Ligand field theory free ions

The role of electronic structure in Mn and Co site preference and mobility can to some extent be understood through ligand-field theory (LFT). LET qualitatively explains how the degeneracy of the 3d orbitals is broken when a free TM ion is surrounded by coordinating anions. The ligand-field splitting of d orbitals in octahedral and tetrahedral coordination is pictured in Figure 6. ... 

We intend in this chapter to consider the manner in which the symmetry of the chemical surroundings of an ion determines the effect of this environment on the energy levels of the ion. In the crystal field and ligand field theories we often wish to regard the effect of the environment as a small perturbation on the states of the free ion. For the benefit of readers not acquainted with certain general features of the electronic structures of free atoms and ions, a brief resume of the subject is given in this section. 

Ligand Field Theory 6.4 FREE-ION TERMS IN LIGAND FIELDS2 5-81 62... 

The parameter A does not affect the d-orbital splitting and as discussed above is absorbed in the orbital energy we are therefore left with the two usual interelectron repulsion parameters for -configurations of ligand field theory F2, F4 or B, C, but these should not be equal to the free ion values because the orbitals ixvXs) eigenfunctions of the mean potential in the complex rather than in the free ion. 

The most interesting applications of ligand field theory have been made when there are several non-bonding electrons. Consider, for instance, an atom or ion with five d electrons in an octahedral ligand field. When the field is weak the electrons will, as in the free atom, occupy different orbitals singly (Fig. 77(a), (b)). But if the field is increased, the dy electrons will eventually fall into d orbitals, the drop in orbital energy outweighing the increase in mutual repulsion of the electrons (Fig. 77(c)). The occupation... 

Thus in order to calculate an energy-level diagram and/or details of magnetic behavior in ligand field theory, one proceeds in the same manner as in crystal field theory except that, instead of assuming the free-ion values for A, B and C, one either assumes somewhat smaller ones or leaves them as parameters to be evaluated from the experimental observations. In this way all the computational and conceptual advantages of the simple electrostatic theory are preserved while allowance is made—in an indirect and admittedly artificial way—for the consequences of finite orbital overlap. One also bears in mind that there are other consequences of the overlap, for example, electron delocalization. 

The energies of the terms for the d -cF electron configurations of the transition metals as free ions, assuming OB = 4.7. [Reproduced from Figgis, B. N. Hitchman, M. A. Ligand Field Theory and Its Applications, Wiley-VCH New York, 2000. This material is reproduced with permission of John Wiley Sons, Inc.]... 

The structure of arene sandwich compounds (like that of cyclopentadienyl, cycloheptatrienyl, etc., derivatives) and the character of the M-arene bond may also be considered on the basis of ligand field theory assuming C ,v symmetry of the compound (cf. Chapter 9). The ligands connected to the metal via carbon atoms create a strong field. Therefore, the splitting parameters are large. The nephelauxetic coefficients P = BIBq, where B is the Racah parameter for the complex and Bq is the Racah parameter for the free metal ion (5o and B represent interelectron repulsion), generally assume values 0.5 0.1 for metallocenes and arene sandwich complexes. Low values of nephelauxetic coefficients indicate considerable covalent character of the metal-hydrocarbon bond. 

This is why our discussion of crystal and ligand theories has been exemplified by complexes formed by elements of the first transition series. Had we included spin-orbit coupling within the crystal field model (and in a more complete treatment this would have been done), within the crystal field model it would have appeared with its free-ion value. Not surprisingly, in ligand field theory it becomes a parameter which, characteristically, is found to have a value somewhat lower than that found for the free ion. 

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