Crystal field theory octahedral

On the basis of crystal field theory octahedral and ef systems are expected to react at comparable rates. Yet [Cr(H20)6] " is inert and [Ni(H20)6] " is labile (half-lives for water exchange are 40 h and 3 x 10 s, respectively). Account for this difference in rate behavior. 

This is an immediate consequence of the lowering of the symmetry as, even in the regular octahedral geometry, group theory tells us that the highest dimension of the irreducible representation is three. This is the basis of Crystal Field Theory, whose deeply symmetry-based formalism was developed by Bethe in 1929 [16]. 

Figure 5.6 Energy level diagram of the splitting of the J-orbitals of a transition metal ion as a result of (a) octahedral co-ordination and (b) tetrahedral coordination, according to the crystal field theory. (From Cotton and Wilkinson, 1976 Figure 23-4. Copyright 1976 John Wiley Sons, Inc. Reprinted by permission of the publisher.)...

Symmetry considerations derived from group theory predict three main absorption-bands for Cr + in an octahedral environment and a number of low-intensity quartet-doublet-transitions in addition. The energies of the corresponding levels are calculated by means of crystal-field theory to be those of table 2 for the special choices AjB = 20 and 30 respectively ). 

Co(II) in chloroform (40), In this latter case, the AF difference is about 5 kcal/mole, so the Ni-Co AF difference is smaller. Compare this with the 20 kcal/mole site-preference energy for octahedral Ni(II) over Co(II), according to crystal-field theory [for example, (56)], The fundamental assumption of crystal-field theory, of course, is that the radial factors in cation-coordination-sphere relations are constant, which is tantamount to saying that bonding does not change. As we have seen in deriving Eq. (24), binding factors are very important (8) and, as the above numerical relations confirm, play by far the dominant role. 

In crystal field theory each ligand is approximated as a point charge or a point dipole and each metal-ligand interaction is taken to be purely electrostatic. So our problem is reduced to one of investigating the effect of point charges (or point dipoles) arranged tetrahedrally or octahedrally about an electron in a dai y or a dXI orbital. 

Another factor comes into play here. In the first coordination sphere, deviations in metal-ligand bond distances are normally small enough to be neglected. The nearest 14 K+ ions lie at seven separate distances, from 4.3 to 6.0 A. The variation in the magnitude of the perturbation with distance must be considered, and it is not straightforward. Classical crystal field theory shows an inverse fifth power dependence of Dq on distance from the metal, but this result is specific to octahedral symmetry, in which lower order dependencies drop out. For individual perturbers we have proposed a dependence of the form aR-3 + bR-5 for both e and e [7]. For counterions we also suggest that the n contribution and the R-5 part of the a contribution can be neglected. 

Crystal field theory d-orbital splitting in octahedral and tetrahedral complexes... 

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