Valence-bond treatment

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. 

It is instructive to compare the simple LCAO and VB (valence bond) treatments, and especially to enquire why the LCAO treatment fails so disastrously at large R. It is easily shown that the LCAO wavefunction can be written... 

What happens when we have a many-electron wavefunction, such as the one below which relates to the simple valence-bond treatment of dihydrogen ... 

Herzberg (Nobel prize for Chemistry, 1971) commented on the two distinct photoionizations from methane that this observation illustrates the rather drastic nature of the approximation made in the valence bond treatment of CH4, in which the 2s and 2p electrons of the carbon atom are considered as degenerate and where this degeneracy is used to form tetrahedral orbitals representing mixtures of 2s and 2p atomic orbitals. The molecular orbital treatment does not have this difficulty". 

Further developments in the fundamental approach to the electronic structure of catalysts were made possible by the development of the quantum mechanical treatments of solids which followed the work of Sommerfeld, Bloch and others. Similarly, Pauling s resonating valence bond treatment has lent further impetus to consideration of metallic catalysts. 

The valence-bond treatment described above involves neglect of the partial ionic character of the bonds in the benzene molecule, and the molecular-orbital treatment overemphasizes it.80... 

Pauling150 has provided an alternative, valence bond treatment of the quadruple bond involving spd hybrid orbitals and four equivalent bent bonds. His model also explains the experimental facts described above and provides a good estimate of the bond length. 

The same phenomenon that leads to Hund s rule of maximum multiplicity in atoms (i.e., quantum-mechanical exchange stabilization) produces polarization of the electron spins in the C-H a bond. In a valence-bond treatment, the bond is comprised of one electron from a carbon sp2 orbital and another from a hydrogen Is orbital. Exchange forces act to polarize the sp2 electron so that its spin is parallel to the unpaired spin in the carbon 2p orbital this leaves the... 

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 contributions of Erich Hiickel to the development of molecular orbital theory have already been mentioned in the subsection on Germany (Section 5.4.1) the development of semi-empirical quantum mechanical treatments in organic chemistry by M. J. S. Dewar has been discussed in Section 5.5. In the early development of the application of quantum mechanics to chemistry, Linus Pauling (1901-1994)359 was pre-eminent. He was associated with CalTech for most of his career. His work before World War II generated two influential books the Introduction to Quantum Mechanics (with E. Bright Wilson, 1935)360 and The Nature of the Chemical Bond (1939).361 He favoured the valence-bond treatment and the theory of resonance. 

The hydrogen molecule molecular orbital and valence bond treatments... 

When we plot E+ and E- against rab, we get the energy curves shown in Fig. 3.2.2. So, once again, the valence bond treatment yields a stable H2 molecule, even though the quantitative results do not match exactly the experimental data. 

After a simple valence bond treatment of H2, we now proceed to study the excited states of H2. Through this discussion, we will recognize that the molecular orbital and valence bond treatments, after modification, can bring about the same quantitative results. 

The primary difference between covalent and ionic bonding is that with covalent bonding, we must invoke quantum mechanics. In molecular orbital (MO) theory, molecules are most stable when the bonding MOs or, at most, bonding plus nonbonding MOs, are each filled with two electrons (of opposite spin) and all the antibonding MOs are empty. This forms the quantum mechanical basis of the octet rule for compounds of the p-block elements and the 18-electron rule for d-block elements. Similarly, in the Heider-London (valence bond) treatment... 

One of the most fruitful theoretical contributions to the interpretation of coupling constants has been the valence bond treatment by Karplus71 of 3JHH in ethanelike fragments, Ha—C —Cb—Ht. The most interesting conclusion is that this coupling depends drastically on the dihedral angle between the H —Ca and the Cj,—Hj bonds. The calculated results were found to fit approximately the relation... 

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