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Complexes

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    Is there a way to determine how many high and low energy levels the degenerate d orbitals will split into, or is it just a case of having to learn it?
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    (Original post by Emissionspectra)
    Is there a way to determine how many high and low energy levels the degenerate d orbitals will split into, or is it just a case of having to learn it?
    Octahedral complexes split into 3 low (t2g) and 2 high (eg) orbitals

    Tetrahedral complexes split into 3 high and two low (although not exactly the same energy)

    Just learn it!
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    (Original post by charco)
    Octahedral complexes split into 3 low (t2g) and 2 high (eg) orbitals

    Tetrahedral complexes split into 3 high and two low (although not exactly the same energy)

    Just learn it!
    Will do, but just out of interest, is there a way to determine it systematically?
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    You can determine the splittings of the orbitals from the symmetry of the complex. This is beyond A level I'm afraid, but you can think of it simply like this:

    The easiest example is an octahedral complex. Let the z-axis run vertically (through two of the ligands). The  d_{z^2} orbital will point towards these ligands. This creates a favourable overlap, lowering the energy of this orbital. Similarly, the  d_{xy} and  d_{x^2-y^2} orbitals will point towards the 4 ligands in the x-y plane, lowering the energy of these orbitals. This gives us three orbitals with low energy. The  d_{xz} and  d_{yz} orbitals do not point towards the ligands and are thus higher in energy.
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    (Original post by Bradshaw)
    You can determine the splittings of the orbitals from the symmetry of the complex. This is beyond A level I'm afraid, but you can think of it simply like this:

    The easiest example is an octahedral complex. Let the z-axis run vertically (through two of the ligands). The  d_{z^2} orbital will point towards these ligands. This creates a favourable overlap, lowering the energy of this orbital. Similarly, the  d_{xy} and  d_{x^2-y^2} orbitals will point towards the 4 ligands in the x-y plane, lowering the energy of these orbitals. This gives us three orbitals with low energy. The  d_{xz} and  d_{yz} orbitals do not point towards the ligands and are thus higher in energy.
    I was under the impression that in an octahedral complex the ligands orient to be between the axes in order to minimise repulsions from the dxy, dxz and dyz orbitals.

    This lowers their energy in comparison to the d(x2-y2) and dz2, which (lying along the axes as they do) are relatively higher in energy due to repulsion effects.
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    (Original post by Bradshaw)
    You can determine the splittings of the orbitals from the symmetry of the complex. This is beyond A level I'm afraid, but you can think of it simply like this:

    The easiest example is an octahedral complex. Let the z-axis run vertically (through two of the ligands). The  d_{z^2} orbital will point towards these ligands. This creates a favourable overlap, lowering the energy of this orbital. Similarly, the  d_{xy} and  d_{x^2-y^2} orbitals will point towards the 4 ligands in the x-y plane, lowering the energy of these orbitals. This gives us three orbitals with low energy. The  d_{xz} and  d_{yz} orbitals do not point towards the ligands and are thus higher in energy.
    Haven't you got that a little bit wrong?

    The d orbitals are all raised in energy as the interaction between the ligand orbitals and the d orbitals is a destabilising one.

    In an octahedral complex, the z^2 and x^2-y^2 (eg set) are both raised in energy more than the others (xy, xz and yz - the t2g set). This is because if you consider the ligands to lie on each of the 3 axes, the eg set point straight at the ligands and are hence raised in energy, and the t2g set point between the ligands and are not raised in energy as much. You can also tell that the orbitals are split in this fashion by looking at the symmetry tables for the Oh point group. The way you described it doesn't give you the orbital degeneracies in the right way.

    (Original post by charco)
    x
    You're right... As far as I understand things.
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    (Original post by illusionz)
    Haven't you got that a little bit wrong?

    The d orbitals are all raised in energy as the interaction between the ligand orbitals and the d orbitals is a destabilising one.

    In an octahedral complex, the z^2 and x^2-y^2 (eg set) are both raised in energy more than the others (xy, xz and yz - the t2g set). This is because if you consider the ligands to lie on each of the 3 axes, the eg set point straight at the ligands and are hence raised in energy, and the t2g set point between the ligands and are not raised in energy as much. You can also tell that the orbitals are split in this fashion by looking at the symmetry tables for the Oh point group. The way you described it doesn't give you the orbital degeneracies in the right way.


    You're right... As far as I understand things.
    Yep silly me, I tried to do this without resorting to the character tables and it shows how much you can confuse your self!

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Updated: June 5, 2012
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