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[![enter image description here][1]][1] This is a graph showing the formation of K+ F- ionic bonds. To my understanding, when the atoms are far apart, their neutral state is more stable. But when they get closer, they form ionic bonds to become more stabilized.

My question is: how do we calculate the distance when K+ and F- start to form ionic bonds? ie the hopping distance?

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Good question

For the neutral state, I think, you can consider only the LJ potential. On the other hand, you can calculate the stabilisation of the LJ potential considering the two ions. So LJ potential and Coulombian effect.

Intrinsicly one ion in the void (or gas phase, as you prefer thinking) is less stable than the neutral atom, here is why the $\Delta E$ is positive when the two are apart. When the two start approach, the Coulombian interaction starts to take over and the total energy of the system starts to decrease. Here you can calculate the zeros of the function and you can get the "hopping distance"

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