# A question about slater-koster approximation

• anahita
In summary, the conversation discusses the use of the Slater-Koster approximation and interatomic matrix elements for calculating the band structure of silicene. It also questions the need for using sp2 hybrids instead of the s, px, and py orbitals. The Hamiltonian matrix is formed in the basis of si, pxi, pyi, pzi, sj, pxj, pyj, and pzj, resulting in an 8x8 matrix with attached components.
anahita
Dear forum people
in the Slater-Koster approximation interatomic matrix elements is a function of the cosine direction.
How to calculate cosine direction for silicene by sp2 hybrid.

From what I understood, you are about to calculate the band structure of silicene in tight binding. I don't see why you have to use sp2 hybrids and don't simply work with the s, px and py orbitals.

DrDu said:
From what I understood, you are about to calculate the band structure of silicene in tight binding. I don't see why you have to use sp2 hybrids and don't simply work with the s, px and py orbitals.
Hamiltonian formed in the basis {si,pxi,pyi,pzi,sj,pxj,pyj,pzj} so Hamiltonian matrix is 8*8.
matrix components are attached.

#### Attachments

• matrix elements.docx
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## 1. What is the Slater-Koster approximation?

The Slater-Koster approximation is a method used to calculate the electronic structure of molecules and solids. It takes into account the overlap of atomic orbitals and the interaction between neighboring atoms.

## 2. How does the Slater-Koster approximation work?

The Slater-Koster approximation uses a set of mathematical equations to describe the overlap and interaction between atomic orbitals. These equations take into account the distance between atoms, the orientation of the atomic orbitals, and the electronic properties of the atoms.

## 3. What are the limitations of the Slater-Koster approximation?

The Slater-Koster approximation is based on simplifying assumptions and does not account for all the complexities of the electronic structure. It also does not take into account the effects of electron correlation or relativistic effects. Additionally, it is only accurate for small displacements from the equilibrium atomic positions.

## 4. When is the Slater-Koster approximation used?

The Slater-Koster approximation is commonly used in computational chemistry and materials science to calculate the electronic structure of molecules and solids. It is particularly useful for predicting the electronic properties of materials with complex structures and large numbers of atoms.

## 5. Are there any alternatives to the Slater-Koster approximation?

Yes, there are several alternative methods for calculating electronic structure, such as density functional theory, Hartree-Fock theory, and tight-binding models. Each method has its own advantages and limitations, and the choice of method depends on the specific system being studied and the level of accuracy required.

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