Multiple interaction potentials for different particle pairs

[drobnyjt]

Now that the CPR and polynomial root-finders are working in the cpr_rootfinder branch, the time has come to move away from universal interatomic potentials. Potentials should be specifiable on a species by species basis.

The simplest way to implement this would be the following:

Each species gets a unique integer tag

These tags correspond to indices on an interaction matrix. So for example, if the system is He-W:

He: 0
W:  1
[[ He-He, He-W],
[W-He, W-W]]

The values of the interaction matrix would be integer tags that each correspond to an interaction potential. Additional parameters could be vectors in a same-shaped matrix (e.g., sigma and epsilon for Lennard-Jones).

[drobnyjt]

This is completed in the Fancy Enums branch (which is the currently open PR). The way these are going to look is the following:

interaction_potential = [
  [ "KR_C", {"LENNARD_JONES_65_6"={epsilon = 1.6E-20, sigma = 1E-10}}],
  [{"LENNARD_JONES_65_6"={epsilon = 1.6E-20, sigma = 1E-10}}, "KR_C"]
  ]
scattering_integral = [
  ["MENDENHALL_WELLER", {"GAUSS_MEHLER"={n_points = 10}}],
  [{"GAUSS_MEHLER"={n_points = 10}}, "MENDENHALL_WELLER"]
  ]
root_finder = [
  [{"NEWTON"={max_iterations = 100, tolerance = 1E-3}}, {"POLYNOMIAL"={complex_threshold = 1E-9}}],
  [{"POLYNOMIAL"={complex_threshold = 1E-9}}, {"NEWTON"={max_iterations = 100, tolerance = 1E-3}}]
  ]

This example is for He-W. For He-W and W-He, the code uses a Lennard-Jones 6.5-6 potential, with sigma=1 Angstrom and epsilon=0.1eV. The LJ potential uses the polynomial rootfinder and Gauss-Mehler integration with 10 points. The matrices correspond to the following interactions:

[[He-He, He-W]
[W-He, W-W]] 

So self interactions are handled using the universal Kr-C potential and He-W is handled with a 6.5-6 potential. This produces trajectories distinct from using Kr-C everywhere (this plot is He on TiO2 - Al - Si

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