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One often sees the two-body potential f(r_{1},r_{2}) being reduced to to f(r_{12}). Can this be done in a more general case (can n-body potentials be reduced to just the distances between all the particles, e.g. f(r_{1},r_{2}) -> f(r_{12}, r_{13}, r_{23}))? I assume that the point particles don't have any internal structure. Do I need to add further constraints? I'm mainly aiming for representations of angular and dihedral (torsional) potentials.

From the looks of it, I'd guess it works at least with 3 point particles, due to the SSS triangle congruence.

Any ideas?

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# On N-body potentials

Can you offer guidance or do you also need help?

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