Angular overlap model parameters

Hoggard PE (2003) Angular Overlap Model Parameters 106 37-57 Hopfl H (2002) Structure and Bonding in Boron Containing Macrocycles and Cages. 103 1-56... 

Crystal field splitting parameter, 2, 309 Crystal field theory, 1, 215-221 angular overlap model, 1, 228 calculations, 1, 220 generality, 1,219 low symmetry, 1,220 /-orbital, 1, 231 Crystal hydrates, 2, 305,306 bond distances, 2, 307 Crystals... 

The term angular overlap model was first used in 1965 to describe a more general treatment, which may also be called the model (12,13). The relative energies of the orbitals in a partly-filled /-shell are expressed in terms of the parameters ex (X = a, rr, etc.), whose coefficients can be calculated from the geometry of the system. The eK model was developed from perturbation theory, but is equivalent to the E2 model when only a-overlap is considered, and to the Yamatera-McClure model for orthoaxial chromophores with linear ligators. The notation ex is often used, where ... 

We shall briefly recall the definitions of some of the parameters used both in the C. F. and angular overlap models. 

Jorgensen has given a classification of the energy levels in NiXs chromophores of Dsh symmetry using the angular overlap model [59). Assuming values for the parameters e< , e, and e which are the same as... 

Figure 14 Energies of a metal d-orbitals as a function of geometry using the parameters of the angular overlap model.

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. 

Table 23 General Relationship Between Angular Overlap Model and Ligand Field Parameters...

This is the issue of transferability, which is one of the reasons that the Angular Overlap Model was conceived. Except for Dq, and sometimes parameters that express differences in Dq, ligand field parameters tend not to be transferable from one complex to another. Thus they carry little chemical information. AOM parameters become useful to the extent that consistency can be demonstrated. Then trends within series of related ligands will have meaning, and comparisons with nonspectroscopic properties can be undertaken. 

Additional uncertainty arises from the inadequacy of the model itself, both specific and nonspecific. The nonspecific refers to the failure of the angular overlap model itself to adequately represent the electronic states of the molecule, and in particular, the inconsistencies in AOM parameter values that result. This can only be assessed by compiling enough data to evaluate those inconsistencies. Specific defects are those in which the metal-ligand interaction is treated unsatisfactorily, but can be improved within the framework of the model. An example is when the 7t-interaction is treated as isotropic, but is actually anisotropic. Specific defects can be assessed immediately by making the proposed alteration, and this works particularly well if no additional parameters are required to make the alteration. 

As a last remark, it should be mentioned that also a few evaluations of the crystal-field parameters of Pr3"1" in LaCH in the scope of the angular overlap model have been made. Urland et al. (1985) andUrland (1989) used the angular overlap model to calculate the crystal-field splittings of LaCHiPr3"1" under pressure. In addition, Gregorian et al. (1989) derived the parameters of both models and found that both approaches were capable to successfully describe the high-pressure results. 

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