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A professor asked me to do something, but I'm not quite sure what he means -- He asked me to use Density Functional Theory (DFT) calculations of the band structure of a certain crystalline metal and adjust the matrix elements of a Tight Binding (TB) model to make a "minimal" TB model.

(To be clear: He doesn't want me to do the DFT calculations myself, just to use already existing results!)

Since a quick search of the literature showed me that the band structure of this metal is very well known, he confirmed that DFT was probably used to calculate it. So I guess I'm just supposed to use a calculated band structure and that's the end of DFT's role?

I'm still not sure how to use the given band structure to get the minimal TB model, though. I know what the TB model is and I've used it in some simple examples. In my textbooks (Ashcroft and Mermin, Phillips), they simplify the Hamiltonian for electrons in a periodic potential until it is really simple, really just an equation of a couple unknowns (that I assume depend on parameters of the material), like this:

[tex]E(\vec{k}) = E_0 - t\sum_\delta e^{i \vec{k} \cdot \vec{\delta}}[/tex]

Where the sum is over nearest neighbors of an atom in the lattice, ##E_0## is due to the background potential, and ##t## is the "hopping matrix element".

Something still doesn't make sense to me, though. Since I have the crystal structure and the band structure, I could try and fit the above equation, but it really only has two parameters, ##E_0## and ##t##. However, my textbook(s) had to make about a million approximations to reach that simple equation, so maybe it's possible one of those isn't valid here, and then there would be more parameters to fit?

Can anyone help me? Does anyone have any resources on this?

Thank you!

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# Using Density Functional Theory to make a Tight Binding model?

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