Ligand field potential

In this approach, the ligand field potential is expressed as... 

Since MM is intrinsically bond centered, the most convenient way to express the LFSE is based on the angular overlap model of Schaeffer and Jorgensen (29). The total ligand field potential, Vlf> is assumed to be the sum of contributions from the M-L bonds each modeled by AOM parameters describing separate a and n interactions as illustrated in Fig. 4. 

LFMM does have a small computational overhead. A 5 x 5 matrix describing the ligand field potential, Vlf, must be constructed... 

Fig. 12. Ligand-field potential curves of a Cr3+ ion in an octahedral field. Splittings are as in Figure 11, and Q is the breathing vibrational mode. Dq = Dqx s 1200 cm-1 at Q = 6eq(M2).

It is common to express a general ligand field potential as a superposition of spherical harmonics (34) and the expressions for the octahedral potential,... 

Let us return then to the problem of low symmetry in transition metal complexes. The most direct and unassuming approach would be to write a symmetry-based expansion of the ligand field potential in terms of spherical harmonics. For a completely unsymmetrical molecule (C,) this would be written as... 

The static Jahn—Teller distortions appear as structural changes which may be associated with the origin of low symmetry terms in the ligand field potential. Here, the separation of the orbital... 

Angular Variables and the Ligand Field Potential Matrix.116... 

In the AOM formalism the ligand field potential matrix in Oh symmetry is... 

Approximate tetragonal symmetry is often also assumed for chelate complexes of the type trans-M(A A)2B2. Without this assumption, but specifying that the B ligands have a cylindrically symmetric 7t-interaction with the metal, the ligand field potential matrix has the general form... 

The key question is what significance can be attached to parameters, specifically AOM parameters and angular variables, derived from spectroscopic data. As these examples were intended to illustrate, it is useful to divide this question into two parts, whether or not a calculation is actually performed this way (1) can the spectroscopically independent elements of the ligand field potential matrix be uniquely determined from the data (2) can the AOM parameters and angular variables be uniquely determined from the spectroscopically independent elements of the potential matrix ... 

The obvious answer to the second part is that the number of spectroscopically independent elements in the ligand field potential matrix is the upper limit to the number of AOM parameters and angular variables that may be determined from them. No matter how many experimental peak positions have been measured, it is the form of the ligand field potential matrix that determines how much information can be extracted. If there are more parameters than spectroscopically independent matrix elements, it may still be possible to... 

Thus, the 5x5 ligand field potential matrix is the key to the acquisition of meaningful information. For some high symmetry situations traditional ligand field theory has defined parameters that are linear combinations of these matrix elements [9]. Some of them have chemical significance, while others do not. Transferability to other complexes, particularly complexes with lower symmetry or different angular geometry, is quite problematic. 

The six elements can be used to generate the n-electron ligand field energies, to which interelectronic repulsion and spin-orbit coupling, which are already defined on the dxy, dX2, dyz, dx2 y2, dz2 basis, are added. Alternatively, the five eigenvalues can be used, but an additional term is necessary to define the correct linear combinations of the dx2 y2 and dz2 orbitals on which to evaluate interelectronic repulsion and spin-orbit coupling. Either way, there are still six total, or five spectroscopically independent, terms in the ligand field potential matrix. 

If the A group is a saturated amine only three parameters remain eaA, a, and p. It should be possible to determine all three from the ligand field potential matrix, or directly from the spectroscopic fit. Our own experience with the ethylenediamine complex, [Cr(en)3]3+, revealed another problem [10] the effects of a and P on the ligand field potential matrix elements and on the calculated band positions, while not identical, are similar enough that they cannot be practically disentangled. It was, however, possible to determine a and P in [Cr(en)3]3+ by using circular dichroism spectra (see Sect. 7). 

D4h (matrix M3) symmetry it does happen that one parameter must be fixed, but that is because there are no off-diagonal elements in the ligand field potential matrix. 

Anisotropic 7r-bonding and phase coupling can each lead to splittings far in excess of what is predicted by classical ligand field theory. When the AOM matrix M10 is used, the ligand field potential matrix for M(A-A)3 assumes the form... 

As elaborated in detail in Ref. (5) there are two principal intensity mechanisms for dimer excitations. The single-ion mechanism is based on the combined action of spin-orbit coupling and an odd-parity ligand field potential at the Cr center. It is by this mechanism that spin-forbidden transitions obtain their intensity in mononuclear complexes. The pair mechanism, on the other hand, is restricted to exchange-coupled systems. It leads to the selection rules AS = 0,... 

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