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Improves the stability of the root finding for species full Gaussian

Nicolas Tancogne-Dejean requested to merge improve_species_full_gaussian into main

Description

The root finding was solving a 4D problem with minimizing the first moment as well as the zero-th moment, where we only need to solve a 3D problem, and to impose the first moment. The code is then change to only solve a 3D problem, which is much more stable.

The code also now uses a more robbust root finder that can detect linear convergence due to multiplicity of the solution larger than 1. This seems to occur when the smearing of the charge is too small (for instance around 0.25, which is the default).

Some documentation is fixed. Closes #647 (closed)

Some error message was too cryptic, so this is also improved.

News snippet

Improves the stability of the root finding for species full Gaussian

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.

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