Delocalized valence bond method

The two chief general methods of approximately solving the wave equation, discussed in Chapter 1, are also used for compounds containing delocalized bonds.2 In the valence-bond method, several possible Lewis structures (called canonical forms) are drawn and the molecule is taken to be a weighted average of them. Each in Eq. (3), Chapter 1,... 

We discuss the application of the valence bond method to systems with delocalized bonds, namely, metallic and anionic systems. We show that the admittance of extra orbitals in these systems is necessary, leading to new types of structures, which are related to processes of charge transfer. 

Cooper, D. L. Cerratt, J. Raimondi, M. Nature 1986,323,699 reported a spin-coupled valence bond method for calculation of molecular electronic structure and concluded that "our results suggest that the Kekule description of benzene, as expressed in the classic VB form, is in fact much closer in reality than is a description in terms of delocalized molecular orbitals."... 

Delocalized bonding was described in the valence-bond method by use of the concept of resonance. In the molecular orbital description, delocalized LCAOMOs are used. For example, in the benzene molecule, six of the electrons occupy delocalized orbitals. 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

A In this exercise we will combine valence-bond and molecular orbital methods to describe the bonding in the SO3 molecule. By invoking a 7t-bonding scheme, we can replace the three resonance structures for SO3 (shown below) with just one structure that exhibits both cr-bonding and delocalized n--bonding. 

Generalized valence bond interaction energies were computed for mono/poly-nitrogenous five- and six-membered heterocycles.203 Results that diverged from those obtained by other methods were obtained only for poly-nitrogenous systems such as pyridazine, benzotriazole, and tetrazole, which may confirm Bird s earlier finding123 204 that electron delocalization is not a stand-alone and direct measure of aromaticity for nitrogenous heterocyclic compounds. 

Further analysis is based on the idea that the characteristic experimental behavior of different classes of compounds and the suitability of those or other models used to describe this behavior is ultimately related to the extent to which the chromophores or electron groups physically present in the molecular system are reflected in these models. It is easy to notice, that the MM methods work well in case of molecules with local bonds designated in Table 1 as valence bonds the QC methods apply both to the valence bonded systems, and for the systems with delocalized bonds (referred as orbital bonds in Table 1). The TMCs of interest, however, not covered either by MM or by standard QC techniques can be physically characterized as those bearing the d-shell chromophore. The magnetic and optical properties characteristic for TMCs are related to d- or /-states of metal ions. The basic features in the electronic structure of TMCs of interest, distinguishing these compounds from others are the following ... 

Both the valence-bond and molecular-orbital methods show that there is delocalization in benzene. For example, each predicts that the six carbon-carbon bonds should have equal lengths, which is true. Since each method is useful for certain purposes, we shall use one or the other as appropriate. 

The perfectly octahedral species conform to the expectations based on the simple MO derivation given above. The nonoctahedral fluoride species do not, but this difficulty is a result of the oversimplifications in the method. There is no inherent necessity for delocalized MOs to be restricted to octahedral symmetry. Furthermore, it is possible to transform delocalized molecular orbitals into localized molecular orbitals. Although the VSEPR theory is often couched in valence bond terms, it depends basically on the repulsion of electrons of like spins, and if these are in localized orbitals the results should be comparable. 

Because the n-networks of benzenoid hydrocarbons are the classical prototypical example of delocalized bonding, they provide a crucial test for chemical-bonding theories. Here there is revealed a systematic organization for valence-bond views to describe such n-bonding. With an initiation near the ab initio realm a sequence of semiempirical valence-bond models is identified and characterized. The refinement from one model to the next proceeds via either a (perturbative) restriction to a smaller model space or orthogonalization of a suitable natural basis for the model space. The known properties of the models are indicated, and possible methods of solution are mentioned. A great diversity of work is outlined, related, systematized and extended. New research is suggested. 

The generalized valence bond (GVB) method was the earliest important generalization of the Coulson—Fischer idea to polyatomic molecules (13,14). The method uses OEOs that are free to delocalize over the whole molecule during orbital optimization. Despite its general formulation, the GVB method is usually used in its restricted form, referred to as GVB SOPP, which introduces two simplifications. The first one is the perfect-pairing (PP) approximation, in which only one VB structure is generated in the calculation. The wave function may then be expressed in the simple form of Equation 9.1, as a product of so-called geminal two-electron functions ... 

BOVB Breathing orbital valence bond. A VB computational method. The BOVB wave function is a linear combination of VB structures that simultaneously optimizes the structural coefficients and the orbitals of the structures and allows different orbitals for different structures. The BOVB method must be used with strictly localized active orbitals (see HAOs). When all the orbitals are localized, the method is referred to as L-BOVB. There are other BOVB levels, which use delocalized MO-type inactive orbitals, if the latter have different symmetry than the active orbitals. (See Chapters 9 and 10.)... 

If we allow for correlation effects within each pair using the GVB-PP method we obtain the SOPP orbitals also shown in Fig. 4. The close relationship between the SOPP orbitals and the LMOs is apparent. Each pair in an LMO is either left-right correlated in the case of a bond or in-out correlated in the case of lone pairs. The dxy LMO or the corresponding pair from the GVB-PP calculation are the only orbitals to exhibit considerable delocalization. In the MO case, this behavior is referred to as back-bonding from the metal to the CO, but in the valence bond situation, our experience is that all... 

As with the smaller compounds, reliable computational descriptions of methyl phenyl sulfoxide excited states are not available. Ground state computations are easily accessible for molecules of this size. At the RHF/6-31G(d,p) level, the HOMO is 7t with regard to the SO bond but delocalized throughout the whole n-system. The next two descending orbitals are localized on the phenyl and SO, respectively. (The sulfur lone pair is the HOMO-2 when the valence bond orbitals are approximated by the Edmiston-Ruedenberg method.) While the LUMO is extensively delocalized, the LUMO-fl is entirely localized on the phenyl ring. 

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