Quantum Theory and Basic Concepts for Electronic Properties in Molecular Structure

Using a one-dimensional tight-binding model, we show the key characteristics of electron propagation in molecular modelling, including band structure, integrated density of state N(E), and density of state (DOS). These characteristics have been computed and the electron propagation on the one-dimensional crystal chain has been studied using the FORTRAN programme. We computed the DOS, the number of eigenvalues smaller than E for both small and high numbers of atoms, and the general band structure. We discovered that the band structure attribute for a single atom in the unit cell was on line. When there are few atoms in the system, the N(E) computation shows a stair-line; when there are many atoms, the line is smooth. These demonstrate how the atoms' intensity within a material has a significant influence in enhancing DOS. The density of state approaches infinity near the band structure's boundaries, and the DOS manifests as a VAN-HOV singularity.