# How to construct a Tight-Binding Hamiltonian from first-principles computations?

Effective Hamiltonian approaches such as the Tight-Binding method played a central role in the reconciliation between chemistry and in physics in the solid state. A classical and complete treatment of the method is found in Walter A. Harrison's book "Elementary Electronic Structure" (an update to his prior text "Electronic Structure and the Properties of Solids: The physics of the chemical bond").

Tight-binding models continue to play a central role in condensed matter and materials physics. As they require certain model parameters, I ask:

• Is it possible to construct a Tight-binding model using Density Functional Theory or another ab initio method as a starting point?

• How is this achieved? Are there available codes that aid in this process?

• There are many 'density functional tight binding' (DFTB) programs and papers :-) For example DFTB.org and references therein May 2 '20 at 1:11
• I knew about DFTB (DFTB+) but I see that as another computational method for modeling materials? Not sure if it is possible to then construct an effective Hamiltonian from DFTB thann can later be manipulated by hand or be used as input in codes such as Kwant for quantum transport. My feeling is that this might be closer to Wannier90 than DFTB+. May 2 '20 at 1:20
• I think you can see the Hamiltonian from Wannier90 as a tight-binding Hamiltonian. For quantum transport you will need to describe the complete system including an external potential eventually. Therefore, you need to upscale the Hamiltonian to the device you want to simulate.
– CKl
May 2 '20 at 10:26

More recent related codes to look at would be PAOFLOW and AFLOW$$\pi$$ from the AFlow consortium.