Molecular orbitals ligand field models

As indicated in Section 1. (i) our approach to the interpretation of the electronic spectra of the hexafluorometallates of the Ad and 5d series closely follows that employed previously (7), and need not be recapitulated in detail. The ligand field model is adopted for the interpretation of the d—d transitions, and the qualitative molecular orbital approach for the treatment of both these and, more particularly, the charge-... 

This behaviour is not easily explained in the molecular orbital approach but may be understood conceptually by recourse to the ligand field picture ). Thus the filling of the 3 d orbitals depends not only on their one-electron energies but also on the total electron-electron interactions between all the electrons within the 3 d levels. Since these electron-electron terms are not identical within the set of 3 d orbitals but depend upon the particular d orbitals that are occupied, the configurations E2g and Ajg(e ajg) possess different electronic repulsions, the former having the smaller values. In the ligand field model the state lies lowest provided EE2< 20B, and consequently with an estimated B value of about 500 cm , the fi state has lower energy than the Ajg state. 

Actually, the recent studies of transition-group spectra have shown that two different models cherished by many theorists— the electrostatic ligand field model and the valency-bond description (more specifically, the Pauling hybridization theory)—cannot be applied to the observed distribution of energy levels. On the other hand, the molecular orbital (M.O.) configurations give an excellent classification of all energy levels of all complexes and a unified description is obtained of all polyatomic molecules. 

An X-ray atomic orbital (XAO) [77] method has also been adopted to refine electronic states directly. The method is applicable mainly to analyse the electron-density distribution in ionic solids of transition or rare earth metals, given that it is based on an atomic orbital assumption, neglecting molecular orbitals. The expansion coefficients of each atomic orbital are calculated with a perturbation theory and the coefficients of each orbital are refined to fit the observed structure factors keeping the orthonormal relationships among them. This model is somewhat similar to the valence orbital model (VOM), earlier introduced by Figgis et al. [78] to study transition metal complexes, within the Ligand field theory approach. The VOM could be applied in such complexes, within the assumption that the metal and the... 

The obvious deficiency of crystal-field theory is that it does not properly take into account the effect of the ligand electrons. To do this a molecular-orbital (MO) model is used in which the individual electron orbitals become a linear combination of the atomic orbitals (LCAO) belonging to the various atoms. Before going into the general problem, it is instructive to consider the simple three-electron example in which a metal atom with one ligand atom whose orbital contains two electrons. Two MO s are formed from the two atomic orbitals... 

Complexes containing anions of the above formulation have attracted a large number of studies because of their alleged simplicity. This is illustrated by the central position such complexes have played in the evolution of crystal field, ligand field and molecular orbital models of bonding in transition metal complexes. 

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