting from its capacity to generate $sp$, $s{p}^2$, and $s{p}^3$ hybridized carbon–carbon bonds. The exploration of novel carbon architectures has remained a pivotal focus in the fields of condensed matter physics and materials science for an extended period. In this paper, we, by using first-principles calculation, carry on a detailed investigation an an all-$s{p}^3$ hybridized carbon structure in a 20-atom tetragonal unit cell with $P{4}_3{2}_{1}2$ symmetry ($D_4^8$, space group No. 96), and call it T20 carbon. The equilibrium energy of T20 carbon is −8.881 eV/atom, only 0.137 eV/atom higher than that of diamond, indicating that T20 is a superstable carbon structure. T20 is also a superhard carbon structure with a large Vicker’s hardness about 83.5 GPa. The dynamical stability of T20 was verified by means of phonon band spectrum calculations. Meanwhile, its thermal stability up to 1000 K was verified via ab initio molecular dynamics simulations. T20 is an indirect band-gap insulator with approximately 5.80 eV of a band gap. This value is obviously greater than the value in the diamond (5.36 eV). Moreover, the simulated X-ray diffraction pattern of T20 displays a remarkable match with the experimental data found in the milled fullerene soot, evidencing that T20 may be a potential modification discovered in this experimental work. Our work has given a systematical understanding on an all-$s{p}^3$ hybridized superstable and superhard carbon allotrope with large band gap and provided a very competitive explanation for previous experimental data, which will also provide guidance for upcoming studies in theory and experiment. Full article

An advanced model of ionic surfactant micellization has been developed. The structural and kinetic properties of micelles were analyzed in parallel from a universally accepted point of view and taking into account the principles of quantum mechanics, the phenomenon of ion pairing in the Stern layer, the symmetry considerations, and the chaos theory. It was shown that a micelle can be considered as a layered fullerene-like structure with a cavity in its center, possessing the solid-like properties of micelles in radial directions and the liquid-like properties in the perpendicular ones, allowing for water penetration between the surfactant head group and nearby methylene groups. The dimensions of the minimal fullerene-like structure formed by the terminal hydrogen atoms of surfactant methyl groups around the central cavity, unable to be occupied by surfactant tail fragments, were estimated. It was indicated that permanently occurring surfactant self-organization/disintegration needs a probabilistic description and revision of processes occurring in micellar systems built by ionic surfactants. It was noted that the probabilistic approach alters the mechanism of colloidal dissolution of hydrocarbon compounds and their solubilization by micelles. The advanced model proposes the same macroscopic properties of micelles as the classical one but modifies the structural characteristics of micelles on the nanoscale. Full article

We report the results of our computations of the spectral polynomials and spectra of a number of graphs possessing automorphism symmetries beyond cubic and icosahedral symmetries. The spectral (characteristic) polynomials are computed in fully expanded forms. The coefficients of these polynomials contain a wealth of combinatorial information that finds a number of applications in many areas including nanomaterials, genetic networks, dynamic stereochemistry, chirality, and so forth. This study focuses on a number of symmetric and semi-symmetric graphs with automorphism groups of high order. In particular, Heawood, Coxeter, Pappus, Möbius–Kantor, Tutte–Coxeter, Desargues, Meringer, Dyck, n-octahedra, n-cubes, icosahedral fullerenes such as C₈₀(I_h), golden supergiant C₂₄₀(I_h), Archimedean (I_h), and generalized Petersen graphs up to 720 vertices, among others, have been studied. The spectral polynomials are computed in fully expanded forms as opposed to factored forms. Several applications of these polynomials are briefly discussed. Full article

The study delves into the relationship between symmetry groups and automorphism groups in polyhedral graphs, emphasizing their interconnected nature and their significance in understanding the symmetries and structural properties of fullerenes. It highlights the visual importance of symmetry and its applications in architecture, as well as the mathematical structure of the automorphism group, which captures all of the symmetries of a graph. The paper also discusses the significance of groups in Abstract Algebra and their relevance to understanding the behavior of mathematical systems. Overall, the findings offer an inclusive understanding of the relationship between symmetry groups and automorphism groups, paving the way for further research in this area. Full article

