Some Valence Bond Results

The first application of quantum mechanics to a rate process was made by London (1929 Eyring el al., 1944). For a two-electron diatomic molecule A—B, there are two allowed wave functions, Jj. Relative to the separated atoms, the corresponding energies are 

For our purposes, it will be sufficient to note that Q, the coulomb integral, and J, the exchange integral, are negative, have the units of energy, and fall off with interatomic distance, rAB. The overlap integral, 

Following London, others developed the VB method for three-atom and higher species (Eyring and Polanyi, 1931 Eyring et al.t 1944). Consider a four-atom, four s electron species ABCD this may be represented, without any geometrical implications, as 

for the six possible diatomic molecules, we can write the energy as 

For a three-center molecule ABC, we simply drop all terms involving D, e.g. Qad=Jad = Qs and the form of (8) is preserved. This is the London (1929) equation. Similarly, one recovers the appropriate expressions (7) for diatomic molecules by removing one atom from ABC. 

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There have been some attempts to compute nonlinear optical properties in solution. These studies have shown that very small variations in the solvent cavity can give very large deviations in the computed hyperpolarizability. The valence bond charge transfer (VB-CT) method created by Goddard and coworkers has had some success in reproducing solvent effect trends and polymer results (the VB-CT-S and VB-CTE forms, respectively). 

It is readily apparent that the three a bonds are capable of holding the six bonding electrons in the a t and e molecular orbitals. The possibility of some 7r-bonding is seen in the molecular orbital diagram as a result of the availability of the a2" orbital, and in fact there is some experimental evidence for this type of interaction. The sum of the covalent radii of boron and fluorine atoms is about 152 pm (1.52 A), but the experimental B-F bond distance in BF3 is about 129.5 pm (1.295 A). Part of this "bond shortening" may be due to partial double bonds resulting from the 7r-bonding. A way to show this is by means of the three resonance structures of the valence bond type that can be shown as... 

The fact that tetrazolo[l,5- ]pyridine reacts with phosphines - via ring opening to the valence bond isomer azide -to give a phosphorane has been long recognized. Some novel applications of this transformation have been published during the recent period. The fused tetrazoles subjected to this reaction, the resulting phosphoranes, and the literature sources are summarized in Table 4. 

Simonetta and Heilbronner (1964) recently carried out calculations by the valence bond (VB) method for some simple cations, and compared the results obtained by this method, inter alia, with the results of Colpa and collaborators (1963) and of Koutecky and Paldus (1963). In the case of the proton addition complexes of mesitylene and cyclohepta-triene, the electron excitation energies calculated by the VB method agree very well with experiments, and also agree to a good approximation with the results of Cl calculations. The calculations also successfully reproduce the electron density of the cycloheptatriene cation. In this, a perturbation calculation allowed for the AO s adjoining the —CHg—CH2-lihkage. 

The separation of chemical species by size exclusion chromatography is more reproducible than any other type of chromatography. Once the SEC columns, the mobile phase (most often a pure solvent like THF or toluene), and the flow rate are selected, the retention volume (or retention time assuming the flow rate does not change) is primarily a function of linear molecular size, which can be obtained from the valence bond structure if the compound is known. Some of the chemical species can interact with the solvent forming complexes with an effective linear size greater than that of the molecule. This causes the expected retention volume, based on "free" molecular structure, to shift to a lower but very reproducible retention volume. Phenols in coal liquids form 1 1 complex with THF (9,10) and carry the effective linear molecular size to increase. As a result phenolic species elute sooner than expected from their... 

The exceptions to the octet rule described in the previous section, the xenon compounds and the tri-iodide ion, are dealt with by the VSEPR and valence bond theories by assuming that the lowest energy available d orbitals participate in the bonding. This occurs for all main group compounds in which the central atom forms more than four formal covalent bonds, and is collectively known as hypervalence, resulting from the expansion of the valence shell This is referred to in later sections of the book, and the molecular orbital approach is compared with the valence bond theory to show that d orbital participation is unnecessary in some cases. It is essential to note that d orbital participation in bonding of the central atom is dependent upon the symmetry properties of individual compounds and the d orbitals. 

In some respects the ligand field theory is closely related, at least qualitatively, to the valence-bond theory described in the preceding sections, and many arguments about the structure of the normal state of a complex or crystal can be carried out in either of the two ways, with essentially the same results.66... 

Normally, C-H bonds are highly resistant to attack by basic reagents, but removal of a proton alpha to a carbonyl group results in the formation of a considerably stabilized anion with a substantial proportion of the negative charge on oxygen, as represented by the valence-bond structure 1a. Carbonyl compounds such as 2-propanone therefore are weak acids, only slightly weaker than alcohols (compare the pKa values for some representative compounds in Table 17-1).1... 

It is a basic assumption in tracer work that labelled and unlabelled molecules have identical reactivities. If the labelling involves one of the atoms attached directly to the valency bond concerned in the reaction, this assumption is not valid. The differences between the reactivities is referred to as an isotope effect. When the isotopes involved are those of hydrogen, the isotope effect is quite large for heavier elements, the effects are much smaller but in the case of carbon they can be detected in careful work. To some extent, isotope effects impose a limitation upon the accuracy of results obtained from tracer studies, but they can also lead to a fuller understanding of the mechanisms of reactions of certain types. In routine tracer work, it is advisable whenever possible to label molecules at sites remote from the points of reactivity. 

The sequence of energy levels obtained from a simple molecular orbital analysis of an octahedral complex is presented in Fig. 1-12. The central portion of this diagram, with the t2g and e levels, closely resembles that derived from the crystal field model, although some differences are now apparent. The t2g level is now seen to be non-bonding, whilst the antibonding nature of the e levels (with respect to the metal-ligand interaction) is stressed. If the calculations can be performed to a sufficiently high level that the numerical results can be believed, they provide a complete description of the molecule. Such a description does not possess the benefit of the simplicity of the valence bond model. 

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