Jahn-Teller orbital ordering

Cooperative displacements of the oxygen atoms from the middle of a (180° - 0) M—0—M bond may be superimposed on the structural modifications introduced by the mismatch of the mean equilibrium (A—O) and (M—0) bond lengths. This situation was first proposed [12] for Mn(III) t e ions in LaMnOs and is now well-established where cooperative oxygen displacements remove a ground-state orbital degeneracy at a localized-electron configuration. This situation represents a cooperative Jahn-Teller orbital-ordering distortion. 

Fig. 4a-c. Cooperative oxygen displacements of oxygen towards one neighboring atom and away from the other found in low-temperature a CaFeOs (disproportionation) b PbTiOs (ferroelectric) c LaMnOs (Jahn-Teller orbital order). Cooperative rotations of the MOg/2 octahedra may coexist with these displacements... 

I = insulator, s.c. = semiconductor, cond. = conductor, AF = antiferromagnetic, F = ferromag-net, scf = strong-correlation fluctuations, J-T = cooperative Jahn-Teller orbital ordering, LS = J-T that maximizes orbital angular momentum, dis. = disproportionation 2(j = e + e, SDW/ CDW = spin/charge-density wave. 

Vibrational stmcture is, at best, only partially resolved. The stmcture in the first and second systems is complex which could be due, in part, to there being a Jahn-Teller effect in each of them. Such an effect may arise when a molecule is in an orbitally degenerate E (or T) state. The Jahn-Teller effect involves a distortion of the molecule in order to destroy the... 

The most recent theoretical study, by Alhrichs and co-workers, deals with the di(phosphino)carbene Id and (phosphino) (phosphonio)carbenes Ie,f.16 The optimized geometry of the di(phosphino)carbene Id is weakly bent (PCP angle 160.5°) and highly unsymmetrical Only one of the phosphorus centers (P1) is in a planar environment, and it is much more closely bonded to the carbenic center than the other one (P1C 1.533 and P2C 1.765 A). The atomic charges (P1 +1.0, C -0.8, P2 +0.6) indicate that the short P bond is a double bond reinforced by Coulombic attraction, while the nature of the molecular orbitals revealed a slight delocalization of the carbene lone pair into the low-lying a (P-N) orbitals of the two phosphino substituents. The distortion from the symmetrical structure can be viewed as a second-order Jahn-Teller effect. 

Oddershede s calculations were limited by the computational facilities and more recent calculations indicate that while Manne s ordering of the occupied molecular orbitals stays unchallenged, there is little significance to assign to virtual orbitals for an anion [6]. It was pointed out [5] that ionization from a degenerate state would lead to a distortion in the system due to the Jahn-Teller theorem. 

---