Geodesic Interpolated Starting Path

[GabrielBram]

Implements the initial path construction specified in: https://pubs.aip.org/aip/jcp/article/150/16/164103/198363/Geodesic-interpolation-for-reaction-pathways.

Code by and large lifted from the repository associated with the paper: https://github.com/virtualzx-nad/geodesic-interpolate/tree/master. However, this implementation honours FixAtoms constraints and periodic boundary conditions in ASE.

Essentially gives a more robust starting guess for the initial path than linear interpolation. Although the full geodesic interpolation algorithm is not implemented, the path should give a better starting guess for IDPP (IDPP uses the linear interpolation as a starting guess and suffers from nasty clashes if two atoms pass through one another).

Test case shows a 120 degree rotation of a CH3 group in ethane, which would otherwise fail spectacularly with the default IDPP interpolation without a better starting guess.

Best use for now would look like:

from carmm.build.neb.geodesic import GeodesicInterpolator
from ase.mep import idpp_interpolate, NEB

Geodesic = GeodesicInterpolator(initial, final, 6, None)
Geodesic.init_path()

idpp_interpolate(Geodesic.images, mic=True)
mep = NEB(Geodesic.images)
...

[codecov]

Codecov Report

Attention: Patch coverage is 96.55172% with 6 lines in your changes are missing coverage. Please review.

Project coverage is 88.84%. Comparing base (001ce56) to head (e8452a0).

Files	Patch %	Lines
carmm/build/neb/geodesic.py	95.83%	4 Missing ⚠️
carmm/build/neb/geodesic_utils.py	96.66%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #158      +/-   ##
==========================================
+ Coverage   88.44%   88.84%   +0.40%     
==========================================
  Files          82       85       +3     
  Lines        3340     3514     +174     
==========================================
+ Hits         2954     3122     +168     
- Misses        386      392       +6     

Flag	Coverage Δ
unittests	88.84% <96.55%> (+0.40%)	⬆️

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[GabrielBram]

(A warning: This is all desperately uncommented)