I probably searched the entire Internet, but I didn't find the answer to this question. I understand that this is due to the dipole moment, but then it would be 1/r^3
The Lennard-Jones potential is a simplified model that yet describes the essential features of interactions between simple atoms and molecules: Two interacting particles repel each other at very close distance, attract each other at moderate distance, and do not interact at infinite distance..The inclusion of many-body potentials is a formality. In the event that the potential energy consists of one-, two-, and three-body terms, in addition to the pair Mayer f-function, one defines a triplet function f(3)(r1, r2, r3) = −1 + exp u(3)(r1, r2, r3). It then follows in a straightforward manner that. (8.66)