Octahedral Reference

Lowest terms Compressed bipyramid Regular octahedron Elongated bipyramid Tetrahedron 

The first excited CFT 2 g is well separated from the ground 2T2g by the energy A0 = 10Dq. The spin-orbit coupling splits the ground term into / (ground) and / 7 multiplets separated by S0/hc = 237 cm 1, which results from the calculations in the complete d1 space spanned by ten functions (Table 70). 

This value is perfectly reproduced by the model-Hamiltonian treatment performed in the first iteration. The above value, however, deviates slightly from the spin-orbit treatment restricted to the ground T-term that predicts a gap of S0 = (3/2) , yielding S0/hc = 232 cnr1. The discrepancy originates in ignoring the Cl of the two rs(2T2g) and r8(2 g) multiplets. 

The 6x6 secular equation within the ground 2T2g term (Table 13) is fully factored and yields analytical formulae for the energy levels (Table 30) also in the case of the different axial (kz) and equatorial (kx) orbital reduction fac- 

Case 1 Orbitally degenerate ground term 2T2g needs a solution of a 6 x 6 secular equation 

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The name octahedral refers to the fact that the six bonds point toward the corners of an octahedron. 

Because of the constraint D = X(gz - gx)f2, with negative D we have the g-factor asymmetry gz < gx < ge (X > 0). These features are well reproduced by the SH formalism. A reasonable TIP value is predicted as well, xtip = 2.96 x 10 9 m3 mol and this matches the high-temperature extrapolation TIP (> 1000). This value is a bit lower relative to the octahedral reference since it involves an increased value of the second excitation energy Axy. 

With the octahedral reference three d-d electron transitions could be detected by the electron spectra A0(3A2g 3T2g) = 10Dq, A2(3A2g 3Tig(F)), and A3(3A2g 3Tig(P)). Sometimes, the spin-forbidden transitions can also... 

The tetragonal and/or trigonal distortions of the octahedral reference can be described by the operators... 

The basic molecular shapes are shown in Figure 8-6. Note that the words tetrahedral and octahedral refer to the four- and eight-sided solids formed by connecting the ligand atoms, not to the coordination numbers, which are 4 and 6, respectively. 

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