5.10 Pauli Repulsion

Before proceeding to a description of chemical bonds, one important point must first be made. While the earlier descriptions of the hydrogen molecular ion and hydrogen molecule produced many important observations about chemical bonds, they are highly misleading in one aspect.

In the hydrogen molecule cases, the repulsive force that eventually stops the atoms from getting together any closer than they do is the electrostatic repulsion between the nuclei. It is important to recognize that this is the exception, rather than the norm. Normally, the main repulsion between atoms is not due to repulsion between the nuclei, but due to the Pauli exclusion principle for their electrons. Such repulsion is called exclusion-principle repulsion or Pauli repulsion.

To understand why the repulsion arises, consider two helium ions, and assume that you put them right on top of each other. Of course, with the nuclei right on top of each other, the nuclear repulsion will be infinite, but ignore that for now. There is another effect, and that is the interesting one here. There are now 4 electrons in the 1s shell.

Without the Pauli exclusion principle, that would not be a big deal. The repulsion between the electrons would go up, but so would the combined nuclear strength double. However, Pauli says that only two electrons may go into the 1s shell. The other two 1s electrons will have to divert to the 2s shell, and that requires a lot of energy.

Next consider what happens when two helium atoms are not on top of each other, but are merely starting to intrude on each other’s 1s shell space. Recall that the Pauli principle is just the antisymmetrization requirement of the electron wave function applied to a description in terms of given energy states. When the atoms get closer together, the energy states get confused, but the antisymmetrization requirement stays in full force. When the filled shells start to intrude on each other’s space, the electrons start to divert to increasingly higher energy to continue to satisfy the antisymmetrization requirement. This process ramps up much more quickly than the nuclear repulsions and dominates the net repulsion in almost all circumstances.

In everyday terms, the standard example of repulsion forces that ramp up very quickly is billiard balls. If billiard balls are a millimeter away from touching, there is no repulsion between them, but move them closer a millimeter, and suddenly there is this big repulsive force. The repulsion between filled atom shells does not ramp up that quickly in relative terms, of course, but it does ramp up quickly. So describing atoms with closed shells as billiard balls is quite reasonable if you are just looking for a general idea.


Key Points
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If electron wave functions intrude on each others space, it can cause repulsion due to the antisymmetrization requirement.

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This is called Pauli repulsion or exclusion principle repulsion.

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It is the dominant repulsion in almost all cases.