Well, if a collection of atoms have formed a stable molecule, then some outside influence is necessary to break it up such as a collision or absorption of a photon or whatever. In the example already given, energy is put into some degree of freedom (vibrational or electronic) such that it's energetically favored for something to break off of the molecule. If you want that in terms of "forces", I guess there's a way to think about, say, a molecule with only two electrons in a valence bonding orbital absorbing a photon and promoting an electron from the bonding to an anti-bonding orbital and because anti-bonding orbitals are always more anti-bonding than bonding orbitals are bonding, the molecule will be unstable. Now, you can call that a quantum phenomenon because it has to do with the way you construct the superpositions that form the bonding or anti-bonding states, or if you have your heart set on calling it a "force", I guess you could say that because there is reduced electron density between the nuclei (due to the node in the anti-bonding state), the "force" that pushes things apart is an electrostatic repulsion, but that's not really the whole story. As you may have guessed by this rambling response, it's not really as simple as "the force that breaks up molecules is X". There's a nice paper out there called "the physical mechanism of the chemical bond" or some such thing that goes through all of the counts of how much is due to kinetic energy lowering, potential energy lowering etc when a bond is formed.