Bond localization, definition

The structure of approximate reasoning is not simple. Consider the Born-Oppenheim approximation (separability of electronic and nuclear motions due to extreme mass difference), which in application produces "fixed nuclei" Hamiltonians for individual molecules. In assuming a nuclear skeleton, the idealization neatly corresponds to classical conceptions of a molecule containing localized bonds and definite structure. All early quantum calculations, and the vast majority to date, invoke the approximation. In 1978, following decades of quiet assumption, Cambridge chemist R. G. Woolley asserted ... 

The calculations of local properties of metal-oxide electronic structure [571,581-583] were made in the cychc-cluster model, in the CNDO approximation. As in the CNDO approximation AOs are supposed to be orthogonalized by the Lowdin procedure (see Chap. 6), the definitions of local properties given in Sect. 9.1.1 for nonorthog-onal basis, have to be modified. In particular, the overlap population (9.9) becomes zero in the CNDO approximation, so that the electronic population is defined only by diagonal density matrix elements In (9.6) and in the bond-order definition... 

FIGURE 20. Top Definition of the phase relationship of the three localized basis 7r-orbitals of a norbornadiene molecule with an exocyclic double bond in position 7. Bottom Correlation diagram of the experimental orbital energies j = —/ of norbornadiene 75, 7-methylidenenorbornadiene 196 and 7-isopropylidenenorbomadiene 206, with those of the corresponding monoenes... 

Since rigorous theoretical treatments of molecular structure have become more and more common in recent years, there exists a definite need for simple connections between such treatments and traditional chemical concepts. One approach to this problem which has proved useful is the method of localized orbitals. It yields a clear picture of a molecule in terms of bonds and lone pairs and is particularly well suited for comparing the electronic structures of different molecules. So far, it has been applied mainly within the closed-shell Hartree-Fock approximation, but it is our feeling that, in the future, localized representations will find more and more widespread use, including applications to wavefunctions other than the closed-shell Hartree-Fock functions. 

In broad definition, regio-control over reactivity (regiochemical control) involves the demonstration of locale preferences for a chemical reaction. Generally, regio-control is thought of in terms of through bond separation of reactive sites, as in the resonance forms for the cyclohexanedionyl anion of Figure 6.1. 

Disulfide bridges are, of course, true covalent bonds (between the sulfurs of two cysteine side chains) and are thus considered part of the primary structure of a protein by most definitions. Experimentally they also belong there, since they can be determined as part of, or an extension of, an amino acid sequence determination. However, proteins normally can fold up correctly without or before disulfide formation, and those SS links appear to influence the structure more in the manner of secondary-structural elements, by providing local specificity and stabilization. Therefore, it seems appropriate to consider them here along with the other basic elements making up three-dimensional protein structure. 

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