Stabilization of half-filled and fully-filled orbitals

[gdlchmst]

The additional stabilization from half-filled (e.g. 3d5, 4f7) and fully filled orbitals (e.g. 3d10, 4f14) is well-known. But can someone give an explanation for this? I'm looking for a theoretical rationalization. Thank you in advance.

 

[alxm]

Half-filled would be due to Hund's rule, which is mostly empirical and not easily justified theoretically. Filled orbitals, because the overall angular momentum is zero.

 

[olgranpappy]

Half-filled would be due to Hund's rule, which is mostly empirical and not easily justified theoretically. Filled orbitals, because the overall angular momentum is zero.

What do you mean by this? Hund's rules apply to all types of atoms regardless of filling. And, regarding the second sentence, how is that fact that filled orbitals have zero angular momentum (and spin) an explanation for their stability?

P.S. These facts are not easily justified analytically, but the theory of atomic structure is well-known... although in practice one has to do numerical calculations.

P.P.S. There are a lot of books which the OP could look into for further explanation. For example, Condon and Shortley's book on atomic structure from the 1930s.

 

[alxm]

What do you mean by this? Hund's rules apply to all types of atoms regardless of filling.

Good point. What I meant was 'for the same reason as Hund's rule'. Which, to justify a bit more: Having the maximum number of electrons in different (degenerate) orbitals tends to 1) minimize the amount of spatial orbital overlap, and electron-electron repulsion and 2) Maximize the amount of exchange energy.

And, regarding the second sentence, how is that fact that filled orbitals have zero angular momentum (and spin) an explanation for their stability?

You have spherical symmetry then.

 

[gdlchmst]

Thanks for replying. But I have figured out the answer. I was looking for a simple QM treatment rather than just invoking Hund's rules. There was an excellent paper published by Antony Blake in J. Chem. Ed., Vol. 58, 1981, p393-398. It gives a very nice and simple QM rationalization for Hund's rules and the exchange stabilization energy.

Cheers.