- At first, the software-project-git repository contains an explanation and example of the program as useful to realize the run processing. Then, it becomes easy to test and calculate for other materials inside the bonds repository. So, for a complete project, first run the project_1 and 2; Then, add the armchair, Zigzag and nanotube; At the ends, by running each mater, the electron bonds will be shown. Besides, the graph shows the schematic of carbon positions. Below is the main object of this project notes.
Molecular Orbital Theory
In this project, we investigate carbon molecule in different structure ( Benzene, BuckyBall, Butadiene, Naphthalene, Toluene) Huckel(H) theory for pi-molecular orbitals.
Introduction: The numerical matrixes for different materials calculate the band level energies and plot the structure of the carbon hexagonal molecule.
Project_1
For a given matrix H, with Alpha diagonals and Beta off-diagonals, we will determine the Eigenvalues and Eigenvectors. for the Huckel Effective Hamiltonian and use them to create an energy level diagram for the electronic configuration of the molecule. In this case, we want to create a class that represents a molecule with a Huckel Matrix and associated methods. Then, plot energy level and direction of atoms in the structures. During the code, after defining Eigenvalue and Eigenvector, the string representation for the molecule is described (Charge Density, deloc Energy & Bond Order). Then, definition numerical matrix elements are required by codes for linear carbon chain. So, denoting spin for electrons from the energy levels clarifies the plot of each bond. Besides, we find the bond order of the molecule.
Project_2
Now, our class is ready, afterward, in Project two, we extend our molecule class to be able to calculate the various properties of Graphene. The hexagonal structure of carbon is used for generating the chain. Now, the structure of each project is ready for calculating different carbon band structure in many bulks. But, before that, we need to consider Armchair as a Graphene molecule matrix calls from Project2. Zigzag matrix as a numerical calculation of neighbor connection in Graphen molecule for charge density and develop energy and plot them (creates a row of linking carbons to wrap zigzag). Nanotube works as a carbon tube for molecule to prepare the graphs.
Graph_Arm: Plot the “ Molecule Structure for Armchair” with different energy levels.
Graph_Zig: Plot the “ Molecule Structure for ZigZag” with different energy levels.
At the end, by calling each material, the plots of band levels and direct of electrons show the energy graph.