[DFTB-Plus-User] Fitting repulsive potential with spline, information about technical details

[Bálint Aradi]

Dear Riccardo,

> where c0 c1 c2 c3 are the spline coefficients in the point c) What is 
> not clear to me is:
> 1) How do I found a1 a2 and a3?

By taking the function value and its first and second derivative a the
left boundary of the 1st spline.

> 2) Why do I need a 5th order spline for the last interval while only a 
> 3rd order one is used before?

You need the 5th order in order to make sure, that the repulsive
vanishes smoothly (value, 1st and 2nd derivative = 0 at rcut).

> 3) How do I decide the number of intervals?

Arbitrary, if you have a proper (smooth) repulsive, it should not really
matter.


Note, if you split splines, make sure, the repulsive is smooth enough,
otherwise you 1st and 2nd derivatives may be very oscillating, which
would mess up vibrations. Usually we fit first a polynomial to the
repulsive with least square and then resample it with splines to ensure
smoothness.

I have a script which does all this. it is undocumented, but if you
wish, you may give it a try. You find it in the sktools branch of my
personal DFTB+ fork:

https://github.com/aradi/dftbplus/tree/sktools

Look for dftbplus/tools/sktools/bin/splinerepfit

Best regards,

Bálint


-- 
Dr. Bálint Aradi
Bremen Center for Computational Materials Science, University of Bremen
http://www.bccms.uni-bremen.de/cms/people/b-aradi/


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