Question about the distances in the SlaterKosterTable

[issac7]

Dear sir,

I'm doping DFTB calculations based on user specified Slater-Koster matrix according to

https://docs.quantumatk.com/tutorials/slater_koster/slater_koster.html#slater-koster-tight-binding-models-in-atk-se.

Here is my question: what does the distance "d" stands for?

I'm confused because the specified d is actually out of the nearest distance between atoms.

Code

# Setup list of distances
epsilon = numpy.linspace(-0.20, 0.20, 41)
distances = [ d_n1*(1.0+x) for x in epsilon ] + [ 0.5*(d_n1+d_n2) ]

Looking forward to your replies. Thanks a lot.

[Anders Blom]

I think the code speaks for itself. d_n1 is the first nearest neighbor distance, d_n2 the second.

[issac7]

Thanks for replying. Sorry for the unclear question. The "d" I put earlier means the <distances=...> in the code. I am confused that the distances that determined the offsite hopping matrix fall out of the nearest atomic distance.

[Anders Blom]

The distances variable basically does two things. It creates a range around the nearest distance, where either the interaction will be constant (to catch any small numerical difference in distances) or a (d/d0)^2 fall-off which is common in these models. The final point is to truncate the interactions at some large distance, it is paired with a zero-term in the hopping elements.