Topological resonance energy method, derived as a variant of Dewar resonance energy concept, and expressed by adjacency algebra formalism, has been for years applied for successful prediction of aromatic properties of conjugated organic and inorganic species. In this work a numerical value of TRE has been discussed in light of its physical meaning. Normalization method of this value has been pr...

topological indices are the numerical value associated with chemical constitution purporting for correlation ofchemical structure with various physical properties, chemical reactivity or biological activity. graph theory is adelightful playground for the exploration of proof techniques in discrete mathematics and its results haveapplications in many areas of sciences. one of the useful indices ...

Topological indices are the numerical value associated with chemical constitution purporting for correlation ofchemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is adelightful playground for the exploration of proof techniques in Discrete Mathematics and its results haveapplications in many areas of sciences. One of the useful indices ...

Pairwise orthogonal topological indices A and Woo derived from the characteristic graphs of alternant polycyclic aromatic hydrocarbons (kata-annellated and peri-condensed systems) correlate with resonance energy per electron, energy of the HOMO and total ;i: electron energy respectively. For topological indices a high discrimination power is necessary but not sufficient to correlate with molecu...

The topological resonance energies (TRE) for various fullerene clusters ( C2a to C,) have been computed and based on this, stabilities of fttllerenes are discussed. Trend in stability predicted by the TRE model is compared with predictions from the conjugated circuit model as well as the MNDO and ab initio methods. Reasonable agreement is found between the TRE model and rigorous quantum mechani...

Two empirical rules are formulated for the topological resonance energy (TRE) of benzenoid hydrocarbons: (a) TRE is roughly linear function of the number of Kekule structures, and (b) in a homologous series containing a linear polyacene fragment, TRE is a linear function of the length of this fragment. In certain cases, however, the TRE model leads to incorrect predictions. There exist pairs of...

In the flurry of experiments looking for topological insulator materials, it has been recently discovered that some bulk metals very close to topological insulator electronic states support the same topological surface states that are the defining characteristic of the topological insulator. First observed in spin-polarized angle resolved photoemission spectroscopy ARPES in Sb D. Hsieh et al., ...

We explore transport properties of a normal metal-superconductor-normal metal (NSN) junction, where the superconducting region supports mixed singlet and chiral triplet pairings. We show that in the subgapped regime when the chiral triplet pairing amplitude dominates over that of the singlet, a resonance phenomena emerges out where all the quantum mechanical scattering probabilities acquire a v...

Spin-orbit coupled superconductors are interesting candidates for realizing topological and potentially nonAbelian states with Majorana fermions. We argue that time-reversal broken spin-orbit coupled superconductors generically can be characterized as having subgap states that are bound to localized nonmagnetic impurities. Such bound states, which are referred to as the Shiba states, can be det...