The Shrödinger Equation & Hydrogen Molecule Bonding

[Higgsono]

In the hydrogen molecule ion, one electron is responsible for the covalent bond between the atoms. But is it possible for one single elctron to create two bonds or more? What happens if we solve the Shrödinger equation for 3 protons and 1 electron?

 

[mfb]

But is it possible for one single elctron to create two bonds or more?

You can have multiple bonds by multiple electrons, e. g. in cyclohexane. I would be surprised if removing all but one electrons from those bonds works - the molecule gets charged a lot which probably breaks the molecule.

 

[Higgsono]

You can have multiple bonds by multiple electrons, e. g. in cyclohexane. I would be surprised if removing all but one electrons from those bonds works - the molecule gets charged a lot which probably breaks the molecule.

Yes, I guess the molecule would be unstable. How would one go about proving this theoretically, in the case of one electron and two protons?

 

[mfb]

By solving the Schrödinger equation - or noting the absence of solutions in this case.

$H_3^+$ is stable with two electrons.