Valence Bond Approaches

We will use the valence bond approach extensively m our discussion of organic molecules and expand on it shortly First though let s introduce the molecular orbital method to see how it uses the Is orbitals of two hydrogen atoms to generate the orbitals of an H2 molecule... 

SECTION 1.1. VALENCE BOND APPROACH TO CHEMICAL BONDING... 

The hybridization concept can also be applied to molecules containing double and triple bonds. The descriptive valence bond approach to the bonding in ethylene and... 

We said in Section 1.5 that chemists use two models for describing covalent bonds valence bond theory and molecular orbital theory. Having now seen the valence bond approach, which uses hybrid atomic orbitals to account for geometry and assumes the overlap of atomic orbitals to account for electron sharing, let s look briefly at the molecular orbital approach to bonding. We ll return to the topic in Chapters 14 and 15 for a more in-depth discussion. 

Monte Carlo simulations [17, 18], the valence bond approach [19, 20], and g-ology [21-24] indicate that the Peierls instability in half-filled chains survives the presence of electron-electron interactions (at least, for some range of interaction parameters). This holds for a variety of different models, such as the Peierls-Hubbard model with the onsite Coulomb repulsion, or the Pariser-Parr-Pople model, where also long-range Coulomb interactions are taken into account ]2]. As the dimerization persists in the presence of electron-electron interactions, also the soliton concept survives. An important difference with the SSH model is that neu-... 

The valence-bond approach may be used to provide a qualitative account of the /lmax values, and hence the hues, of many dyes, particularly those of the donor acceptor chromogen type. The use of this approach to rationalise differences in colour is illustrated in this section with reference to a series of dyes which may be envisaged as being derived from azobenzene, although in principle the method may be used to account for the colours of a much wider range of chemical classes of dye, including anthraquinones (see Chapter 4), polymethines and nitro dyes. 

The spectral data for a further group of donor-acceptor aminoazoben-zenes are given in Table 2.3. The valence-bond approach may be used to provide a good qualitative account of the data in the table. Some relevant resonance structures, which may be used to explain the 2max values of cyano compounds 16a-d, are shown in Figure 2.9. 

The PPP-MO method is suitable for the treatment of large molecules, does not present major computing demands and programs are now routinely used as a tool to calculate the colour properties of dyes. Unlike the HMO method, it handles heteroatomic species well. The method has been remarkably successful in calculating /lmax values for a wide range of dyes from virtually all of the chemical classes. For example, the method provides a reasonably accurate account of substituent effects in the range of aminoazobenzene dyes, including compounds 15a-f and 16a-f which have been discussed in terms of the valence-bond approach in the previous section of this chapter. 

Table 2.4 shows a comparison of the experimental and PPP-MO calculated electronic spectral data for azobenzene and the three isomeric monoamino derivatives. It is noteworthy that the ortho isomer is observed to be most bathochromic, while the para isomer is least bathoch-romic. From a consideration of the principles of the application of the valence-bond approach to colour described in the previous section, it might have been expected that the ortho and para isomers would be most bathochromic with the meta isomer least bathochromic. In contrast, the data contained in Table 2.4 demonstrate that the PPP-MO method is capable of correctly accounting for the relative bathochromicities of the amino isomers. It is clear, at least in this case, that the valence-bond method is inferior to the molecular orbital approach. An explanation for the failure of the valence-bond method to predict the order of bathochromicities of the o-, m- and p-aminoazobenzenes emerges from a consideration of the changes in 7r-electron charge densities on excitation calculated by the PPP-MO method, as illustrated in Figure 2.14. 

Such a "general form of wave function is easily written explicitly for each set of values of N, S, and MS- Any appropriate form of approximate wave functions, like determinantal functions composed of one-electron functions ( molecular spin orbitals ), the "bond eigenfunctions" used in the valence bond approach, and so on, is shown to fulfil this requirement. 

In this chapter, the descriptions of molecular structure will be primarily in terms of a valence bond approach, but the molecular orbital method will be discussed in Chapter 5. As we shall see, construction of molecular orbital diagrams for polyatomic species is simplified by making use of symmetry, which will also be discussed in Chapter 5. 

Although the simple valence-bond approach to the bonding in coordination compounds has many deficiencies, it is still useful as a first attempt to explain the structure of many complexes. The reasons why certain ligands force electron pairing will be explored in Chapter 17, but it is clear that high- and low-spin complexes have different magnetic character, and the interpretation of the results of this technique will now be explored. 

The valence-bond approach to this multiple bonding can be shown in terms of the resonance structures ... 

In other words, the valence bonds approach is suitable for compounds showing purely ionic or purely covalent behaviour we require molecular orbitals for a more mature description of the bonding in such materials. So the yellow colour of silver iodide reflects the way the bonding is neither ionic nor covalent. We find, in fact, that the charge clouds of the silver and iodide ions overlap to some extent, allowing change to transfer between them. We will look at charge transfer in more detail on p. 459. 

The first calculations on a two-electron bond was undertaken by Heitler and London for the H2 molecule and led to what is known as the valence bond approach. While the valence bond approach gained general acceptance in the chemical community, Robert S. Mulliken and others developed the molecular orbital approach for solving the electronic structure problem for molecules. The molecular orbital approach for molecules is the analogue of the atomic orbital approach for atoms. Each electron is subject to the electric field created by the nuclei plus that of the other electrons. Thus, one was led to a Hartree-Fock approach for molecules just as one had been for atoms. The molecular orbitals were written as linear combinations of atomic orbitals (i.e. hydrogen atom type atomic orbitals). The integrals that needed to be calculated presented great difficulty and the computations needed were... 

In 1976 Warshel and Levitt introduced the idea of a hybrid QM/MM method [23] that treated a small part of a system (e.g., the solute) using a quantum mechanical representation, while the rest of the system, which did not need such a detailed description (e.g., the solvent) was represented by an empirical force field. These hybrid methods, in particular the empirical valence bond approach, were then used to study a wide variety of reactions in solution. The combined QM/MM methods use the MM method with the potential calculated ab initio [24]. 

Alternate double and single bonds are often used in drawing aromatic structures, although it is fully understood these form a closed loop (tc-system) of electrons. The reason is that these classical structures are used in the valence bond approach to molecular structure (as canonical forms), and they also permit the use of curly arrows to illustrate the course of reactions. 

Hybridization is a concept normally associated with the valence bond approach but may also be derived from molecular orbital theory by using second-order perturbation theory in the following way (78, 117, 190). 

Two points of view are applicable to these species, as they also are to the isoelectronic noble gas fluorides (1) a valence bond approach with promotion of electrons to d orbitals and (2) three-center, four-electron bonds. The same arguments, pro and con. apply as given previously, so they will not be repeated here. Independent of die alternative approaches via VB or MO theory, all are agreed that Madelung energy ( ionic character ) is very important in stabilizing both the polyhalide tons and the polyhalogens.27... 

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