Undergrad Where do the vibrational modes of molecules come from?

[asphy]

TL;DR

Where vibrational modes of molecules come from?

Hello everyone. First, sorry for my english. Second, I have got question where vibration mode of H2+ molecule (I think it is the most simple molecule for this topic explanation) comes from. If I should get basics before asking this tell me :). By my count the most important factor behind "being" oscillator is force that returns nuclei to the equilibrium position (I say about nuclei because I read in internet that in vibration are involved nuclei). As the motor force of nuclei repulsion (when nuclei are closer together than in eqilibrium position) I see Coulomb force, but if nuclei are further apart than in equilibrium position what force cause them to change direction and come closer to each other? In conclusion, what force (attracting nuclei) is counterpart of spring in classical oscillator?

 

[TeethWhitener]

In a molecule, there is a balance between repulsive (electron-electron and nucleus-nucleus) forces and attractive (electron-nucleus) forces. The total force is zero at the equilibrium bond length. If you stretch or compress the bond, the imbalance of attractive and repulsive forces will pull the atoms back toward equilibrium.

This is probably as close an explanation as I can give you without invoking quantum mechanics.

 

[DrDu]

At large distances, you have attraction between a positive proton and a polarisable H atom. At small distances, the repulsion between the two nuclei dominates. Hence there must be at least one bound state and the distance of the two atoms can oscillate around the equilibrium distance.