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Tutorial on Kohn-Sham inversion and fixes

Nicolas Tancogne-Dejean requested to merge tutorial_inversion_and_fixes into main

Description

Tutorial on Kohn-Sham inversion and fixes.

This also revisit the two-particle part of the Kohn-Sham inversion. In particular, in the 1D case, the computation of the Laplacian is replaced by the evaluation of the second derivatives using splines, with a staggered grid in order to force interpolation. This allows for reducing the threshold of what is a small density to a much lower value of 5e-12 with almost no numerical noise.

Closes #924 (closed)

News snippet

Tutorial and improvements on Kohn-Sham inversion in the two-particle case.

Checklist

  • I have checked that my code follows the Octopus coding standards
  • I have added tests for all the new features added in this request.
Edited by Nicolas Tancogne-Dejean

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