How to calculate the interaction forces between 2 atoms which are in angle, dihedral and improper group

Dear Everyone,

I have a question on how to calculate the interaction forces between 2 atoms which are in angle, dihedral and improper group (please see the figure attached).

How to determine the direction of such 2-atom interaction?

Thank you for your time,

Lili Zhang

Force between 2atoms in the angle group.jpg

(As you probably suspect), I'm not sure it makes sense to define the
force between pairs of atoms when many-body forces are used.

If you want to invent something analogous to the interaction energy
between two particles, you could try something similar to this:

(E(+i,+j) + E(-i,-j)) - (E(+i,-j) + E(-i,+j))

...I think... I hope I wrote this down this correctly.

--- notation ---

E(+i,+j) is the energy of the entire system,
   (including both particles i and j)
E(-i,+j) is the energy of the system missing particle i
E(+i,-j) is the energy of the system missing particle j
E(-i,-j) is the energy missing both particles i and j

Then, you can take derivatives of that quantity (numerically, by
moving the atoms slightly, and computing the new energies).

I'm not sure if this is really what you want to do. (There is no
guarantee the forces will be equal and opposite.)
Why do you need this?

Cheers
Andrew