Crystal Field Theory CFT

The bonding in transition metal complexes has been described by three different theories crystal field theory (CFT), valence bond theory (VBT), and molecular orbital theory (MOT). Detailed descriptions of these three approaches are given in the standard inorganic texts and are not repeated here. However, some general statements concerning the applicability of these various bonding descriptions for metal 7r-complexes are noted. 

Thus the CFT formalism, while having the advantages of being relatively simple mathematically and giving an easily understood physical interpretation of the destruction of the fivefold degeneracy of the d orbitals under the influence of a nonspherically symmetrical electric field, clearly has only very limited applicability to the tremendous number of transition metal complexes that have been prepared and well characterized since Werner s time. 

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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. 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

The crystal field theory (CFT) was developed for crystalline solids by the physicist Hans Bethe in 1929. The model takes into account the distance separating the positively and... 

Crystal Field Theory (CFT) has also been used considerably to rationalize visible absorption spectra, hydration energies, stabilities of complexes, rates and mechanism of reaction, and redox potentials of transition element ions. These applications of CFT are summarized in a book by Basolo and Pearson 1B6). 

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 chapter, we discuss mostly the bonding in mononuclear homoleptic complexes ML using two simple models. The first, called crystal field theory (CFT), assumes that the bonding is ionic i.e., it treats the interaction between the metal ion (or atom) and ligands to be purely electrostatic. In contrast, the second model, namely the molecular orbital theory, assumes the bonding to be covalent. A comparison between these models will be made. 

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 1951, chemists trying to make sense of metal complex optical spectra and color returned to an emphasis on the ionic nature of the coordinate covalent bond. Coordination chemists rediscovered physicists Hans Bethe s and John van Vleck s crystal field theory (CFT),... 

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. 

The crystal field theory (CFT), an ionic bonding model, is focused on the d-orbital set and the way this degenerate set of five orbitals on the bare metal ion is split in the presence of a set of ligands into different energy levels. It provides a fair understanding of spectroscopic and magnetic properties. 

LFT originated as a purely electrostatic model - crystal-field theory (CFT) [18], in which d-electronic multiplets of transition metals are perturbed by ligands as point charges or point dipoles. The CF operator (Equation 1) acts within the space of Slater determinants (SD) composed of purely d-spin-orbitals in which two-electron energies are taken into account with the Coulomb operator and one-electron energies with a crystal-field potential (vcp), the first and second terms in Equation 1, respectively. 

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. 

Werner s coordination theory, with its concept of secondary valence, provides an adequate explanation for the existence of such complexes as [Co(NH3)6]Cl3-Some properties and the stereochemistry of these complexes are also explained by the theory, which remains the real foundation of coordination chemistry. Since Werner s work predated by about twenty years our present electronic concept of the atom, his theory does not describe in modem terms the nature of the secondary valence or, as it is now called, the coordinate bond. Three theories currently used to describe the nature of bonding in metal complexes are (1) valence bond theory (VBT), (2) crystal field theory (CFT), and (3) molecular orbital theory (MOT). We shall first describe the contributions of G. N. Lewis and N. V. Sidgwick to the theory of chemical bonding. 

Most of the transition metal oxides and salts may be treated as ionic crystals. The valence electrons of s symmetry (4s, 5s, or 6s) are stripped off. The metal forms an ion that is considerably smaller than the atom. The inner (n - l)d electrons (3d, 4d, or 5d) are degenerate in the central field approximation of the atom. In the next step, multiplets are formed (Section 2.4). In the third step, the transition metal ions interact with the crystal field, which is dominated by repulsion from the neighboring negative ions. This leads to a splitting of the 3d orbital energies. The theory describing the splitting of the electronic states in a crystal field is due to the American physicists Hans Bethe and John van Vleck and is called crystal field theory (CFT). 

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