Extremal tricyclic, tetracyclic, and pentacyclic graphs with respect to the Narumi–Katayama index

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Covalently Bonded Fullerene Nano-Aggregates (C60)n: Digitalizing Their Energy–Topology–Symmetry

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

Topological Anisotropy of Stone-Wales Waves in Graphenic Fragments

Stone-Wales operators interchange four adjacent hexagons with two pentagon-heptagon 5|7 pairs that, graphically, may be iteratively propagated in the graphene layer, originating a new interesting structural defect called here Stone-Wales wave. By minimization, the Wiener index topological invariant evidences a marked anisotropy of the Stone-Wales defects that, topologically, are in fact preferably generated and propagated along the diagonal of the graphenic fragments, including carbon nanotubes and graphene nanoribbons. This peculiar edge-effect is shown in this paper having a predominant topological origin, leaving to future experimental investigations the task of verifying the occurrence in nature of wave-like defects similar to the ones proposed here. Graph-theoretical tools used in this paper for the generation and the propagation of the Stone-Wales defects waves are applicable to investigate isomeric modifications of chemical structures with various dimensionality like fullerenes, nanotubes, graphenic layers, schwarzites, zeolites

Bondonic Effects in Group-IV Honeycomb Nanoribbons with Stone-Wales Topological Defects

This work advances the modeling of bondonic effects on graphenic and honeycomb structures, with an original two-fold generalization: (i) by employing the fourth order path integral bondonic formalism in considering the high order derivatives of the Wiener topological potential of those 1D systems; and (ii) by modeling a class of honeycomb defective structures starting from graphene, the carbon-based reference case, and then generalizing the treatment to Si (silicene), Ge (germanene), Sn (stannene) by using the fermionic two-degenerate statistical states function in terms of electronegativity. The honeycomb nanostructures present η-sized Stone-Wales topological defects, the isomeric dislocation dipoles originally called by authors Stone-Wales wave or SWw. For these defective nanoribbons the bondonic formalism foresees a specific phase-transition whose critical behavior shows typical bondonic fast critical time and bonding energies. The quantum transition of the ideal-to-defect structural transformations is fully described by computing the caloric capacities for nanostructures triggered by η-sized topological isomerisations. Present model may be easily applied to hetero-combinations of Group-IV elements like C-Si, C-Ge, C-Sn, Si-Ge, Si-Sn, Ge-Sn

Kinetic Monte Carlo approach to Schottky defects in noble metal nanoclusters

© 2016, Springer International Publishing Switzerland. Abstract: The vacancy concentration dependence on temperature and diameter of noble metal (gold, silver, and copper) nanoclusters is investigated using a Kinetic Monte Carlo method. Icosahedral and decahedral nanoclusters are studied, with diameters up to 3.73 nm for icosahedral clusters and up to 6.65 nm for decahedral clusters. The cohesive energy is calculated using a coordination number approach, resulting in a linear relation with cluster size. Random Schottky defects are frozen into the clusters at low temperatures (100–600 K) and we find that the vacancy concentration increases with smaller diameters and higher temperatures. We develop a model for this behavior, which explains the temperature and size dependence. This model predicts silver icosahedra to have the highest concentration of vacancies in the clusters studied. Vacancy concentrations are related to the ratio of surface/interior sites based on nearest neighbor calculations. The modified enthalpy and entropy of constant diameter clusters are derived from a logarithmic model for the Gibbs energy. Melting entropy and enthalpy are calculated in this coordination type model and compare well with previously published molecular dynamics results. Graphical Abstract: [Figure not available: see fulltext.]status: publishe

Topological Modelling of Nanostructures and Extended Systems

XV, 575 p. 308 illus., 175 illus. in color.onlin

Structural Descriptors of Benzenoid Hydrocarbons: A Mismatch between the Estimates and Parity Effects in Helicenes

Benzenoid hydrocarbons have regular structures, attracting the opportunity to test the structural descriptors of their series. In the present study, we compared information entropy, Wiener indices, topological efficiencies, topological roundness, and symmetries of oligoacenes, phenacenes, and helicenes. We found and discussed the mismatches between the descriptors and the symmetry of benzenoids. Among the studied series, helicenes demonstrate the parity effect when the information entropy and topological roundness form saw-like functions depending on the number of the member, odd or even. According to our quantum chemical calculations, this parity effect has no consequences for such molecular properties as molecular polarizability and frontier molecular orbital energies. Further, we demonstrated that the changes in the structural descriptors upon the chemical reactions of benzenoids could be used for the numerical description of chemical processes. Interestingly, the view of the information entropy reaction profile is similar to the energy profiles of chemical reactions. Herewith, the intermediate chemical compounds have higher information entropy values compared with the initial and final compounds, which reminisce the activation barrier