Ligand Field Theory LFT

The effects of the bonding electrons upon the d electrons is addressed within the subjects we call crystal-field theory (CFT) or ligand-field theory (LFT). They are concerned with the J-electron properties that we observe in spectral and magnetic measurements. This subject will keep us busy for some while. We shall return to the effects of the d electrons on bonding much later, in Chapter 7. 

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. ... 

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. 

In this description the quantity AKt or 10Z)t (oct) of CFT is identified with the tlgn e MO separation. This is the basis of the ligand field theory (LFT) concept. 

The directionality in the bonding between a d-block metal ion and attached groups such as ammonia or chloride can now be understood in terms of the directional quality of the d orbitals. In 1929, Bethe described the crystal field theory (CFT) model to account for the spectroscopic properties of transition metal ions in crystals. Later, in the 1950s, this theory formed the basis of a widely used bonding model for molecular transition metal compounds. The CFT ionic bonding model has since been superseded by ligand field theory (LFT) and the molecular orbital (MO) theory, which make allowance for covalency in the bonding to the metal ion. However, CFT is still widely used as it provides a simple conceptual model which explains many of the properties of transition metal ions. 

In solid-state laser materials, such as ruby (chromium doped alumina, AljOjiCr " ) (1) and emerald (chromium doped beryl, Be,Al,(Si03)5 Cr ) (2), transitions between multiplets of impurity states are utilized. These states mainly consist of 3d orbitals of the impurity chromium ions. For the analysis of these multiplet structures, the semi-empirical ligand-field theory (LFT) has been frequently used (3). However, this theory can be applied only to the high symmetry systems such as O, (or T ). Therefore, the effect of low symmetry is always ignored in the analysis based on the LFT, although most of the practical solid-state laser materials actually possess more or less distorted local structures. For example, in ruby and emerald, the impurity chromium ions are substituted for the aluminum ions in the host crystals and the site symmetry of the aluminum ions are C, in alumina and D, in beryl. Therefore, it is important to clarify the effect of low symmetry on the multiplet structure, in order to understand the electronic structure of ruby and emerald. 

The application of organometallic compounds in medicine, pharmacy, agriculture and industry requires the accurate determination of these metals as part of their application. Most % complexes characterised by direct carbon-to-carbon metal bonding may be classified as organometallic and the nature and characteristics of the n ligands are similar to those in the coordination metal-ligand complexes. The -complex metals are the least satisfactorily described by crystal field theory (CFT) or valence bond theory (VBT). They are better treated by molecular orbital theory (MOT) and ligand field theory (LFT). There are several uses of metal 7i-complexes and metal catalysed reactions that proceed via substrate metal rc-complex intermediate. Examples of these are the polymerisation of ethylene and the hydration of olefins to form aldehydes as in the Wacker process of air oxidation of ethylene to produce acetaldehyde. 

Such discrepancies between empirical observations and theory evenmally prescribed a need to describe the bonding in complexes of various symmetries not only taking into account the electrostatic interactions but also the overlap interactions of the molecular orbitals. This theory is referred to as the ligand field theory (LFT). Consider... 

C. J. Ballhausen contributed mightily to coordination chemistry with his groundbreaking 300 page book on ligand field theory (LFT) [4], which was written in... 

O. 916 calibrated to the difference between the 4Aig and 6Aig terms. Such an agreement validates the use of the ligand-field theory (LFT), which has been extended by the author and... 

A holistic molecular orbital theory description of bonding in complexes provides a more sophisticated model of bonding in complexes, leading to ligand field theory (LFT), which deals better with ligand influences. Both CFT and LFT reduce to equivalent consideration of d electron location in a set of five core d orbitals. 

The basic difficulty with the CFT treatment is that it takes no account of the partly covalent nature of the metal-ligand bonds, and therefore whatever effects and phenomena stem directly from covalence are entirely inexplicable in simple CFT. On the other hand, CFT provides a very simple and easy way of treating numerically many aspects of the electronic structures of complexes. MO theory, in contrast, does not provide numerical results in such an easy way. Therefore, a kind of modified CFT has been devised in which certain parameters are empirically adjusted to allow for the effects of covalence without explicitly introducing covalence into the CFT formalism. This modified CFT is often called ligand field theory, LFT. However, LFT is sometimes also used as a general name for the whole gradation of theories from the electrostatic CFT to the MO formulation. We shall use LFT in the latter sense in this Chapter, and we introduce the name adjusted crystal field theory, ACFT, to specify the form of CFT in which some parameters are empirically altered to allow for covalence without explicitly introducing it. 

Ligand field theory (LFT) can be considered as a combination of crystal field theory (CFT) and molecular orbital (MO) theory [25]. Unlike in CFT where interactions between ligands and center metal atoms are described with electronic interactions, LFT takes into account the overlap between atomic orbitals as ligands approach a metal center. Thus in LFT, the metal-ligand bonding is by its very nature partially covalent. 

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