# Where does the Pauli Repulsive Force come from that counteracts the attraction between atoms and ions? [duplicate]

I'm learning about such things as ionic and covalent bonds, and the reason given for the ionic bonds is electrostatic attraction. However, if that were true, then the two ions would accelerate toward each other and shortly collide with each other. There must be a force opposite the electrostatic force that is repelling the ions, with exactly the same magnitude so as to cancel out the electrostatic force. (Edit: I'm actually referring to the ionic bond between cations and anions in this first paragraph, like sodium and chloride ions. Below is what I found by researching this topic, dealing mainly with covalent/molecular bonding.)

The following quote is from The Mechanical Universe:

For example, the potential energy of a pair of Hydrogen atoms has a position of stable equilibrium. The potential energies of interaction between atoms are due to the electrical forces between them, causing attraction when they're far apart. At smaller distances, they resist being squeezed together. The result is an equilibrium position where attraction and repulsion are in perfect balance. At that position, they bind in a Hydrogen molecule.

I understand that on a larger (planetary) scale, there is a centrifugal potential that is inversely proportional to the distance $r$ that adds up with the gravitational potential to create this graph:

I'm looking for an analogue to this on the molecular scale. I've recently found out about the Lennard-Jones Potential, which gives this equation and curve:$$V_{LJ}=\epsilon \left[ \left(\frac{r_m}{r}\right)^{12} - 2\left(\frac{r_m}{r}\right)^6 \right]$$

In the wikipedia article, it says

...the repulsive term describes Pauli repulsion at short ranges due to overlapping electron orbitals

Later on it is noted that

The repulsive term has no theoretical justification.

So then this is my question: What is the nature of the "Pauli repulsive force"?

If it's possible, I would appreciate an answer with cited sources.

Edit: After some more research, I've found that attraction between two hydrogen atoms (which are both neutral) comes from Induced Dipole-Induced Dipole interaction AKA London Dispersion Forces. Collectively, the attraction and repulsive forces at the molecular scale are dubbed the Van der Waals forces. The wiki on Van der Waals forces mentions A repulsive component resulting from the Pauli exclusion principle that prevents the collapse of molecules. I would like to learn more about how the Pauli exclusion principle manifests itself as a repulsive force between any two atoms/ions.

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## marked as duplicate by John Rennie, Manishearth♦Jun 29 '13 at 10:26

What do you mean by collide together? To what extent? If you mean for the protons to actually come together, there is clearly powerful repulsion to be overcome. Obviously, protons do collide, which is how we get Helium, etc. Multi-proton nuclei are held together by the nuclear strong force, and with the help of inter-spaced neutrons. – Kaz Jun 27 '13 at 4:53
@Kaz I believe he's asking why H2 just doesn't turn into Helium – Justin L. Jun 27 '13 at 4:54
@Kaz I'm meaning that the electrostatic potential alone cannot describe the bond between two ions, as it drops down to negative infinity at $r=0$. There is this pauli-repulsion that is opposing the attraction of the two oppositely-charged atoms, which is what I'm confused about. – Greg Jun 27 '13 at 4:56
Why not just ask, since electrons and protons are opposite charges, why doesn't the hydrogen atom's electron just crash into the proton and make a neutron. van.physics.illinois.edu/qa/listing.php?id=1199 – Kaz Jun 27 '13 at 5:02
Possible duplicate of How can I stand on the ground? EM or/and Pauli? – John Rennie Jun 27 '13 at 7:04

The reason is the coulombic repulsion of the two protons. The same is true for $H_2^+$ , the simplest molecule in nature, that has only one electron, and a bound ground state. You can derive the molecular potential analytically if you want and need not think of L-J form with these simple molecules. A place to start is the seminal work by Morse and Stueckelberg, http://prola.aps.org/abstract/PR/v33/i6/p932_1