Origin of 12th power dependency of Pauli repulsion?

[Infinigon]

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?

 

[DrDu]

The twelfth power dependence has no physical justification. Any high power or exponential dependence will do. However it is mathematical convenient to choose the repulsive term as the square of the attractive term.

 

[Infinigon]

Seeing that the Lennard Jones potential involves the Pauli repulsion term minus an inverse 6th power dependency as a summation of potentials, doesn't the relative value of the Pauli repulsion to the dipole dipole attraction matter greatly? How is it that they can just choose "any high power or exponential dependence"?

 

[DrDu]

The Pauli repulsion dominates completely at small distances over the dipole dipole attraction, while at larger distances it is the other way round. There is only a small region where the two potentials are of comparable size and the location of this region can be fixed by the two free parameters.