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I am a high schooler and I read in my chemistry book that half filled degenerate orbitals are stable because electrons with the same spin in those degenerate orbitals exchange their positions and this leads to release in some energy.

But one thing which I didn't understand is why do those electrons exchange their position if their respective orbitals had same initial energy.

And also why (and how) does this exchange release energy and cause stability ?

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  • $\begingroup$ Could you provide a source for this? $\endgroup$
    – Jason Funderberker
    Feb 6, 2021 at 12:45
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    $\begingroup$ Don't take the word exchange that literally. $\endgroup$
    – user137289
    Feb 6, 2021 at 13:07
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    $\begingroup$ @Pieter then how should I take it ;)? $\endgroup$
    – Ankit
    Feb 6, 2021 at 13:11
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    $\begingroup$ @Astudent I am not a theorist. But in for example an atom with five electrons in the $d$ orbitals, the symmetry of the wave function (when exchanging labels) makes that the electrons are automatically furthest apart when their spins are parallel. This gives then the smallest electrostatic repulsion between them. It is basically due to the Coulomb interaction. $\endgroup$
    – user137289
    Feb 6, 2021 at 13:45
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    $\begingroup$ @Pieter That should be an answer, but for five electrons occupying 5 different orbitals the spins are not restricted by Coulomb matrix element. It is the direct exchange matrix element that favors parallel spins. $\endgroup$
    – my2cts
    Feb 6, 2021 at 14:44

1 Answer 1

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The Pauli exclusion principle holds that a wave function must be antisymmetric under exchange of identical fermions. This leads to an extra electrostatic interaction term, on top of the Coulomb repulsion, namely the exchange interaction. For direct exchange this interaction favors parallel spins. (Without more context, I infer that your post is about direct exchange.)

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