guy
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Crystal Field theory question
I've seen pictures in textbooks where the d orbitals all are raised to a higher energy with the dx2-y2 and z2 (e2g) orbitals higher than the dxy, dyz,
dxz(t2g). But I have also see diagrams where only the e2g are raised (by 6Dq) and the t2g are <i>lowered</i> by 4Dq. So are they both
raised or what?
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turd
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Crystal field theory is complete nonsense, but can give correct predictions.
What you want is ligand field theory, which is based on MO theory. You also have to consider if you're looking at MOs or AOs.
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guy
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No not really. Crystal field deals with the repulsion of the electrons and orbitals rather than the bonding. They are actually two views of the same
thing and give the same result.
Anyway back to my question...
[Edited on 8/9/2006 by guy]
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turd
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Wrong. Crystal field theory is complete and utter nonsense - it simply is not what is happening. This is one of those cases where macroscopic level
phenomena can not be applied to the quantum world. Actually it's the exact *opposite* that is happening: the d orbitals (or at least a few of them,
depending on the ligands), give *lower* energy MO orbitals (releasing the bonding energy). What crystal field theory interprets as energy increase are
actually the *antibonding* orbitals, which have nothing to do with electric repulsion. The fact that crystal field theory gives (sometimes) correct
results is sheer luck. If two theories say the opposite, they can't both be true. 
You're question is a bit like asking what would the moon taste like if it was made from cheese. The correct thing from an AO point of view and
degenerate orbitals would be that the total energy stays the same. Now if you look at total energy of the system, if you introduce an electric field,
I guess all orbitals gain energy. Just guessing, because it's quite pointless.
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guy
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Ok so MO is a better theory.
My question is because the there are two views of orbital splitting I've seen and I want to know which one is the right one. Theres one where the eg
is +6Dq and the t2g is -4Dq. The one in high-school textbooks show both raised (one more than the other).
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Nick F
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In an octahedral crystal field, the dx2-y2 and dz2 orbitals are each raised in energy by 3 delta (oct) and the dxy, dyz and dxz orbitals are each
lowered in energy by 2 delta (oct), relative to the ion in a uniform (spherical) crystal field.
This is because the lobes of the dx2-y2 and dz2 orbitals are pointing along the axes, in other words, they are pointing directly at the ligands, and
so they experience the greatest electronic repulsion from the ligand fields, and so they are raised in energy.
The other orbitals must be lowered in energy to ensure that the total energy of the ion remains the same as it would be in a spherical crystal field,
which is higher in energy than the free ion.
So in the diagram you have where both sets of orbitals are raised, this is probably relative to the free ion. In the other diagram, it's probably
shown relative to the ion in a spherical crystal field.
But yeah, an MO approach is better...
[Edited on 9-8-2006 by Nick F]
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