Origin of 12th power dependency of Pauli repulsion?

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Discussion Overview

The discussion centers on the origin and justification of the 12th power dependency of Pauli repulsion within the context of the Lennard-Jones potential, comparing it to the 6th power dependency of dipole-dipole interactions. Participants explore the theoretical basis for this dependency and its implications for modeling intermolecular forces.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes understanding the derivation of the 6th power dependency of dipole-dipole interactions but questions the lack of theoretical justification for the 12th power dependency of Pauli repulsion, suggesting it approximates repulsion due to overlapping electron orbitals.
  • Another participant asserts that the 12th power dependence has no physical justification and that any high power or exponential dependence could suffice, emphasizing the mathematical convenience of choosing the repulsive term as the square of the attractive term.
  • A different participant raises concerns about the significance of the relative values of Pauli repulsion and dipole-dipole attraction, questioning the rationale behind selecting "any high power or exponential dependence."
  • It is mentioned that Pauli repulsion dominates at small distances, while dipole-dipole attraction prevails at larger distances, with a small region where both potentials are comparable, which can be adjusted by free parameters.

Areas of Agreement / Disagreement

Participants express differing views on the justification for the 12th power dependency, with some arguing it lacks physical basis while others question the implications of this choice. The discussion remains unresolved regarding the appropriateness of the power dependency used in the Lennard-Jones potential.

Contextual Notes

Participants highlight the mathematical convenience of the chosen dependencies and the significance of the parameters that define the balance between repulsion and attraction, but do not resolve the underlying theoretical justifications or implications.

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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?
 
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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.
 
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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"?
 
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.
 

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