I was reading about the Lennard-Jones potential, and I believe I understand the derivation of the 6th power dependency of dipole dipole interactions (Van der Waal forces) well. The most I have been able to find about the 12th power dependency of Pauli repulsion is that is has no theoretical justification but approximates repulsion at short ranges due to overlapping electron orbitals well and happens to be the square of the Van der Waals term. I was wondering if there is any more detail to this. Does a 12th power dependency work better than a 10th power dependency, for instance? Is the difference great enough to matter? In what way did this term of the Lennard-Jones potential come about exactly?