Orbitals tetragonally distorted octahedral

A quantitative consideration on the origin of the EFG should be based on reliable results from molecular orbital or DPT calculations, as pointed out in detail in Chap. 5. For a qualitative discussion, however, it will suffice to use the easy-to-handle one-electron approximation of the crystal field model. In this framework, it is easy to realize that in nickel(II) complexes of Oh and symmetry and in tetragonally distorted octahedral nickel(II) complexes, no valence electron contribution to the EFG should be expected (cf. Fig. 7.7 and Table 4.2). A temperature-dependent valence electron contribution is to be expected in distorted tetrahedral nickel(n) complexes for tetragonal distortion, e.g., Fzz = (4/7)e(r )3 for com-... 

Several of the transition metals have ions with a single d-clcctron (see Table 3.3). In tetragonally distorted octahedral (D4h) symmetry, the unpaired electron is in the dq,-orbital and the -values are given by... 

For a d9 (Cu11) ion in tetragonally distorted octahedral symmetry (D4h), the unpaired electron is in the Cu dx y orbital if the distortion is such that the bonds along the z-axis are elongated. Thus,... 

Analogous expressions apply to crystal field states for electronic configurations involving these orbitals (cf. fig. 3.13). These energy separations are shown in fig. 3.21. All three parameters, Dq(eq)y Dt and Ds, may be determined experimentally provided that energies of three absorption bands originating from transition metal ions in tetragonally distorted octahedral sites occur in the crystal field spectra. Equation (3.15) yields the Dq( a) parameter, so that the mean Dq parameter, Dq(m) may be calculated from... 

For a small distortion, a and h should have the octahedral values of a2 = % and b2 = %. Using these values, the first-order terms in Eq. (49) become identical to those in Eq. (40) for a tetragonal distortion. The second-order terms contributed by the eg orbitals are quite different, however. This difference shows up markedly when we examine Eq. (49) in the limit of 7] < 1, where gl and g become... 

Fjg. 11,12 An octahedral complex (a) undergoing axis elongation such that it becomes tetragonally distorted (bj and finally reaches the square planar limit (c). The a i (d ) orbital may lie below the e idn and dy ) orbitals in the square planar complex... 

Fig. 11.47 Alteration of octahedral orbital energies (center) under tetragonal distortion (a) z ligands oui (b) ligands bi. Drawing is not lo scale fi > >...

Figure 29.2 (a) Octahedral and (b) tetrahedral crystal fields represented as point charges around a central ion. Arrows show the effect of a tetrahedral distortion to the crystal field, (c) d-Orbital energy level diagrams for octahedral crystal field and octahedral crystal field with tetragonal distortion, and (d) tetrahedral crystal field and tetrahedral crystal field with tetragonal distortion. 

On small tetragonal distortion the situation resembles the octahedral pattern there is a need for solving the 9x9 secular equation for the ground state % manifold. With a stronger axial CF the ground CFT is 3A2g (Aax > 0) and is further split by the spin-orbit to A and A multiplets. Now the ZFS appears in the form... 

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