Understanding the MO Energy Level Diagram for H3+ Cyclic Structure

[gravenewworld]

H3+ ion has been observed but its structure has been the cause of some controversy. Prepare a MO energy level diagram for H3+ assuming cyclic structure.




I have no idea how in the hell I am supposed to do this problem since the only MO diagrams we have done in class have been only with 2 atoms. Please can someone help?

 

[chem_tr]

You may try H⁺ and H₂ on the other side.

 

[movies]

Okay, so your basis set is the three hydrogen 1s orbitals, right? Think of the productive ways that you can have those overlap and then start changing the phase of the orbitals one at a time to get the higher energy forms. There will be three molecular orbitals in all. They should look roughly like this:

X

X​

X


X

.​

O


X

O​

X

Where X indicates one phase, O indicates the other, and . indicates a node. So the one on the top has no nodes, the other two have one node each. These are a crude representation of the molecular orbitals. Each orbital can "hold" two electrons. You have two electrons to deal with in this case, so place them in the lowest energy orbital (the one with no nodes).

Some things to note:
1) You start with three atomic orbitals and you get three molecular orbitals. You MUST always end up with the same number of molecular orbitals as you had atomic orbitals.
2) The filled molecular orbital (the top one) represents delocalization of the electrons evenly between each hydrogen atom. This is what you would expect intuitively. This agreement is important!