How many improper torsion RMSDs should there be per trivalent center?

[mattwthompson]

Consider triazine, a molecule which can be described as having 18 (topological) improper torsions. Sage only assigns three:

(Pdb) triazine
Molecule with name '' and SMILES '[H]c1nc(nc(n1)[H])[H]'
(Pdb) triazine.n_impropers
18
(Pdb) len([*ForceField("openff_unconstrained-2.2.1.offxml").label_molecules(triazine.to_topology())][0]["ImproperTorsions"])
3

Should the internal coordinate RMSD analysis use topological (18) or assigned (3) torsions? The inherited code gives 3, but I could see either as a reasonable expectation.

[lilyminium]

For clarity, the other 15 are just permutations of the 3 real torsions, right?

I'm fairly ambivalent but would lean towards 3 here as that's easier to deal with. I would just want to be sure that these are easily computable, i.e. the order of the improper torsion is logical and deterministic (e.g. all non-central atoms are ordered left-to-right, for example). Which looks to be correct in the code you pasted.

[jameseastwood]

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[j-wags]

I'm also in favor of 3. I don't see major benefit from measuring each improper center 6 times (the angles may be slightly different, but that doesn't seem like a good reason for the duplication)

[mattwthompson]

Let me try to explain this a little better. This molecule has three trivalent centers (each carbon bonded to two nitrogens and an oxygen). The toolkit expands this out from 3 into 18, permuting over every order of the three non-central atoms (central atom second):

In [45]: for improper in molecule.impropers:
    ...:     print([molecule.atom_index(atom) for atom in improper])
    ...:
[0, 1, 6, 2]
[6, 1, 0, 2]
[7, 5, 4, 6]
[6, 5, 4, 7]
[7, 5, 6, 4]
[8, 3, 2, 4]
[4, 3, 2, 8]
[8, 3, 4, 2]
[6, 5, 7, 4]
[2, 1, 0, 6]
[4, 3, 8, 2]
[0, 1, 2, 6]
[2, 3, 8, 4]
[4, 5, 7, 6]
[4, 5, 6, 7]
[2, 3, 4, 8]
[6, 1, 2, 0]
[2, 1, 6, 0]

This is the most natural implementation because, when the geometry of a particular conformer of a molecule, it's the Molecule API that's most natural to reach for and parameter assignment doesn't naturally come to mind.

ForceField.label_molecules tell us each trivalent center will be assigned a torsion (central atom still second):

In [46]: [*[*ForceField("openff_unconstrained-2.2.1.offxml").label_molecules(molecule.to_topology())][0]['ImproperTorsions']]
Out[46]: [(0, 1, 2, 6), (2, 3, 4, 8), (4, 5, 6, 7)]

And these are expanded out into trefoils within Interchange's bookkeeping (central atom first):

In [47]: pprint([*ForceField("openff_unconstrained-2.2.1.offxml").create_interchange(molecule.to_topology())['ImproperTorsions'].key_map.keys
       ⋮ ()])
[
│   ImproperTorsionKey(atom_indices=(1, 0, 2, 6), mult=0, phase=None, bond_order=None),
│   ImproperTorsionKey(atom_indices=(1, 2, 6, 0), mult=0, phase=None, bond_order=None),
│   ImproperTorsionKey(atom_indices=(1, 6, 0, 2), mult=0, phase=None, bond_order=None),
│   ImproperTorsionKey(atom_indices=(3, 2, 4, 8), mult=0, phase=None, bond_order=None),
│   ImproperTorsionKey(atom_indices=(3, 4, 8, 2), mult=0, phase=None, bond_order=None),
│   ImproperTorsionKey(atom_indices=(3, 8, 2, 4), mult=0, phase=None, bond_order=None),
│   ImproperTorsionKey(atom_indices=(5, 4, 6, 7), mult=0, phase=None, bond_order=None),
│   ImproperTorsionKey(atom_indices=(5, 6, 7, 4), mult=0, phase=None, bond_order=None),
│   ImproperTorsionKey(atom_indices=(5, 7, 4, 6), mult=0, phase=None, bond_order=None)
]

however, this only gets us to 9, not 18, seemingly because of how trefoils are defined (instead of using 6-foils).

This confusion of mine stems from how different parts of our pipeline disagree on how many proper torsions are at each trivalent center (1, 3, or 6). There is a separate issue I've run into which I'll discuss elsewhere dealing with trivalent centers that don't get assigned parameters.

[mattwthompson]

Please also see #201 for a better demonstration of what I originally meant to ask