Generalized valence-bond theory

FIGURE 6.37 The electron density for the if/g and ifil wave functions in the simple valence bond model for H2. (a) The electron density pg for if/g and Pu for calculated analytically as described in the text, (b) Three-dimensional isosurface of the electron density for the ipg wave function, as calculated numerically by Generalized Valence Bond Theory (GVB). 

FIGURE 6.40 Isosurface representation of the electron densities in the a bond and the two 77 bonds calculated by Generalized Valence Bond Theory (GVB). 

Correlation in atoms introduces largely quantitative changes. As seen above, qualitative changes can come about in condensed phases. Here, we consider briefly the case of the stretched H2 molecule, going back to the work of Coulson and Fischer [48] (CF). Their work is a forerunner of the so called generalized valence bond theory. 

We have attempted to summarize some qualitative aspects of bonding obtained from recent quantitative calculations which include important electronic correlation effects ignored in molecular orbital theory. The resulting valence bond concepts derived from the calculations, which have long been ignored as only qualitative and without sound theoretical foundation, are made quantitative and computationally accessible through the generalized valence bond theory. The concept of bent-bonds (Q-bonds), much discussed in the chemical... 

GVB generalized valence bond theory. A method by W. A. Goddard to include... 

A journey from generalized valence bond theory to the full Cl complete basis set limit ... 

In 1978, Caltech s W. A. Goddard proposed a different mechanism for the hydroxylation of phenolic compounds and attempted to show how flavin coenzymes carry out such oxidations. It is a theoretical proposal based on wave functions and quantum mechanics using generalized valence bond theory, applied to biological problems (297). An example is shown in Fig. 7.7 for the oxidation of phenol to catechol. 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-conhgurational self-consistent held (MCSCF), conhgu-ration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

We can generalize from these examples to the description of a multiply bonded species according to valence-bond theory ... 

The generally accepted theory of electric superconductivity of metals is based upon an assumed interaction between the conduction electrons and phonons in the crystal.1-3 The resonating-valence-bond theory, which is a theoiy of the electronic structure of metals developed about 20 years ago,4-6 provides the basis for a detailed description of the electron-phonon interaction, in relation to the atomic numbers of elements and the composition of alloys, and leads, as described below, to the conclusion that there are two classes of superconductors, crest superconductors and trough superconductors. 

Most of the commonly used electronic-structure methods are based upon Hartree-Fock theory, with electron correlation sometimes included in various ways (Slater, 1974). Typically one begins with a many-electron wave function comprised of one or several Slater determinants and takes the one-electron wave functions to be molecular orbitals (MO s) in the form of linear combinations of atomic orbitals (LCAO s) (An alternative approach, the generalized valence-bond method (see, for example, Schultz and Messmer, 1986), has been used in a few cases but has not been widely applied to defect problems.)... 

Delocalization occurs in molecules wherever it is possible by symmetry considerations and wherever an energetic advantage can be gained from its operation. MO theory deals very satisfactorily with delocalization, but with valence bond theory the concept is somewhat clumsily incorporated as an addition to the conventional two-electron, two-centre bonding. In general, the stability conferred upon a molecule by delocalization is because the orbitals are more extensive, so that interelectronic repulsion is minimized. 

We have used the concepts of the resonance methods many times in previous chapters to explain the chemical behavior of compounds and to describe the structures of compounds that cannot be represented satisfactorily by a single valence-bond structure (e.g., benzene, Section 6-5). We shall assume, therefore, that you are familiar with the qualitative ideas of resonance theory, and that you are aware that the so-called resonance and valence-bond methods are in fact synonymous. The further treatment given here emphasizes more directly the quantum-mechanical nature of valence-bond theory. The basis of molecular-orbital theory also is described and compared with valence-bond theory. First, however, we shall discuss general characteristics of simple covalent bonds that we would expect either theory to explain. 

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