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Tetrahedrally adapted metal d-orbitals?

  1. Feb 2, 2005 #1
    Usually the d-orbitals are displayed adapted to octahedral symmetry. But as I understand it, one could just as well picture degenerate representations of the same orbitals in other high symmetries.

    Does anyone have a link to a page containing pictures of the d-orbitals in the form adapted to tetrahedral symmetry? I reckon three of them should be "more combinable" with tetrahedrally coordinated ligands, since in ligand-field theory the d-orbitals split into one set of doubly and of triply degenerate orbitals, of which the triply degenerate ones form MOs with the (T1g I think) Td adapted orbitals of the ligands.
    It would be fun to see what the tetrahedral representations of the d-metals would look like (especially the two that won't combine).
  2. jcsd
  3. Feb 2, 2005 #2


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    I have found one link, you may view it from http://pages.pomona.edu/~wes04747/handout/fig3.gif [Broken]. It reads that sp3 hybrid orbitals of the ligand combine with metal's 3d, 4s, and 4p orbitals to form four bonds.
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  4. Feb 2, 2005 #3


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    I too have heard of the rare instances of hybrid d-orbitals with tetrahedral symmetry, but was simply told that the reason for the symmetry was pretty complex. Never followed up on that, though.
  5. Feb 2, 2005 #4
    OK, pretty much like in McCleverty's Oxford Primer on the 3d metals. I was hoping for some visualisation of the shapes of metal LCAOs but it seems that it is actually hard to explain this bonding?

    Shriver&Atkins apply CFT to both tetrahedral and octahedral complexes but LFT only to octahedral complexes. I don't really know why they treat CFT as much as they do, since it gives a totally confusing picture of what is going on. (The t2g set having less overlap - "repulsion" :bugeye:!! - with the ligands and hence being lower in energy, which really is a nonphysical explanation, since it is the overlap of the eg set with ligand orbitals that lowers the total energy of the electrons of the complex, although raising the energy of the non- or partly filled metal-centred eg orbital set.) McCleverty does a much better job just relating to CFT as a simple but wrong model, and thus not spending too much time on it, while Shriver&Atkins actually try an argument like the doubly degenerate pair pointing less directly at the ligands and hence being lower in energy than the t2 triplet. The more I think of it, the more stupid it occurs to me to "overuse" this totally wrongful model in this way. If there were more symmetries than octahedral, or octahedral-derived, and tetrahedral, this argument would definitively fail. One shouldn't argue in this way, since this actually makes MO-based theories harder to grasp instead of making it easier. Since they're going to mention LFT anyway, they could've waited with treating tetrahedral complexes until LFT for octahedral complexes had been treated, and the same for all other effects of the splitting, like ligand-field splitting parameters, magnetism, Jahn-Teller effect, this all could be mentioned in the ligand-field paragraph as well, just making the CFT a parenthesis for introducing one way to "justify" the splitting of octahedral compexes.

    Hmm... my Holleman-Wiman has arrived, how come I haven't checked that supreme book yet? :rolleyes:
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  6. Feb 2, 2005 #5
    I think this link really proves that one could fully pedagogically introduce LFT without starting with CFT, once MO theory has been treated (which thus also could be done in Shriver-Atkins). In this link it is even used as an illustration of how to use MO theory! My compliments to the lecturer of this general chemistry course!
    In an inorganic course, however, one should of course be made aware of the fact that there is a "simpler" theory with a different name, that is not based on molecular orbitals but rather assuming repulsion between atomic orbitals (whether containing electrons or not!!). Since some students may have had the above excellent lecturer in their general chemistry course, while others may have come in contact with CFT only, an inorganic chemistry textbook should mention BOTH first, maybe quickly review the theories' main implications, and then mainly treat LFT, by applying the MO strategies treated in an earlier chapter of the same book.
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  7. Feb 2, 2005 #6
    Hmmm... some confusion of terms: it seems as if swedish Gunnar Hägg and german Holleman&Wiberg use the term ligand field theory for what Shriver calls crystal field theory, whereas what he calls ligand field theory is referred to simply as molecular orbital theory for d-metal complexes.
  8. Feb 2, 2005 #7
    So nobody has seen pictures of the shapes of tetrahedrally adapted atomic d-orbitals?
    Aren't the familiar d(z2), d(x2-y2), d(xz), d(xy) and d(yz) orbitals just one of several possible sets of atomic d-orbital shapes? Or have I misunderstood this point?
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