Can I get Bandgap of 3D material with 1D Hamiltonian

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SUMMARY

Arya inquired about calculating the bandgap of a three-dimensional material using a one-dimensional Hamiltonian derived from the potential U(x,y,z) obtained from first principles. The response clarified that this approach is fundamentally flawed, as a one-dimensional chain represents a different physical system than a three-dimensional bulk material. The significant approximations involved in this method further invalidate the results, making it impossible to accurately derive the bandgap of the original 3D material.

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Arya_
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Hi All,

Greetings!

I have a 3d material and I use result from first principal for getting the potential (U(x,y,z)). I then find average U(x) from U(x,y,z). Now if I write one dimensional Hamiltonian in X direction and use this value of U(x), can I get bandgap of the original 3d material (I am not interested to see the bandstructure, bandgap is what I need)

Thanks,
_Arya
 
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No. Why do you think this should be possible? A one-dimensional chain of something is a completely different physical system than a 3d bulk material. (And that is not even considering the /massive/ approximations in what I can only guess you are doing)
 

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