Valence-bond method ionic structures

Under the Born-Oppenheimer approximation, two major methods exist to determine the electronic structure of molecules The valence bond (VB) and the molecular orbital (MO) methods (Atkins, 1986). In the valence bond method, the chemical bond is assumed to be an electron pair at the onset. Thus, bonds are viewed to be distinct atom-atom interactions, and upon dissociation molecules always lead to neutral species. In contrast, in the MO method the individual electrons are assumed to occupy an orbital that spreads the entire nuclear framework, and upon dissociation, neutral and ionic species form with equal probabilities. Consequently, the charge correlation, or the avoidance of one electron by others based on electrostatic repulsion, is overestimated by the VB method and is underestimated by the MO method (Atkins, 1986). The MO method turned out to be easier to apply to complex systems, and with the advent of computers it became a powerful computational tool in chemistry. Consequently, we shall concentrate on the MO method for the remainder of this section. 

Empirical Valence Bond Methods. - To examine some important questions relating to enzyme action (e.g. to analyse the causes of catalysis, i.e. why an enzymic reaction proceeds faster than the equivalent, uncatalysed reaction in solution), it is necessary to use a method that not only captures the essential details of the chemical reaction, but also includes the explicit effects of the enzyme and solvent enviroment. One notable method in this area is the empirical valence bond (EVB) model.143 In the empirical valence bond approach, resonance structures (for example ionic and covalent resonance forms)... 

Either the molecular orbital or the valence bond method may be used to analyse the interaction of substituents on the reactant, products, and transition states. Substituents which stabilise the transition state more than reactants will accelerate the reaction, while those which stabilise the reactant more than transition state will slow down the reaction. In valence bond theory, the reactants are represented hy a nucleophile lone pair as an anion (Fig. 6-21, path a) and a neutral nucleophile (path b), and the carhonyl by the covalent and ionic re.sonance structures [70]. 

The valence-bond method has been used in an ab initio study of the potential surface for H4 186). The basis orbitals were linear combinations of gaussian functions with a polarization factor. Calculations were performed with and without inclusion of ionic structures, and with and... 

A is a parameter that can be varied to give the correct amount of ionic character. Another way to view the valence bond picture is that the incorporation of ionic character corrects the overemphasis that the valence bond treatment places on electron correlation. The molecular orbital wavefimction underestimates electron correlation and requires methods such as configuration interaction to correct for it. Although the presence of ionic structures in species such as H2 appears coimterintuitive to many chemists, such species are widely used to explain certain other phenomena such as the ortho/para or meta directing properties of substituted benzene compounds imder electrophilic attack. Moverover, it has been shown that the ionic structures correspond to the deformation of the atomic orbitals when daey are involved in chemical bonds. 

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. 

The empirical valence bond (EVB) method of Warshel [19] has features of both the structurally and thermodynamically coupled QM/MM method. In the EVB method the different states of the process studied are described in terms of relevant covalent and ionic resonance structures. The potential energy surface of the QM system is calibrated to reproduce the known experimental... 

The results of a valence bond treatment of the rotational barrier in ethane lie between the extremes of the NBO and EDA analyses and seem to reconcile this dispute by suggesting that both Pauli repulsion and hyperconjugation are important. This is probably closest to the truth (remember that Pauli repulsion dominates in the higher alkanes) but the VB approach is still imperfect and also is mostly a very powerful expert method [43]. VB methods construct the total wave function from linear combinations of covalent resonance and an array of ionic structures as the covalent structure is typically much lower in energy, the ionic contributions are included by using highly delocalised (and polarisable) so-called Coulson-Fischer orbitals. Needless to say, this is not error free and the brief description of this rather old but valuable approach indicates the expert nature of this type of analysis. 

The flexibility of the valence bond self-consistent field (VBSCF) method can be exploited to calculate VB wave functions based on orbitals that are purely localized on a single atom or fragment. In such a case, the VBSCF wave function takes a classical VB form, which has the advantage of giving a very detailed description of an electronic system, as, for example, the interplay between the various covalent and ionic structures in a reaction. On the other hand, since covalent and ionic structures have to be explicitly considered for... 

Predictions can be made about the suitability of different system trajectories on the basis of orbital symmetry conservation rules (207). The most suitable trajectory is an approximation to the reaction path of the reaction under study. The rules can also yield information about the possible structure of the activated complex. The correlation diagram technique has been improved in a series of books by Epiotis et al. (214-216). The method is based on self-consistent field-configuration interaction or valence bond (SCF-CI or VB) (including ionic structures) wave functions. Applications on reactions in the ground states as well as in the excited electronic states are impressive however, the price to be paid for the predictions seems to be rather high. 

An alternative to the MO method for the quantum mechanical treatment of molecular systems is the so-called Valence-Bond (VB) theory where molecular wavef unctions Eire obtained as linear combinations of covalent and ionic structures. It was shown long ago 181> that for distances larger than equilibrium distances, VB approximate wave functions should be better than MO functions of the same level, and hence VB theory should find its most profitable application in the evaluation of potential surfaces and reaction paths. Although true in principle, this statement has little influence in practice this is mostly because VB theory has only recently been formulated in a nonempirical form 182-184) so that applications are only just beginning to appear. 

In constructing the spatial part of the electronic wave function the Valence-Bond (VB) method is useful. This method (similar to the Heitler-London approach) postulates that a linear combination of several product functions (called covalent structures or ionic structures ) is appropriate... 

Figure 6.5b shows the breathing orbital valence bond (BOVB) computed energy curves of various state wave functions. The first one on the left-hand side shows the energy of the fundamental structure 55 plotted along the Li- -Li distance. It is seen that this structure is repulsive, much like the corresponding structure for the FM state of H2 (Figure 6.2). The second plot shows a Hnear combination of the fundamental structure with the two triplet ionic structures. It is seen that the addition of 3>j (ion) results in an incipient FMNP bond. Adding the other structures in the third and fourth plots deepens the energy well to its final BOVB value, which is D = 0.639 with a cc-pVDZ basis set and 0.888 kcal mol for cc-pCVTZ [2a] the CCSD values for the two basis sets are 0 =0.738 and 0.902 kcal mol h The agreement of VB with the standard coupled cluster method is satisfactory. The final VB wave function is shown in Eq. (6.1) ...

The generalized valence bond (GVB) approach was one of the first methods where semilocalized orbitals, as developed by Coulson and Fischer, have been employed to polyatomic molecules [66-72]. GVB is typically applied within a restricted formulation introducing two simplifications for the construction of the VB structures (for a simple diatomic molecule AB, there are two VB structures the so-called ionic structures, and A B+, and a covalent structure, A-—B). In... 

Valence bond (VB) method (p. 520) covalent structure (p. 521) resonance theory (p. 520) Heitler-London function (p. 521) ionic structure (p. 521)... 

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