Long-bond structure

C. A. Coxjlson I believe that we are not justified in drawing any detailed conclusions from these calculations. But we may quite properly make very general conclusions, such as the order of magnitude (but not the exact value) of the weight of the long-bonded structures —O H O and —O H O. 

As an application, let us compare the energies of two isomers of hexatrienes. The linear s-trans conformation can be described as a resonance between the canonical structure 15 and long-bond structures 16-18 (Scheme 3.7), where one short bond is replaced by a long one. On the other hand, the branched isomer is made of only structures 19-21, since it lacks an analogous structure to 18. 

The resulting LBOs are fairly localized, one on Ci — C2 the other on C3—C4. Elowever, the delocalization tails are significant even though we used Hiickel orbitals. These large localization tails reflect the fact that butadiene has some conjugation between the n-bonds and in terms of VB theory is describable by a linear combination of the major Kekule structure and the minor long bond structure. 

By using this expression, the expectation value of the spin density can be determined immediately and is shown in part (d) of the figure. The distribution is very different than in the ground state. Note that absolute values of the spin are identical on all carbons since we neglected the long-bond structures. When these are added in the computations, the spin distribution on the terminal carbons decreases and on the internal carbons it increases. The middle carbon retains a spin density of —1/3. More details are given in Exercise 8.5. 

In the Appendix, a further justification for the inclusion of long-bond stmc-tures is provided. It is based on consideration of the magnitudes of the overlap and Hamiltonian matrix elements in the secular equations (ct Section 1-3). The wave-function T3 for the long-bond structure overlaps better with the wavefimctions Ti and if2 for the standard structures than do the latter wavefimctions with each other. 

The coefficient of 0.07 for the long-bond structure provides theoretical support for the unimportance of this stracture. 

Two of these structures carry zero formal charges on all atoms, and involve a long O-F or 0-0 bond. Roso s bond-eigenfimction coefficients for all structures are reported in the Figure, and they imply that these long-bond structures may be more important than is the standard Lewis structure a. 

It is easy to verify that long-bond structures are not components of increased-valence structures for 3-electron 3-centre bonding units. Further discussion of increased-valence structures for 3-electron 3-centre bonding units is provided in Chapter 25, Section 2. 

The electron-spin theory which is appropriate for the increased-valence mechanism of 1,3 dipolar cycloaddition is (iescribed in some detail in Ref 11, where the importance of the long-bond structures (such as (26)) for the electronic stracture and reactivity of any 1,3 dipolar molecule has also been stressed. The latter conclusion has received support from a number of valence-bond calculations and Goddard and Walch have used structure (26) alone to represent the electronic structure of CHjNj. 

Both T (IVHL) and T (IVBO) include the standard and long-bond structure wavefimctions Tj and Tu. In Table 23-3, the P(TVHL) and the T(NPSO) are the low-energy functions in each case, with T(NPSO) being the slightly better function. 

If we want to use one valence-bond structure to summarize resonance between the long-bond structure (2) and other canonical stiuctures, in Section 23-4 we have found that we may also use the NPSO structure (10). Because this structure summarizes resonance between the canonical structures (1), (2), (3) and (4), T (NPSO) must generate a lower energy than do the wave-functions for either... 

For the ground-states of other electron-rich molecules, the results of valence-bond calculations from different laboratories - see for example references 24-29 of Chapter 2 - also indicate also indicate that long-bond structures are more important than is usually supposed, and therefore they need to be included in qualitative valence-bond descriptions of their electronic stmcture. This book describes how this can be done, and some of the resulting consequences for the interpretation of the electronic structure, bond properties and reaction mechanisms for various electron-rich molecules. When appropriate, molecular orbital and valence-bond descriptions of bonding are compared, and relationships that exist between them are derived. Considerable attention is given to the use of Pauling 3-electron bonds (A--B as A-B) for providing qualitative valence-bond descriptions of electronic structure. The increased-valence structures for electron-rich molecules - for example... 

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