Ligand field theory octahedral fields

FIGURE 16.36 I1ie tear-shaped objects are representations of the six ligand atomic orbitals that are used to build the molecular orbitals of an octahedral complex in ligand field theory. They might represent s- or p-orbitals on the ligands or hybrids of the two. 

The successful rationalization of these transition-metal inverse spinel structures in terms of the relative LFSE s of tetrahedral and octahedral sites is another attractive vindication of ligand-field theory as applied to structure and thermodynamic properties. Once again, however, we must be very careful not to extrapolate this success. Thus, we have a clear prediction that LSFE contributions favour tetrahedral over octahedral coordination, except for d" with n = 0, 5 or 10. We do not expect to rationalize the relative paucity of tetrahedral nickel(ii) species relative to octahedral ones on this basis, however. Many factors contribute to this, the most obvious and important one being the greater stabilization engendered by the formation of six bonds in octahedral species relative to only four bonds in tetrahedral ones. Compared with that, the differences in LSFE s is small beer. Why , one asks, was our rationalization of spinel structures so successful when we neglected to include consideration of the bond count The answer is that cancellations within the extended lattice of the spinels tend to diminish the importance of this term. 

Warren KD (1984) Calculations of the Jahn-Teller Coupling Constants for d Systems in Octahedral Symmetry via the Angular Overlap Model. 57 119-145 Warren KD (1977) Ligand Field Theory off-Orbital Sandwich Complexes. 33 97-137 Warren KD (1976) Ligand Field Theory of Metal Sandwich Complexes. 27 45-159 Watson RE, Perlman ML (1975) X-Ray Photoelectron Spectroscopy. Application to Metals and Alloys. 24 83-132... 

From a consideration of the combination of ligand and metal orbitals, it should be apparent that the overlap is much more effective in an octahedral complex (in which orbitals are directed at ligands) than in a tetrahedral complex (where orbitals are directed between ligands). The result is that the energy difference between the e and t2 orbitals in a tetrahedral complex is much smaller than that between the t2g and eg orbitals in an octahedral complex. As we saw when considering the two types of complexes by means of ligand field theory, At is only about half as large as A0 in most cases. 

At an early stage in the development of ligand field theory, it was found that A the splitting parameter for tetrahedral MX4, should be equal to (4/9) of A0, the splitting parameter for octahedral MX6, and experimental data are in good agreement with this prediction. However, this takes no account of the fact that the M—X distance in tetrahedral MX4 is usually some 8—10% shorter than in octahedral MX6. In the pointcharge crystal field model, A is proportional to R-5, so that if the difference in R between MX4 and MX6 is taken into account, we predict (At/A0) to be 0.6—0.7, compared with the experimental value of about 0.5. An AOM treatment (131) leads to better results, since here we find ... 

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. ... 

Jorgensen (55) considers that the absorption bands in the near ultraviolet of yellow [Co(CN)sH]3- and [Co(CN)sCH3]3 described by ligand field theory unequivocally indicate the spectroscopic oxidation state cobalt(III) in the octahedral chromophores (56) CofllllCsH and Co(III)C6 comparable to other [Co(CN)5X] . On the other hand, when T1+ reacts with [CofCNjs] to form the dimer (54) [(NC)5CoTlCo(CN)5] , the spectroscopic oxidation state is no longer clearcut. 

Many additional studies have since been made. A summary of the results for a number of octahedral complexes is given in Table 10.5. The predictions of ligand field theory are clearly borne out by the results, which show pronounced depopulation of the field-destabilized e g orbitals and increased population of the stabilized t2g(eg, ag) orbitals relative to the distribution in the high-spin spherical atom. 

The extension to non-octahedral complexes is possible, but must be carried out with great care The orbitals chosen can be expressed as a linear combination of the usual orbitals for an octahedron, and electron-electron repulsions can then be calculated from those for the octahedral case. It is not necessarily adequate for tetrahedral complexes of the first row transition elements, to use ligand field theory in the strong field limit, even for powerful ligands in V(mesityl)4 the ligand field splitting is only 9250 cm ... 

Ligand-field theory predicted (10, 22) that tetrahedral nickel(II) complexes should be unstable with respect to octahedral ones, at least so long as the two extra ligands were available. This arises because, if one accepts the d-orbital center of gravity as an energy-zero (a point which should be raised more often), the crystal-field stabilization of an octahedral complex works out to be 0.84 A greater than that of a tetrahedral complex with... 

An interesting and useful method of theoretical treatment of certain properties of complexes and crystals, called the ligand field theory, has been applied with considerable success to octahedral complexes, especially in the discussion of their absorption spectra involving electronic transitions.66 The theory consists in the approximate solution of the Schrddinger wave equation for one electron in the electric field of an atom plus a perturbing electric field, due to the ligands, with the symmetry of the complex or of the position in the crystal of the atom under consideration. 

Two main aspects of the HDW approach are important for the present discussion. One aspect is that the model is valid only in the absence of orbital angular momentum contributions to the system, so that its use has been broadly restricted to (say) binuclear complexes of iron(LLl), octahedral nickel(II), or distorted octahedral copper(II). The other aspect concerns the fact that the parameter is a global parameter of the system sequestering many contributions from various ligands and orbitals and, in this respect, may be compared with how Dq in ligand-field theory represents the net effect of electrostatic and covalent (o and rr) effects in the tjg — eg orbital splitting. Attempts to localize our conception of the exchange phenomenon have been made by various... 

The familiar set of the three t2g orbitals in an octahedral complex constitutes a three-dimensional shell. Classical ligand field theory has drawn attention to the fact that the matrix representation of the angular momentum operator t in a p-orbital basis is equal to the matrix of — if in the basis of the three d-orbitals with t2g symmetry [2,3]. This correspondence implies that, under a d-only assumption, l2 g electrons can be treated as pseudo-p electrons, yielding an interesting isomorphism between (t2g)" states and atomic (p)" multiplets. We will discuss this relationship later on in more detail. 

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