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Bill Harrison
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 Posted: Mon Jul 28, 2003 7:55 pm Post subject: Second-order JT distortion |
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Hello all,
Could somebody please point me to a reference for (or derive??)
a schematic MO diagram for an octahedral "complex" undergoing a
*second-order* Jahn-Teller distortion, e.g. a (nominal) regular TiO6
octahedron containing titanium(IV) distorting to a situation with one
short, four intermediate and one long Ti-O bond.
Thanks,
Bill |
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William David Thweatt
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| Posted: Mon Jul 28, 2003 7:59 pm Post subject: Re: Second-order JT distortion |
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Bill Harrison (w.harrison@abdn.ac.uk) wrote:
: Hello all,
: Could somebody please point me to a reference for (or derive??)
: a schematic MO diagram for an octahedral "complex" undergoing a
: *second-order* Jahn-Teller distortion, e.g. a (nominal) regular TiO6
: octahedron containing titanium(IV) distorting to a situation with one
: short, four intermediate and one long Ti-O bond.
Why not try a cross-referenced Citation Index search of "second-order"
with the original JT paper (Proc. Roy. Soc. London, Ser. A., v161 p220
(1937))?
--
--
William "Dave" Thweatt
Robert E. Welsh Postdoctoral Fellow
Chemistry Department
Rice University
Houston, TX
thweatt@ruf.rice.edu
dave.thweatt@us.army.mil |
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abc
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| Posted: Tue Jul 29, 2003 3:31 pm Post subject: Re: Second-order JT distortion |
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Bill Harrison wrote:
[quote]Hello all,
Could somebody please point me to a reference for (or derive??)
a schematic MO diagram for an octahedral "complex" undergoing a
*second-order* Jahn-Teller distortion, e.g. a (nominal) regular TiO6
octahedron containing titanium(IV) distorting to a situation with one
short, four intermediate and one long Ti-O bond.
Thanks,
Bill
Hello Bill,[/quote]
I thought about your problem overnight. So here is my conclusion:
If you start from an octahedral geometry Oh and move one atom along the
z-Coordinate nearer to the central atom and the other away from it,
the symmetry will be broken to C4v.
For some reason I will not use Oh but D4h to classify the orbitals and
vibrations.The orbitals dxz and dyz will span the Eg representation, the
orbital dxy the B1g. These three orbitals are originally degenerate,
because they span the T2g representation of Oh.
The orbital dx^2-y^2 spans the B2g representation and the orbital dz^2 A1g.
The movement of the two ligands, which I will call Vz, spans A2u. As these
ligands move on a line which lies in the nodal plane of the orbitals dxz,
dyz dx^2-y^2 and dxy ,
the energies of these orbitals will change very little.
The energy that changes most is that of dz^2.
Due to symmetry, the matrix element for the first order change in energy
<dz^2 Vz dz^2> vanishes, but the dz^2 orbital can mix with the pz orbital
which belongs to the symmetry A2u. As the p-Orbitals lie higher in energy
than the d-Orbitals the second order stabilization energy
|<dz^2 Vz pz>|^2/(E_dz^2-Epz) should be negative, corresponding to a
stabilization.
So the doubly degenerate Eg term under Oh splits into two levels, one
corresponding to dx^2-dy^2 which remains more or less unshifted, and the
level dz^2 whose energy lowers quadratically with Vz.
Hope that helps,
Florian |
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Bill Harrison
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| Posted: Tue Jul 29, 2003 7:00 pm Post subject: Re: Second-order JT distortion |
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Thanks everyone, for the very useful information.
Bill |
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