Crystal-field terms

In octahedral symmetry, the F term splits into Aig + T2g + Tig crystal-field terms. Suppose we take the case for an octahedral nickel(ii) complex. The ground term is 2g. The total degeneracy of this term is 3 from the spin-multiplicity. Since an A term is orbitally (spatially) non-degenerate, we can assign a fictitious Leff value for this of 0 because 2Leff+l = 1. We might employ Van Vleck s formula now in the form... 

S is the ionic spin and D, ID, and a are crystal field parameters describing the strength of the axial, the rhombohedral, and the cubic crystal field terms, respectively. The coordinate system of the cubic crystal field (ij, rj, g) may differ from that used to describe the axial and the rhombohedral crystal field interactions (x,y,z). 

Table 1.2 Non-vanishing crystal field terms (Stevens formalism) for common lanthanide point symmetries.

Depending upon the size of the crystal field term //cf in comparison to these three free ion terms, different approaches can be considered to the solution of Equation (5.1) by perturbation methods ... 

Electron configuration of Bp" is (6s) (6p) yielding a Pip ground state and a crystal field split Pap excited state (Hamstra et al. 1994). Because the emission is a 6p inter-configurational transition Pap- Pip. which is confirmed by the yellow excitation band presence, it is formally parity forbidden. Since the uneven crystal-field terms mix with the (65) (75) Si/2 and the Pap and Pip states, the parity selection rule becomes partly lifted. The excitation transition -Pl/2- S 1/2 is the allowed one and it demands photons with higher energy. 

The second contribution on the right-hand side is the shift in the on site energy due to the neighbouring atomic potentials. In the spirit of our earlier treatment of diatomic molecules we will neglect this crystal field term. It does not fundamentally alter the band structure of either transition metals or semiconductors. The band structure, E(k), can, therefore, be written within the approximation as... 

Angular Momentum Among Crystal-Field Terms... 

Classification of Crystal-field Terms and Multiplets Double Groups... 

The lowest crystal-field terms IR(parent terms), energy 2Eg(D, T2g), 0 2T2g(D), 0 2B2g(D, T2g), 0... 

The lowest crystal-field terms IRfparent terms), energy ... 

Relaxation of complicated ligands may occur as a step in both pathways. Diebler and Eigen 461 indicated the ways in which such mechanisms could be analysed using fast reaction methods. Several studies of Ln(III) complex formation and of the formation of Ln(III) mixed complexes have been analysed. Generally the dissociative mechanism is considered to dominate and we are then concerned with the water exchange rate. Several studies have shown that the rate decreases from La(III) to Lu(III) but there seems to be a minimum rate around Tm(III). This is also seen in the rate of rotation of ligands on the surface of the ions, Fig. 7. There may be a small crystal field term, or another contribution to a tetrad -like effect from the 4f electron core. However in the hydrate the precise relationship between the inner and outer sphere water may also be important as we saw when we discussed the heat and entropy of complex ion formation. 

TABLE 2 Theoretical spin orbit and crystal field terms appearing in EQN (1) for InN. 

The term VP(o)P) in Eq. (27) is called the crystal field term. From Eqs. (29) and (31) it is clear that this term is invariant under all rotations of the global frame that correspond to symmetry operations on the lattice. As a... 

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