You can tell high school students that a bond is formed because two nuclei "share" electrons. There is no explanation that uses the classical formalism and still explains the experimental observations. What is the force that leads to this energy well? I think if you can answer any of these questions, you will know the answer why two atoms should become bonded together. The energy levels of benzene are much lower than predicted from an isolated double bond. You can find many energy wells, but I don't think you will find an explanation which uses one of the four forces of nature (or a new fifth force). You can see that I have not and cannot answer your question. If you heat water to 2500 oC, you can homolyze it to give hydrogen and oxygen, think Fukushima and resultant explosion. Adding an acid to increase the pull upon a pair of electrons does not give radicals. If NaOH is added, a lot more can be ionized. Which is easier, to ionize water or homolyze it? A very small amount of pure water is ionized. So, you may ask yourself, which is stronger, e-e cohesion or e 2-proton or nucleus force.
If you were to require that an energy difference can only exist due to the application of a force, then if you can find an energy well, you may ask what is the force? Lewis said that in some circumstances electrons may form pairs. If you are asking for yourself, then you might agree with Gilbert Lewis. If you are asking for a class, I'm fairly confident the quantum theory answer is the right one. Maybe it does, but I still don't understand it. Undoubtedly, some will answer that quantum theory explains it. The questions being asked are good ones and they have existed for a very long time. This will assuredly increase the number of flags I can get. This is a topic that I have to be careful with.
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