I assume it is the electrostatic force between the 2 atoms and as the distance between them decreases, the forces between them increases. If the atoms are of similar charge, the force is repulsive and it is attractive if the atoms are of different polarity.
It is not the electrostatic force, it is complex quantity, but in short it is the derivative of the total energy with respect to the coordinates of the atoms.
There are many contributions to these forces, some are repulsive, others are attractive, hence there is alot og information in the forces. However one thing is easy to say, that there is a force minimum between the two atoms at a finite range, where all the forces cancels out. This is the equilibrium distance.
Question 1: When the force is non-zero and of different polarity, does it mean that if I leave the two atoms be, they will move towards each other? (and hence decreasing the distance between them and increasing the attractive force between them). This would be true even if the force is small (0.05eV/Ang?).
Sort of yes. If the atomic forces on Atom 7 is (0.03 eV/Ang, -0.2 eV/Ang, 1.2 eV/Ang), it will have an acceleration in the direction of this forces in standard Newton mechanics.
Question 2: Can I interpret the force as such that it is the force required to increase the distance between the atoms?
Well mostly no and a little yes. The force calculated, is the force acting on the atom in the current configuration, and if the forces are not zero, then the system is not in equilibrium, but if you are really want to, you could say that in order to move an infinitismal distance the atom in the oppesite direction of the force, would require at least the force calculated.
If you ask me, I would calculate the total energy as a function of the distance between the atoms instead.