We have developed novel polynomials called delta polynomials, which are, in turn, derived from the characteristic and matching polynomials of graphs associated with polycyclic aromatic compounds. Natural logarithmic aromatic indices are derived from these delta polynomials, which are shown to provide new insights into the aromaticity of polycyclic aromatic compounds, including the highly symmetric C₆₀ buckminsterfullerene, several other fullerenes, graphene, kekulene series and other cycloarenes, such as polycyclic circumcoronaphenes and coronoids. The newly developed aromatic index yields a value of 6.77 for graphene, 6.516865 for buckminsterfullerene C₆₀(I_h), 5.914023 for kekulene (D_6h symmetry), 6.064420 for coronene (D_6h), 6.137828 for circumcoronene (D_6h), 6.069668 for dicronylene and so forth. Hence, the novel scaled logarithmic aromatic delta indices developed here appear to provide good quantitative measures of aromaticity, especially when they are used in conjunction with other aromatic indicators. Full article

We performed quantum chemical calculations on the geometries, electronic structures, bonding properties, and stability strategy of endohedral metallofullerenes TM@C₂₈ (TM = Sc⁻, Y⁻, La⁻, Ti, Zr, Hf, V⁺, Nb⁺, Ta⁺). Our calculations revealed that there are three different lowest-energy structures with C_2v, C_3v, and T_d symmetries for TM@C₂₈. The HOMO–LUMO gap of all these structures ranges from 1.35 eV to 2.31 eV, in which [V@C₂₈]⁺ has the lowest HOMO–LUMO gap of 1.35 eV. The molecular orbitals are mainly composed of fullerene cage orbitals and slightly encapsulated metal orbitals. The bonding analysis on the metal–cage interactions reveals they are dominated by the Coulomb term ΔE_elstat and the orbital interaction term ΔE_orb, in which the orbital interaction term ΔE_orb contributes more than the Coulomb term ΔE_elstat. The addition of one or two CF₃ groups to [V@C₂₈]⁺ could increase the HOMO–LUMO gap and further increase the stability of [V@C₂₈]⁺. Full article

The topological partition theory states that icosahedral group affine extensions (fullerenes symmetry) are the most effective way to energetically optimize the surface covering. In recent decades, potential applications of fullerene symmetry have emerged in the major fields of biology, like enzyme inhibition and antiviral therapy. This research suggests a novel perspective to interpret the underlying spatial organization of cell populations in tissues from the polyhedral graph theory. We adopted this theoretical framework to study HUVEC cell in vitro angiogenesis assays on Matrigel. This work underscores the importance of extracellular ${\mathrm{C}\mathrm{a}}^{2+}$ gradients, both from conditioned BJ and pretreated HUVEC cells, in angiogenesis fullerene-rule spatial minimization. Full article

Background: The system of self-consistent models is an attempt to develop a tool to assess the predictive potential of various approaches by considering a group of random distributions of available data into training and validation sets. Considering many different splits is more informative than considering a single model. Methods: Models studied here build up for solubility of fullerenes C60 and C70 in different organic solvents using so-called quasi-SMILES, which contain traditional simplified molecular input-line entry systems (SMILES) incorporated with codes that reflect the presence of C60 and C70. In addition, the fragments of local symmetry (FLS) in quasi-SMILES are applied to improve the solubility’s predictive potential (expressed via mole fraction at 298’K) models. Results: Several versions of the Monte Carlo procedure are studied. The use of the fragments of local symmetry along with a special vector of the ideality of correlation improves the predictive potential of the models. The average value of the determination coefficient on the validation sets is equal to 0.9255 ± 0.0163. Conclusions: The comparison of different manners of the Monte Carlo optimization of the correlation weights has shown that the best predictive potential was observed for models where both fragments of local symmetry and the vector of the ideality of correlation were applied. Full article

We have developed a highly efficient computation method based on density functional theory (DFT) within a set of fully symmetrized basis functions for the C₆₀ buckyball, which possesses the icosahedral ($I_h$) point-group symmetry with 120 symmetry operations. We demonstrate that our approach is much more efficient than the conventional approach based on three-dimensional plane waves. When applied to the calculation of optical transitions, our method is more than one order of magnitude faster than the existing DFT package with a conventional plane-wave basis. This makes it very convenient for modeling optical and transport properties of quantum devices related to buckyball crystals. The method introduced here can be easily extended to other fullerene-like materials. Full article

