Atomic Distortion and the Combining Rule for Repulsive Potentials

The exponential repulsion between atoms, molecules, and ions with closed-shell structure arising from the Pauli exclusion principle is examined in the light of a distortion model. The repulsion energy arises mainly from the distortion of the two atoms, each of which is constrained by the presence of the other to terminate at an intermediate surface, which is often approximately planar. The location of this surface is determined by minimizing the total distortion energy, with the result that the restoring forces in each atom are equal and opposite. There results a new combining rule for these repulsive potentials, allowing the potential for $\mathrm{AB}$ to be deduced from those for $A_2$ and $B_2$, which reduces in some special cases to the previously assumed geometric-mean rule. A further consequence is a relationship between the instantaneous collisional dipole moments in a family of asymmetric collisions such as HeNe, NeAr, and ArHe, provided that they are all measured at equal values of the collision force.