Stabilization of half-filled and fully-filled orbitals

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In summary, according to this paper, the stability of filled orbitals is due to the fact that they have zero angular momentum and spin. This is a simplification of a more complicated theory, but it's a good starting point for someone who wants to learn more about this topic.
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gdlchmst
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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.
 
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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.
 
  • #3
alxm said:
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.
 
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  • #4
olgranpappy said:
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.
 
  • #5
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.
 

1. What is "stabilization of half-filled and fully-filled orbitals"?

Stabilization of half-filled and fully-filled orbitals refers to the phenomenon in which electrons in an atom or molecule tend to occupy orbitals in a way that maximizes their stability. This is due to the fact that half-filled and fully-filled orbitals have lower energy levels than partially-filled orbitals.

2. Why do half-filled and fully-filled orbitals have lower energy levels?

This is due to a concept known as Hund's rule, which states that electrons tend to occupy separate orbitals within a subshell before pairing up. This results in half-filled and fully-filled orbitals, which are more stable due to the repulsion between paired electrons being minimized.

3. How does the stability of half-filled and fully-filled orbitals affect chemical reactions?

The stability of half-filled and fully-filled orbitals plays a crucial role in determining the reactivity of atoms and molecules. Atoms with partially-filled orbitals are more reactive, as they have a higher energy state and are therefore more likely to undergo chemical reactions in order to achieve a more stable state.

4. Can the stability of half-filled and fully-filled orbitals be manipulated?

Yes, the stability of half-filled and fully-filled orbitals can be manipulated through the addition or removal of electrons. This can be achieved through chemical reactions, such as oxidation and reduction, or through external influences such as temperature, pressure, and electric or magnetic fields.

5. What are some real-world applications of the concept of stabilization of half-filled and fully-filled orbitals?

The concept of stabilization of half-filled and fully-filled orbitals has many applications in fields such as materials science, environmental science, and pharmaceuticals. For example, understanding the stability of orbitals is crucial in designing new materials with specific properties, studying the reactivity of pollutants in the environment, and developing new drugs that target specific biological processes.

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