Transition metal complexes molecular orbitals

The importance of hybridization (see Addendum 3.11), between d-, s- and p-metal orbitals in chemical bonding is easily understood for the molecular organometallic transition-metal complexes. The bonding in the tetrahedral Ni(C0)4 complex, for instance, can best be understood by initially considering the 5d-atomic orbitals doubly occupied with 10 electrons. 

Dioxygen activation in transition metal complexes in the light of molecular orbital calculations. R. Boca, Coord. Chem. Rev., 1983, 50,1-72 (245). 

Molecular orbital theory of transition metal complexes. D. A. Brown, W. J. Chambers and N. J. Fitzpatrick, Inorg. Chim. Acta, Rev., 1972, 6, 7-30 (193). 

Koga, N., and K. Morokuma, Ab initio molecular orbital studies of catalytic elementary reactions and catalytic cycles of transition-metal complexes. Chem. Rev., 91, 823-842 (1991). 

The redox ability of a metal complex will be considered in the context of its molecular orbital composition and spin state. In this regard, Figure 1 shows the molecular orbital diagrams for the most common geometries encountered in transition metal complexes. 

Fig. 5. The molecular orbital scheme for d square planar transition metal complexes.

Fenske, R. F. Semi-empirical molecular-orbital theory for transition-metal complexes. Inorg. Chem. 4, 33 (1965). 

Complexes of transition metal ions with a formally empty d shell often show intense broadband emission with a large Stokes shift of 10,000-20,000 cm k The most important examples for minerals are VO ", WO ", MoO " and TiOg . Atomic orbitals s,p, d of the central atom andp orbitals of oxygen form molecular orbitals of the complexes (Fig. 5.60). The excited state is considered to... 

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... 

Jean, Y. Molecular Orbitals of Transition Metal Complexes. OUP Oxford,... 

Application of LC AO-MO ideas to transition metal complexes faces no special restrictions (13, 17, 25, 37, 69, 236). Molecular orbitals are expressed as linear combinations of 1-electron atomic wave functions,... 

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. 

For conciseness, the title of this chapter is simply Ligand Field Theory. However, many of the principles which will be developed are as much a part of crystal field theory and the molecular orbital theory of transition metal complexes as they are of ligand field theory. Indeed the three theories are very closely related, and hence it seems advisable to begin this chapter with a brief, historically oriented discussion of the nature of these theories. 

Ligand field theory may be taken to be the subject which attempts to rationalize and account for the physical properties of transition metal complexes in fairly simple-minded ways. It ranges from the simplest approach, crystal field theory, where ligands are represented by point charges, through to elementary forms of molecular orbital theory, where at least some attempt at a quantum mechanical treatment is involved. The aims of ligand field theory can be treated as essentially empirical in nature ab initio and even approximate proper quantum mechanical treatments are not considered to be part of the subject, although the simpler empirical methods may be. 

In the next chapter we shall discuss molecular orbital theory as applied to transition metal complexes. Since we shall be dealing with d orbitals, the power of the symmetry methods developed up to this point will be clearly shown. 

The transition metal ions possess a very stable set of d orbitals, and it is likely that d orbitals are involved in bonding in all transition metal complexes, regardless of structure. The common structures that use d valence orbitals for forming a bonding molecular orbitals are square-planar, tetrahedral, and octahedral. Examples of these structures are given in Figure 8-1. 

The valence orbitals taken for a molecular-orbital calculation of a transition metal complex are the nd, (n + l)s, and (n + l)p metal orbitals and appropriate a and n functions of the ligands. Many of these valence orbitals are not individually basis functions for an irreducible representation in the symmetry under consideration. Symmetry basis functions transforming properly must be constructed, by methods analogous to those used throughout this volume. The results for a number of important symmetries are tabulated in this volume in various places, as follows ... 

It is apparent that the molecular orbital theory is a very useful method of classifying the ground and excited states of small molecules. The transition metal complexes occupy a special place here, and the last chapter is devoted entirely to this subject. We believe that modem inorganic chemists should be acquainted with the methods of the theory, and that they will find approximate one-electron calculations as helpful as the organic chemists have found simple Hiickel calculations. For this reason, we have included a calculation of the permanganate ion in Chapter 8. On the other hand, we have not considered conjugated pi systems because they are excellently discussed in a number of books. 

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