Sinclair- Band Theory and Jahn Teller Effect and Insulators Flashcards
Jahn-Teller theorem
Electron configurations with unequal occupancy of degenerate orbitals are not stable
Jahn-Teller effect
A geometric distortion of a non-linear molecular system that reduces it’s symmetry and energy. The distortion is most commonly observed among octahedral complexes where the two axial bonds can be shorter or longer than the equatorial bonds. Effects depends on electronic state of system (for TMOs corresponds to number of d electrons on TM cation).
JT elongation
Axial bonds are longer than equatorial. Stabilisation of d orbitals with a z component means all orbitals with a z component have lower energy than the other on in t2g and eg. Other orbitals are destabilised (higher energy). Lowers electrostatic repulsion between electron pair on non-metal ligand and any electrons in orbitals with z component thus lowering energy of complex.
JT compression
Equatorial bonds longer than axial. De-stabilisation of d orbitals with z component (higher energy). Orbitals without z component in t2g and eg stabilise (lower energy)
What are elongation and compression effects dictated by?
The amount of overlap between the metal and ligand orbitals
How does distortion from JT effect vary?
Varies greatly depending on type of metal and ligands. In general the stronger the metal-ligand orbital interactions are, the greater the chance for a JT effect to be observed
Structure of La2CuO4
Hybrid of rocksalt (AX) and perovskite (ABX3) so is (LaO)(LaCuO3). The Cu is 2+ with d9. Orthorhombic cell. Corner sharing CuO6 octahedra which are elongated
What does band theory predict about La2CuO4?
Predicts it to be a metal. Is d9 cation. Orbitals with z component stabilise. Full band for t2g orbitals. Full narrow band for d(z^2) orbital. Half full narrow band for d(x^2-y^2) orbital. This is wrong as it is actually an antiferromagnetic insulator. In narrow bands electron-electron repulsion effects become significant.
Features of Mott-Hubbard model
Electron-electron repulsion effects cause narrow band to split into 2 sub bands. Lower band is lower Hubbard band (LHB) and upper band is upper Hubbard band (UHB). The total narrow band has width W. The peaks of the sub bands are separated by energy gap U. Ef in middle of U
When is something a metal or insulator for Mott-Hubbard model?
If W>U there will be finite overlap between sub bands and metallic ground state will result.
If W is less than U the LHB and UHB will not overlap and the material will be insulating
How to modify W in TMOs
Chemical doping (size and/or charge that alter bond lengths/angles and/or [e/h]). Can switch metal to insulator or reverse
Mott-Hubbard model for La2CuO4
W is less than U and the e-e repulsion effects are strong and two, one electron bands colour rather than the formation of a half filled d(x2-y2) band. Means the single d(x2-y2) electron is strongly localised on the Cu ions and that a large activation energy U inhibits any electron migration (and therefore conduction) via the Cu ions
Why is La2CuO4 AFMI?
Spin-spin correlations that arise through PEP serve to render the insulating ground state antiferromagnetic. Superexchange mechanism between Cu2+ 3d(x^2-y^2) ions via O2- 2px and 2py ions.
What does the covalency between Cu and O ions mean?
Mixing of O 2p-band and Cu 3d(x^2-y^2) LHB in the final band picture.
Overall band picture for La2CuO4
LHB for Cu 3d9 in middle and sticks out of O 2p band which is wider. UHB above and empty with no overlap. Energy gap Eg between top of O 2p band and bottom of UHB less than U so is known as a charge transfer insulator (CTI) rather than a Mott-Hubbard insulator