Tight-Binding Models

Tight binding models are a type of model used to describe the electronic structure of solids and molecules. In tight binding models, the electronic wave functions are expanded in terms of a set of localized basis functions, which are usually chosen to be atomic orbitals. The expansion coefficients, or tight-binding parameters, are then determined by fitting to experimental data or by performing first-principles calculations.

The tight binding model can then be used to calculate various properties of the electronic structure, such as the band structure, density of states, and electrical conductivity. Tight binding models are particularly useful for quickly and accurately calculating the electronic structure of materials, particularly when only the nearest-neighbor interactions are important.

There are several different approaches to constructing tight binding models, including the Slater-Koster approach, which includes only the nearest-neighbor interactions between atoms, and the extended tight binding approach, which includes longer-range interactions as well.

Slater-Koster Tight Binding

Slater-Koster tight binding is a method for modeling the electronic structure of solids and molecules using a simplified Hamiltonian that includes only the nearest-neighbor interactions between atoms. The method is based on the idea that the electronic structure of a solid can be approximated by a set of localized atomic orbitals, which are then connected by a set of tight-binding parameters that describe the strength of the interactions between the orbitals.

In the Slater-Koster approach, the tight-binding parameters are determined by fitting to experimental data or by performing first-principles calculations. The resulting tight-binding model can then be used to calculate various properties of the electronic structure, such as the band structure, density of states, and electrical conductivity.

Slater-Koster tight binding is a useful tool for quickly and accurately calculating the electronic structure of materials, particularly when only the nearest-neighbor interactions are important. It is also relatively simple to implement, making it a popular choice for modeling the electronic structure of solids and molecules.