Jahn-Teller axis

An interesting aspect of the bridging hydride structure concerns the direction of the Jahn-Teller axis on nickel. With the hydride, there are five ligands around nickel and one of these are therefore forced to... 

The symmetry argument actually goes beyond the above deterniination of the symmetries of Jahn-Teller active modes, the coefficients of the matrix element expansions in different coordinates are also symmetry determined. Consider, for simplicity, an electronic state of symmetiy in an even-electron molecule with a single threefold axis of symmetry, and choose a representation in which two complex electronic components, e ) = 1/v ( ca) i cb)), and two degenerate complex nuclear coordinate combinations Q = re " each have character T under the C3 operation, where x — The bras e have character x. Since the Hamiltonian operator is totally symmetric, the diagonal matrix elements e H e ) are totally symmetric, while the characters of the off-diagonal elements ezf H e ) are x. Since x = 1, it follows that an expansion of the complex Hamiltonian matrix to quadratic terms in Q. takes the form... 

Since the d orbitals have quadrupolar character, this distortion must be modelled using a point electric quadrupole with the shape of the d i orbital oriented with a negative pole along the z axis and the positive pole in the x-y equatorial plane (Fig. 8.7(a)). No fluxes have been calculated for Jahn-Teller distorted cations, either with or without the quadrupolar contribution but, as in the other cases, the experimental bond valences are expected to provide a good approximation to the bond fluxes. 

A Jahn-Teller distortion should also occur for configuration d. However, in this case the occupied orbital is a t g orbital, for example d, this exerts a repulsion on the ligands on the axes x and y which is only slightly larger than the force exerted along the z axis. The distorting force is usually not sufficient to produce a perceptible effect. Ions like TiF or MoClg show no detectable deviation from octahedral symmetry. 

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