Strong-field case

The foregoing discussion applies to complexes that are weak-field cases. Spectral analysis for strong-field cases is somewhat different and will not be discussed here. For complete analysis of the spectra of strong-field complexes, see the book by A. B. P. Lever, Inorganic Electronic Spectroscopy, listed in the references at the end of this chapter. 

If, in addition to the cubic crystal field, a component of lower symmetry is present, such as one having tetragonal or trigonal symmetry (as for the Al sites in a-AUOa), further splitting will occur as shown in Fig. 24. Crystal field splittings for other configurations in both the weak and strong field cases are summarized in a review article by Moffitt and Ballhausen... 

With these considerations in mind lei us consider in turn the two extreme possibilities, known respectively as the strong-field and die "weak-ficld case. If A Is very large the tendency for electrons to go inlu separate orbitals will be outweighed by their tendency to occupy the orbitals (as against the eg orbitals) in circumstances where these two tendencies conflict. In the strong-field case, therefore, a complex with up to six d electrons will have all these in ti, orbitals with the maximum number of unpaired spins consistem with the restriction to the 12, orbitals. As examples we may take the hcxacyanoferrates(U) and (111) which possess six and live d electrons, respectively, all in r,e orbitals wilh the maximum number of unpaired spins consistent wilh the restriction to the ti, orbitals. As examples we may take the hexacyanoferrales(ll) and bexaeyanoferrates III) which possess six and five d electrons respectively all in (2, orbitals. The former has no unpaired electrons and the latter one. The next four electrons will then enter the e, orbitals the first two will go into different e, orbitals with their spins parallel as in the octahedral complexes of NiJ+ In Co2+ there is just one eg electron. 

SOLUTION (a) In the strong-field case, all five electrons enter the t2g-orbitals and to do so, some of them must pair (20). There is one unpaired electron in this configuration, (b) In the weak-field case, the five electrons occupy all five orbitals without pairing (21). There are now five unpaired electrons. 

Fig. 90 Effective magnetic moment for nearly-octahedral d7, S = 3/2 complexes. Left-. Figgis theory for the 4Tig pattern (k = 1, X < 0, A = 1 - strong field case) solid line - v = 0 (octahedron) dashed - v = -10 (compressed bipyramid, Aax >0) dot-dashed - v = + 10 (elongated bipyramid, Aax < 0). Right calculation in a complete d7space for a weak-field Co(II) complex on tetragonal distortion with F4(xy) = 5000 cm-1 dashed - compressed bipyramid with F4(z) = 6000 cm-1 solid - octahedron with F4(z) = 5000 cm-1 dot-dashed - elongated bipyramid with F4(z) = 4000 cm-1...

The weak-field case like the free ion obeys Hund s rule while in the strong-field case Hund s rule is overcome by the increased relative stability of the t-type relative to the e-type orbitals... 

A third case arises when the perturbation from the ligand field is intermediate between the weak-field case and the strong-field case. There is no sharp dividing line between the three cases given here. The calculational approach to be used depends on the identities of the transition metal ion and the ligands. The results of this third case have been presented by Figgis. Applications have also been discussed by Mabbs and Machin. ... 

The strong-field case gives one unpaired electron, which agrees with the experimental observation. The CN- ion is a strong-field ligand toward the Fe3+ ion. 

The crystal field model allows us to account for the differences in the magnetic properties of Co(NH3)63 + and CoF63. The Co(NH3)63+ ion is known to be diamagnetic and thus corresponds to the strong-field case, also... 

V). c. In aqueous solution, Co3 +, forms the hydrated transition metal complex, Co(H20)63 +. In both complexes, Co(H20)g3+ and Co(en)33+, cobalt exists as Co3+, which has 6 d electrons. Assuming a strong-field case, the d-orbital splitting diagram for each is... 

The same is true in (FeCl4) , although the positions of d and d orbitals are reversed and, in admitting covalency, the appropriate hybrids would be 4s 4p (tetrahedral). Such systems are often described as spin-free, outer orbital or high spin. In potassium hexacyanoferrate(III), however, [Fe(CN)g] occurs, and the moment (2.5 fjt indicates only one free spin evidently this is the strong-field case (Fig. 77(c)). The 3d orbitals are thus made available for bonding, and d sp hybrids overlap with, and partly accept, the carbon lone pairs of the CN groups, to produce six covalent bonds. Such systems are called spin-paired, inner orbital, or low spin complexes. 

Strong-field case relatively large orbital splitting... 

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