Is There Spin-Orbital Coupling in S-Orbitals with L=0?

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Discussion Overview

The discussion centers on the concept of spin-orbit coupling in quantum chemistry, specifically regarding S-orbitals where the orbital angular momentum quantum number L is equal to zero. Participants explore whether coupling occurs in this case and the implications for energy splitting in the absence of an external magnetic field.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether spin-orbit coupling exists when L=0 in S-orbitals, suggesting that if L=0, then J=1/2 and there would be no splitting.
  • Another participant agrees that without an external magnetic field, there would be no energy splitting for L=0, but notes that for L>0, multiple values of J can lead to energy differences due to LS-coupling.
  • A further inquiry is made about whether the nucleus' magnetic field contributes to different energy states and the resulting LS-couplings.
  • Another participant introduces a classical perspective, explaining that the motion of the nucleus can be viewed as a current loop, which generates a magnetic field that interacts with the electron's spin, leading to LS-coupling.

Areas of Agreement / Disagreement

Participants express differing views on the existence of spin-orbit coupling in S-orbitals with L=0, with some asserting that no coupling occurs while others provide explanations involving external magnetic fields and classical interpretations. The discussion remains unresolved regarding the role of the nucleus' magnetic field and its effects on energy states.

Contextual Notes

Participants have not fully explored the assumptions regarding the conditions under which spin-orbit coupling may or may not occur, and the implications of external magnetic fields on energy splitting are not definitively established.

Mortendk
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Hi everyone.
Im reading quantum chemistry due to an exam, but there are a few things, that I am not sure of:

1. I'm not sure, but as far as i understand, there is coupling between spin and orbital angular momentum, but if L = 0, in an S-orbital: is there then any coupling ?


2. Does energisplit happen without interference from an foreign magnetic field?

Hope you can help me.
 
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1. If L=0 then J=1/2 only as S=1/2 for an electron and so there is no splitting.

2. In the above case there would be no splitting and magnetic field would be required to
cause it (by Zeeman effect) but if L>0 then J can have more than one value and each will
have different energy due to LS-coupling so splitting will occur without magnetic field present.

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Is it the nucleus' magnetic field that gives rise to the different energy states? - which makes the different LS-couplings have different energies, and futhermore makes splitting occur
 
Last edited:
Another question concerning spin-orbit coupling.

I have read that phosphorescense might be caused by spin-orbit coupling. How can that be explained?

Thanks a lot
 
In classical consideration, an electron orbits the nucleus and in electron's frame of reference it looks like the nucleus is orbiting the electron. A moving nucleus could essentially be regarded as a current loop and you can then calculate the magnetic field generated by this motion. This is how the LS-coupling arises, basically the magnetic field depends on momentum of the nucleus (L), higher momentum means more revolutions around the electron and greater current. The magnetic moment of the electron depends on its spin (S) and the usual interaction of magnetic field with a magnetic moment proportional to m.B (greek mu is usually used for m) becomes proportional to L.S where L and S are replaced with quantum operators.

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Last edited by a moderator:

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