The d orbitals

The extension to / orbitals offers nothing new in principle. They do not occur in many useful examples, so they will not be considered in this book. 

The organic chemist who has had enough can skip to the next chapter with little loss he or she has probably already done so. 

These six geometrically identical AOs evidently have the same energy as long as the quadrupolar field is vanishingly small, but only five of them can be independent. We can get rid of the redundancy by taking orthogonal combinations of two of them, conventionally those shown in a and b of Fig. 2.10. The symmetry properties of the orbitals are the same as those of their indices, so we simply combine the latter  

The positive combination is not a new orbital but merely the negative phase of dx2-y2. The negative combination, usually abbreviated to d 2 after its dominant term, reproduces Fig. 2.10 g, the fifth independent d AO. 

The familiar splitting of the d level in square-planar, tetrahedral or octahedral molecules and complex ions are less conveniently discussed in terms of a quadrupolar field, because their symmetry is higher than T 2h- The symmetry point groups involved D4/1, Tj and O/i, are non-commutative by which is meant that the product of two symmetry operations may depend on the order in which they are carried out. The relevant properties of non-commutative symmetry point groups are illustrated below with the smallest of the three, D4/1. It contains just twice the number of sym-ops as its subgroup The relation 

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The detailed theory of bonding in transition metal complexes is beyond the scope of this book, but further references will be made to the effects of the energy splitting in the d orbitals in Chapter 13. 

The d orbital splitting depends on the oxidation state of a given ion hence twb complex ions with the same shape, ligands and coordination number can differ in colour, for example... 

The splitting of the d orbital energy levels when ligands are bonded to a central transition atom or ion has already been mentioned (p. 60). Consider the two ions [Co(NH3)g] and [Co(NH3)g] we have just discussed. The splitting of the d orbital energy levels for these two ions is shown in Figure 13.2. 

The ions and have 7 and 6 d electrons respectively. Where there are orbitals of the same (or nearly the same) energy, the electrons remain unpaired as far as possible by distributing themselves over all the orbitals. In the case of [CofNHj) ] -, the energy split in the d orbitals due to octahedral attachment of the six... 

More recent developments are based on the finding, that the d-orbitals of silicon, sulfur, phosphorus and certain transition metals may also stabilize a negative charge on a carbon atom. This is probably caused by a partial transfer of electron density from the carbanion into empty low-energy d-orbitals of the hetero atom ( backbonding ) or by the formation of ylides , in which a positively charged onium centre is adjacent to the carbanion and stabilization occurs by ylene formation. 

Eor transition metals the splitting of the d orbitals in a ligand field is most readily done using EHT. In all other semi-empirical methods, the orbital energies depend on the electron occupation. HyperChem s molecular orbital calculations give orbital energy spacings that differ from simple crystal field theory predictions. The total molecular wavefunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals are the residue of SCE calculations, in that they are deemed least suitable to describe the molecular wavefunction. 

The unique nature of the electronic configuration of copper, which contributes to its high electrical and heat conductivity, also provides chemical properties intermediate between transition and 18-sheU elements. Copper can give up the 4s electron to form the copper(I) ion [17493-86-6] or release an additional electron from the >d orbitals to form the copper(Il) ion [15158-11-9]. 

N occupy an sp lone-pair in the plane of the ring (or the plane of the local PNP triangle) as in Fig. 12.26a. The situation at P is less clear mainly because of uncertainties concerning the d-orbital energies and the radial extent (size) of these orbitals in the bonding situation (as distinct from the free atom). In so far as symmetry is concerned, the sp lone-pair on each N can be involved in coordinate bonding in the jcy plane... 

Class-b acceptors on the other hand are less electropositive, have relatively full d orbitals, and form their most stable complexes with ligands which, in addition to possessing lone-pairs of electrons, have empty n orbitals available to accommodate some charge from the d orbitals of the metal. The order of stability will now be the reverse of that for class-a acceptors, the increasing accessibility of empty d orbitals in the heavier halide ions for instance, favouring an increase in stability of the complexes in the sequence... 

Table 24.3 lists representative examples of the compounds of these elements in their various oxidation states. The wide range of the oxidation states is particularly noteworthy. It arises from the fact that, in moving across the transition series, the number of d electrons has increased and, in this mid-region, the d orbitals have not yet sunk energetically into the inert electron core. The number of d electrons available for bonding is consequently maximized, and not... 

Frontier Molecular Orbital theory is closely related to various schemes of qualitative orbital theory where interactions between fragment MOs are considered. Ligand field theory, as commonly used in systems involving coordination to metal atoms, can be considered as a special case where only the d-orbitals on the metal and selected orbitals of the ligands are considered. 

As six ligands approach a central metal ion to form an octahedral complex, they change the energies of electrons in the d orbitals. The effect (Figure 15.10, p. 419) is to split the five d orbitals into two groups of different energy. 

To see why this splitting occurs, consider what happens when six ligands (e.g., HzO, CN-, NH3) approach a central metal cation along the x-, y-, and z-axes (Figure 15.9). The unshared electron pairs on these ligands repel the electrons in the d orbitals of the cation. 

Hie fifth-row transition elements have general similarity to the fourth-row transition elements. The electron structure is essentially the same except that the 4d orbitals are filling instead of the 3d orbitals. Near the beginning of the sixth-row transition elements there is a change the/ orbitals begin to fill to form fourteen elements before the d orbitals can be occupied to give the typical transition elements. This chapter will dis-... 

Like palladium(II) and platinum(II), gold(III) has the d8 electronic configuration and is, therefore, expected to form square planar complexes. The d-orbital sequence for complexes like AuC14 is dx2 yi dxy > dvz, dxz > dzi in practice in a complex, most of these will have some ligand character. 

The structural features and the spectroscopic characteristics of the thiirene dioxide system (22) are of special theoretical interest since, on the basis of analogy with cyclopropenone (23), it is a possible nonbenzenoid aromatic system with all the physical and chemical implications involved. Aromatic and/or conjugative effects, if any, require transmission through the d-orbitals of the sulfur atom. 

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