Information entropy indices are widely used for numerical descriptions of chemical structures, though their applications to the processes are scarce. We have applied our original information entropy approach to filling fullerenes with a guest atom. The approach takes into account both the topology and geometry of the fullerene structures. We have studied all possible types of such fillings and found that information entropy (Δh_R) and symmetry changes correlate. Δh_R is negative, positive or zero if symmetry is increased, reduced or does not change, respectively. The Δh_R value and structural reorganization entropy, a contribution to Δh_R, are efficient parameters for the digital classification of the fullerenes involved into the filling process. Based on the calculated values, we have shown that, as the symmetry of the fullerene cage becomes higher, the structural changes due to the filling it with a guest atom become larger. The corresponding analytical expressions and numerical data are discussed. Full article

The high-regioselective synthesis of bisadducts based on low-symmetry C₇₀ has been a challenging work due to the large amount of formed regioisomers, which require tedious separation procedures for isomeric purity and block their application in different fields. Herein, we successfully obtained a novel 1, 2, 3, 4-bis(triazolino)fullerene[C₇₀] 2 with high regioselectivity by the rigid tether-directed regioselective synthesis strategy and the corresponding molecular structure was unambiguously confirmed by single-crystal X-ray crystallography characterization. The crystal data clearly show that the addition occurs at the domain of corannulene moiety at the end of ellipse C₇₀ as well as the 1, 2, 3, 4-addition sites located at one hexagonal ring with a [6,6]-closed addition pattern. Furthermore, 2 was applied as an additive of perovskite layer to construct MAPbI3-based regular (n-i-p) perovskite solar cells, affording the power conversion efficiency (PCE) of 18.59%, which is a 7% enhancement relative to that of control devices without additive. Full article

This review article highlights recent developments in symmetry, combinatorics, topology, entropy, chirality, spectroscopy and thermochemistry pertinent to 2D and 1D nanomaterials such as circumscribed-cyclopolyarenes and their heterocyclic analogs, carbon and heteronanotubes and heteronano wires, as well as tessellations of cyclopolyarenes, for example, kekulenes, septulenes and octulenes. We establish that the generalization of Sheehan’s modification of Pólya’s theorem to all irreducible representations of point groups yields robust generating functions for the enumeration of chiral, achiral, position isomers, NMR, multiple quantum NMR and ESR hyperfine patterns. We also show distance, degree and graph entropy based topological measures combined with techniques for distance degree vector sequences, edge and vertex partitions of nanomaterials yield robust and powerful techniques for thermochemistry, bond energies and spectroscopic computations of these species. We have demonstrated the existence of isentropic tessellations of kekulenes which were further studied using combinatorial, topological and spectral techniques. The combinatorial generating functions obtained not only enumerate the chiral and achiral isomers but also aid in the machine construction of various spectroscopic and ESR hyperfine patterns of the nanomaterials that were considered in this review. Combinatorial and topological tools can become an integral part of robust machine learning techniques for rapid computation of the combinatorial library of isomers and their properties of nanomaterials. Future applications to metal organic frameworks and fullerene polymers are pointed out. Full article

Hydrogenated small fullerenes (C_n, n < 60) are of interest as potential astrochemical species, and as intermediates in hydrogen-catalysed fullerene growth. However, the computational identification of key stable species is difficult due to the vast configurationally space of structures. In this study, we explored routes to predict stable hydrogenated small fullerenes. We showed that neither local fullerene geometry nor local electronic structure analysis was able to correctly predict subsequent low-energy hydrogenation sites, and sequential stable addition searches also sometimes failed to identify most stable hydrogenated fullerene isomers. Of the empirical and semi-empirical methods tested, GFN2-xTB consistently gave highly accurate energy correlations (r > 0.99) to full DFT-LDA calculations at a fraction of the computational cost. This allowed identification of the most stable hydrogenated fullerenes up to 4H for four fullerenes, namely two isomers of C₂₈ and C₄₀, via “brute force” systematic testing of all symmetry-inequivalent combinations. The approach shows promise for wider systematic studies of smaller hydrogenated fullerenes. Full article

Fullerene dimers and oligomers are attractive molecular objects with an intermediate position between the molecules and nanostructures. Due to the size, computationally assessing their structures and molecular properties is challenging, as it currently requires high-cost quantum chemical techniques. In this work, we have jointly studied energies, topological (Wiener indices and roundness), and information theoretic (information entropy) descriptors, and have obtained regularities in triad ‘energy–topology–symmetry’. We have found that the topological indices are convenient to indicating the most and least reactive atoms of the fullerene dimer structures, whereas information entropy is more suitable to evaluate odd–even effects on the symmetry of (C₆₀)_n. Quantum chemically assessed stabilities of selected C₁₂₀ structures, as well as linear and zigzag (C₆₀)_n, are discussed. Full article