A Simple Model for the Pauli Repulsion with Possible Utility in QM, MM and Chemical Education

The Pauli repulsion is the intermolecular force responsible for the volume and low compressibility of condensed-phase matter at normal conditions. A simple model for this force is presented, wherein per-atom electron densities are represented as spherical charge distributions that are prevented from significantly overlapping. In the example of two noble gas atoms approaching one another beyond their van der Waals radii, the distance between the centers of the electronic charge distributions becomes larger than the distance between the nuclei, giving rise to an unfavorable electrostatic interaction. For the purpose of calculating this interaction, the model is further simplified by representing the per-atom electron density as a negative point charge, loosely inspired by the classical Drude oscillator. The dispersion interaction is simplified to an R^-6 term, centered on the aforementioned point charges. Despite the gross simplicity of the resulting formalism, near-quantitative agreement with high-level QM interaction energies of noble gas dimers is achieved. Accordingly, the present model is thought to have utility in force fields, in post-HF and post-DFT dispersion corrections, and in chemical education.