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In Introduction to Mechanics by Kleppner and Kolenkow they talk about the tension force of a string and its microscopic origins. They explain how applying a force on a string slightly increases the distances between the molecules and makes them attract each other, in a way that balances the applied force. In their explanation, they present the following graph, which qualitatively describes the force between two molecules as a function of their distance.

enter image description here

For $r<r_0$ it is repulsive, then attractive for $r>r_0$; moreover it reaches a maximum and then decays to $0$.

I'm interested in an explanation for this behavior. Which forces govern it? Why is the graph shaped as it is?

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Qualitatively:

Very close, electron clouds try to overlap, resulting in a repulsive electrostatic force.

In the medium distance, the polarity of the electron cloud distribution means that there is some configuration in which a molecule can line up net positive charge to net negative charge, resulting in an attractive electrostatic force between neutral molecules.

The farther apart the molecules are, the more they just look like neutral points, instead of distributed net neutral charge arrangements.

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