The Valence Bond Approach

For the reaction Ha + Ha- Hs + H,270 VBCI calculations were performed on all the points considered. Five attitudes of approach of H2 and Hi and three attitudes of retreat of and H were considered, while the geometries of H2, Hi, and H+ were fixed at their respective calculated equilibrium values. The steepest approach potential is found to be one in which the H+ axis bisects the Ha axis. The steepest retreat potential is one in which the H atom leaves the triangular H, ion on the same axis on which it entered. With this general reaction path defined, the calculations were repeated with the optimization of the H-H bond distance. A minimum was found at H-H and H-H + distances of 1.66 a.u. and 4.11 a.u., respectively, while the distance from the leading H atom of the H+ ion to the bisector of the Ha molecule is 1.44 a.u. The binding energy is found to be 3.6 kJ mol-1. 

---

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... 

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. 

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... 

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). 

In the valence-bond approach, the 7r bond of ethene is considered to be a hybrid of all reasonable electronic configurations of two indistinguishable paired electrons distributed between two p orbitals. Each of the configurations that can be written, 4a, 4b, 4c, and 4d, have identical locations of the atomic nuclei in space ... 

The valence bond model constructs hybrid orbitals which contain various fractions of the character of the pure component orbitals. These hybrid orbitals are constructed such that they possess the correct spatial characteristics for the formation of bonds. The bonding is treated in terms of localised two-electron two-centre interactions between atoms. As applied to first-row transition metals, the valence bond approach considers that the 45, 4p and 3d orbitals are all available for bonding. To obtain an octahedral complex, two 3d, the 45 and the three 4p metal orbitals are mixed to give six spatially-equivalent directed cfisp3 hybrid orbitals, which are oriented with electron density along the principal Cartesian axes (Fig. 1-9). 

A couple of immediate targets for applying the general methodology proposed in this book can be indicated, based on an analysis of the literature. The first candidate might be the valence bond approach to the analysis of stereochemistry of compounds of heavy transition metals (e.g. tungsten) proposed in a series of works [2-4]. It... 

The chemist is accustomed to think of the chemical bond from the valence-bond approach of Pauling (7)05), for this approach enables construction of simple models with which to develop a chemical intuition for a variety of complex materials. However, this approach is necessarily qualitative in character so that at best it can serve only as a useful device for the correlation and classification of materials. Therefore the theoretical context for the present discussion is the Hund (290)-Mulliken (4f>7) molecular-orbital approach. Nevertheless an important restriction to the application of this approach must be emphasized at the start viz. an apparently sharp breakdown of the collective-electron assumption for interatomic separations greater than some critical distance, R(. In order to illustrate the theoretical basis for this breakdown, several calculations will be considered, the first being those for the hydrogen molecule. 

The main difficulty with the valence-bond approach is that the atomic orbitals, whether hybridized or not, result from the interaction of electrons with a single central force field— that of the atomic nucleus. An electron that spends most of its time between two nuclei will find itself in a very different, two-center force field, and this will give rise to new types of orbitals that are better characterized as molecular, rather than as atomic orbitals. 

---