Orbital angular momentum of O2

[Pete99]

Hi,

I have read several texts where it says that the paramagnetic behavior of O2 molecule is due to two unpaired electrons in a degenerate pi* orbital.

I have not read, however, any comment about the orbital angular momentum of these pi* states.

Is there any reason why the orbital angular momentum is not considered? Is it zero? Why?

Thanks for any help!

 

[DrDu]

Thats an interesting question. In the ground state ^3\Sigma_g^-, the orbital angular momenta of the occupied antibonding pi orbitals combine to total orbital angular momentum 0 (hence the \Sigma). Classically, the two unpaired electron orbit around the molecular axis in different directions. In the lowest excited state (singlett oxygen)
^1\Delta_g the total spin of the electrons is zero but the orbital angular momentum is 2 hbar. Hence the paramagentism of singlet oxygen is nearly as high as that of ground state oxygen although spins are paired.

 

[Pete99]

Thanks for your answer!

Is it always the case that the combined angular momentum of a set of degenerate states adds to zero? I know that it is zero for an atom (for example px, py, pz).

 

[DrDu]

Thanks for your answer!

Is it always the case that the combined angular momentum of a set of degenerate states adds to zero? I know that it is zero for an atom (for example px, py, pz).

Quite on the contrary! According to Hunds rules, both S and L tend to be maximal in the ground state of an atom with degenerate shell.

 

[Pete99]

Maybe I did not make myself clear, or I am totally wrong, but in an atom such as nitrogen in the ground state, the electronic configuration would be 1s2 2s2 2p3

To maximize S we would have the three electrons with parallel spins in the three degenerate p states, but then L would be zero, isn't it?

 

[DrDu]

Yes, for sure. As long as you only consider atoms or ions of main group elements with maximally p orbitals L cannot be greater as 1 if S is to be maximal. The Hund rules become more interesting for atoms and ions with open d or f shells, like lanthanides.