Qualitative molecular orbital diagrams

Covalency of ligands clearly influences the positions and intensities of absorption bands in crystal field spectra of oxides and silicates, so that it is pertinent to discuss the types of covalent bonds that exist when transition elements are present in mineral structures. In this section, the more qualitative aspects of molecular orbital theory are described. 

The fundamental premise of molecular orbital theory is that the overlap of orbitals depends on the spatial and symmetry properties of metal and ligand orbitals. Principles of group theory are used to ascertain which orbitals may or may not overlap, based on symmetry and directional requirements. The results of these considerations may be summarized as follows. 

Conversely, electrons that occupy any of the antibonding molecular orbitals are predominantly metal electrons. Any electrons in the t2g orbitals will be purely metal electrons when there are no n molecular orbitals. Thus, the t2g and antibonding e orbitals are predominantly of metal 3d orbital character. 

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Figure B A qualitative molecular orbital diagram for ferrocene. The subscripts g and u refer to the parity of the orbitals g (German gerade, even) indicates that the orbital (or orbital combination) is symmetric with respect to inversion, whereas the subscript u (ungerade, odd) indicates that it is antisymmetric with respect to inversion. Only orbitals with the same parity can combine.

Having considered the case of the H20 molecule, we would like to be able to use the same procedures to construct the qualitative molecular orbital diagrams for molecules having other structures. To do this requires that we know how the orbitals of the central atom transform when the symmetry is different. Table 5.5 shows how the s and p orbitals are transformed, and more extensive tables can be found in the comprehensive books listed at the end of this chapter. 

If we now consider a planar molecule like BF3 (D3f, symmetry), the z-axis is defined as the C3 axis. One of the B-F bonds lies along the x-axis as shown in Figure 5.9. The symmetry elements present for this molecule include the C3 axis, three C2 axes (coincident with the B-F bonds and perpendicular to the C3 axis), three mirror planes each containing a C2 axis and the C3 axis, and the identity. Thus, there are 12 symmetry operations that can be performed with this molecule. It can be shown that the px and py orbitals both transform as E and the pz orbital transforms as A, ". The s orbital is A/ (the prime indicating symmetry with respect to ah). Similarly, we could find that the fluorine pz orbitals are Av Ev and E1. The qualitative molecular orbital diagram can then be constructed as shown in Figure 5.10. 

FIGURE 17.18 A qualitative molecular orbital diagram for a tetrahedral complex. 

Therefore, in the final analysis, the quadruple bond consists of one a bond, two it bonds, and one S bond. The configuration in which the Cl atoms are in eclipsed positions provides maximum overlap. From the rather intuitive analysis provided here, it is possible to arrive at a qualitative molecular orbital diagram like that shown in Figure 21.23 to describe the Re-Re bond. 

Fig. 1 Qualitative molecular orbital diagrams for the alkene fragment of benzoquinone and dioxygen highlighting the key differences in their respective frontier orbitals...

Various theoretical methods and approaches have been used to model properties and reactivities of metalloporphyrins. They range from the early use of qualitative molecular orbital diagrams (24,25), linear combination of atomic orbitals to yield molecular orbitals (LCAO-MO) calculations (26-30), molecular mechanics (31,32) and semi-empirical methods (33-35), and self-consistent field method (SCF) calculations (36-43) to the methods commonly used nowadays (molecular dynamic simulations (31,44,45), density functional theory (DFT) (35,46-49), Moller-Plesset perturbation theory ( ) (50-53), configuration interaction (Cl) (35,42,54-56), coupled cluster (CC) (57,58), and CASSCF/CASPT2 (59-63)). 

Figure 6.5 Qualitative molecular orbital diagram of [Au(phosphine)2]+ species.

Construct a qualitative molecular orbital diagram lor CIO and compare it to the one (resented in Figure 531 for NOT. 

Fig. 15.33 Qualitative molecular orbital diagram fora metallocene. Occupation of the orbitals enclosed in the box depends on the identity of the metal, for ferrocene it is e L-[From Lauher, J. W. Hoffmann. R. J. Am. Cfie/n. Soc. 1976. 98, 1729-1742. Reproduced with permission.)...

Figure 1. Partial and qualitative molecular orbital diagram of the Cr(CN)g -molecule. Circles indicate electron occupation.

Fig. 6. Qualitative molecular orbital diagram for the Cp2M2(/r-CO)3 molecules 8-13 based on calculations for Cp2Fe2(M-CO)3 (8) (79). The S level is the HOMO for the Group 7 molecules whereas there are two unpaired electrons in the ir level for the Group 8 species.

A qualitative molecular orbital diagram involving the valence electrons in FeF was presented by Allen and Ziurys [244] and is shown in figure 10.89. The main covalent... 

Figure 10.89. Qualitative molecular orbital diagram for FeF, involving the fluorine 2p and iron 4.v. 3 d atomic orbitals [244], The energies of the iron non-bonding orbitals (15, 9 a, 4 it) are very close to that of the 10cr antibonding orbital.

Figure 7. Qualitative molecular orbital diagram for the Tp CufNO) complexes (based on analogous diagrams for MNO 10 systems described in references 61 and 64.) (Reproduced from reference 53. Copyright 1993 American Chemical Society.)...

After all the basis orbitals have been labelled by their symmetry behavior, a qualitative molecular orbital diagram may be drawn (Figure 20). 

Nickel tetracarbonyl, Ni(CO)4, is an 18-electron species. Using a qualitative molecular orbital diagram, explain the stability of this 18-valence electron molecule. (Reference A. W. Ehlers, S. Dapprich, S. V. Vyboishchikov, and G. Frenking, Organometallics, 1996,15, 105)... 

Fig. 16. Qualitative molecular orbital diagram of hexasila-Dewar ben/ene.

Fig. 16.32 (a) Siructure of SjN7 and (b) qualitative molecular orbital diagram. [From Chivers, T. Oakley. R. T. Top. Curr. Cliem. 1982. 102, 117. Reproduced with permission.]... 

Fig. 16.60 Qualitative molecular orbital diagram for dinuciear rhenium and molybdenum complexes. All of the bonding molecular orbitals are filled for [ReiClsJ " (c) and a bond order of 4 results from one

Fig. 14. Qualitative molecular orbital diagram for quadruply bonded metal-metal species for which the electronic configuration of the metal ion is d (04, nomenclature)...

Before describing the Fenske-Hall method itself, we will examine an example of the behavior described above. Our example will be ferrocene (Tri -C5H5)2Fe, whose qualitative molecular orbital diagram is shown in Scheme 40.1. The principal bonding... 

Fig. 20-42. A qualitative molecular orbital diagram for an M(CO)6 or [M(CN)6]"-compound. [Adapted from H. B. Gray and N. A. Beach, J. Amer. Citem. Soc., 1963,...

Fig. 20-44. A qualitative molecular orbital diagram for a square ML4 complex. The arrangement here should be essentially correct for PtClJ-.

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