Electrostatic crystal field model

Any computational treatment of TM systems must account for the LFSE. QM methods achieve this implicitly but d-electron effects must be explicitly added to MM (4). Some effects can be modeled within conventional MM. For example, low-spin d8 complexes are planar by virtue of the LFSE (21,22), but a planar structure can also be enforced using a normal out-of-plane term (22). However, the simplest general model for describing d-orbital energies is ligand field theory (LFT) (23) which was itself derived from the earlier electrostatic crystal field theory (CFT) (24) approach. 

According to the crystal field model, the crystalline electrostatic field of ligands in a crystal structure influences the 3d orbital energy levels of a central transition metal ion in a coordination site. There is a two-fold influence of temperature on a crystal structure. First, increased thermal motion results in increased amplitudes of atoms vibrating about their crystallographic positions. Second, thermal expansion causes small increases in interatomic distances, so that according to eq. 

Ligand field, like crystal field, theory is confined to the role of d orbitals, but unlike the crystal field model, the ligand field approach is not a purely electrostatic model. It is a freely parameterized model, and uses and Racah parameters (to which we return later) which are obtained from electronic spectroscopic (i.e. experimental) data. Most importantly, although (as we showed in the last section) it is possible to approach the bonding in d-block metal complexes by using molecular orbital theory, it is incorrect to state that ligand field theory is simply the application of MO theory. ... 

Figure 24.28 Representation of the metal-ligand bond in a complex as a Lewis acid-base interaction. The ligand, which acts as a Lewis bas donates charge to the metal via a metal hybrid orbital. The bond that results is strongly polar, with some covalent character. It is often sufficient to assume that the metal-ligand interaction is entirely electrostatic in character, as is done in the crystal-field model. 

In the crystal-field-theory formulation of a metal complex, we consider the ligands as point charges or point dipoles. The crystal-field model is shown in Fig, 9-8. The point charges or point dipoles constitute an electrostatic field, which has the symmetry of the complex. The effect of this electrostatic field on the energies of the metal d orbitals is the subject of our interest, /... 

The electrostatic and spin-orbit parameters for Pu + which we have deduced are similar to those proposed by Conway some years ago (32). However, inclusion of the crystal-field interaction in the computation of the energy level structure, which was not done earlier, significantly modifies previous predictions. As an approximation, we have chosen to use the crystal-field parameters derived for CS2UCI6 (33), Table VII, which together with the free-ion parameters lead to the prediction of a distinct group of levels near 1100 cm-. Of course a weaker field would lead to crystal-field levels intermediate between 0 and 1000 cm-1. Similar model calculations have been indicated in Fig. 8 for Nplt+, Pu1 "1 and Amlt+ compared to the solution spectra of the ions. For Am t+ the reference is Am4" in 15 M NHhF solution (34). 

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