We study the band gap in some semi-conducting polymers with two models: Hückel molecular orbital theory and the socalled free electron model. The two models are directly related to spectral theory on combinatorial and metric graphs. Our numerical results reproduce qualitatively experimental results and results from much more complex density-functional calculations. We show that several trends c...

In this second paper, we develop transferable semiempirical extended Hückel theoretical EHT parameters for the electronic structure of another technologically important material, namely, silicon. The EHT parameters are optimized to experimental target values of the band dispersion of bulk silicon. We quantitatively benchmark our parameters to bulk electronic properties such as band edge energie...

The interpretation of topological resonance energy (TRE), the mathematical measure of energetic chemical aromaticity at the Hückel level of theory, is revisited by providing a concise analysis of the matching polynomial of a chemical graph. Whereas the matching (or acyclic) polynomial is not a properly characteristic polynomial in general, it is the arithmetic mean of the characteristic polynom...

Graphs are used to model chemical compounds and drugs. In the graphs, each vertex represents an atom of molecule and edges between the corresponding vertices are used to represent covalent bounds between atoms. The Wiener polarity index W p (G) of a graph G is the number of unordered pairs of vertices u, v of G such that the distance between u and v is equal to 3. The trees and unicyclic graphs...

In this extension of the main IET tutorial, we will deal with the mis-alignment issue that is inherent in Extended Hückel (EH) theory. In such method, the energies of states in different materials are parametrized differently. As a result, the position of the Fermi levels (EF ) of different materials are not referenced to the same vacuum energy. [1] This causes an issue in that a supercell cont...

A system of three electrolytes separated by two parallel planes is considered. Each region is described by a dielectric constant and a Coulomb fluid in the Debye-Hückel regime. In their book Dispersion Forces, Mahanty and Ninham have given the van der Waals free energy of this system. We rederive this free energy by a different method, using linear response theory and the electrostatic Maxwell ...