Chapter 5 - Electronic structure of solids and molecules

Abstract

In this chapter, we try to investigate the mechanism of the electronic structure of condensed matter and molecules, briefly. Many of their properties, which are related to the material's structure and atomic position in the chemical compositions, can be concluded directly by the many-body Hamiltonian, fundamental quantum mechanical equation, for the electrons. One of the important techniques for examining the properties of a many-body system (such as solids and molecules) is called the density functional theory (DFT). In this theory, instead of the ground state function, we consider the single-particle electron density of the ground state. The DFT shows that the energy of the ground state in a many-particle system is expressed in terms of a function of the single-electron density. Minimizing this function allows us to calculate the density of the actual ground state and the properties related to the ground state. The success of DFT is to provide simple and precisely reasonable approximations of the function to be minimized. Characteristic of the density functional method compared with the many-body theory, it is possible to achieve a single-particle Schrödinger equation with an effective potential for studying the electron density of the ground state of the particle. Additionally, the calculation based on time-dependent density functional theory (TD-DFT) can be used to study the effect of short laser pulses on a solid or molecular system and calculate the resulting photoelectron spectrum. For example, we try to calculate the electronic and optical properties (such as the charge density, electrostatic potential, density of states (DOS), the effect of ultraviolet–visible spectrum, HOMO and the LUMO states) of three organic molecules: anthracene, indigo, and isoindigo, and also the solvent effects on them as isolated systems. The geometry optimizations and electronic calculations are carried out using DFT as implemented in the Siesta as well as Gaussian packages. Finally, the electronic properties of ideal MoS 2 monolayer as a periodic system are investigated based on the DFT using the Siesta package.