# Model for diatomic molecule

1. Mar 25, 2014

### Runei

Hello,

I'm working here with a model for a diatomic molecule. The potential is modelled as two finite wells. For a given distance between the wells, the energy of the ground state will be minimized. If you move the "atoms" closer to each other, the energy rises, and if you move them away from each other, the energy rise. All well and good.

However, I always thought (before quantum mechanics course) that the reason for the repulsive force experienced when you tried to force the atoms together was due to the positive nucleus of the atoms. But quantum mechanics have now shown me (or at least thats what I believe I am being told by the theory) that the repulsiveness is simply due to the quantum mechanical behaviour and how the wave function will have to rise in energy.

Is this the correct interpretation?

Thank you :)

2. Mar 27, 2014

### DrDu

Obviously, the model of a bond you consider is a very crude one.
You are also right in that the repulsion at small distances is mainly due to the repulsion of the nuclei.
However, this is not at variance with what you have learned from your model.
Why? Because it is a question of at what distances the electrons can screen the nuclear charges.
To screen the nuclear charges at small distances of the nuclei, the electrons would have to get localized in a very small region between the nuclei, i.e. in a deep but small potential through. However, as you learned from your model, this would cost a lot of energy whence the energy of a molecule goes invariably up at small distances of the nuclei.

3. Mar 27, 2014

### Staff: Mentor

But remember where that quantum mechanical behaviour comes from: in the Hamiltonian, there is a potential energy term
$$\frac{Z_1 Z_2 e^2}{4 \pi \epsilon_0 R}$$
where $R$ is the internuclear distance.