Localized bond definition

We have assumed a classical model for molecules in which the majority of the electrons are localized on definite atoms or in definite two center bonds. Although this assumption works well in practice, it certainly needs justification, for in a correct LCAO MO description of a typical molecule, each MO is composed of AO s contributed by all the atoms present and there is nothing in this description that corresponds even remotely to the classical idea of localized bonds. 

Whether or not the localized bond model will be sufficiently accurate in any given case can of course be determined only by experiment, for existing a priori quantum chemical methods cannot be applied to problems of such complexity. Experiment6 implies that the localized bond model works well for all classical molecules, i.e. molecules for which only single classical structures can be written. Here the localization is probably assisted by correlation effects that tend to concentrate the electrons in pairs in definite two-center bonds. 

Although the theory behind BLW is more general, a typical application of the method is the energy calculation of a specific resonance structure in the context of resonance theory. As a resonance structure is, by definition, composed of local bonds plus core and lone pairs, a bond between atoms A and B will be represented as a bonding MO strictly localized on the A and B centers, a lone pair will be an AO localized on a single center, and so on. With these restrictions on orbital extension, the SCF solution can be... 

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 ... 

Actually, this definition relies on the definitions of a local bond and a proton donor. 

In Section 1.1 we described the basic bonding patterns of organic molecules and the properties of different types of localized bonds. The concepts introduced were mostly fairly classical valence bond concepts. They have definite predictive power, and that is an important measure of the value of any model. However, the picture we are about to present also has the... 

As we have seen above chemical bonding in crystals (as well as in molecules) is analyzed in terms of the local properties of the electronic structure, obtained from the one-electron density matrix, written in a localized basis. Since local properties of electronic structure are essential ingredients of a number of theories and models (for example, the numerical values of atomic charges are used in the atom-atom potentials of the shell model), their estimation is of great importance. TVaditionally, the same AO basis is used both in LCAO SCF calculations and in the local properties definition, as was noted above. However, this approach is not always reliable, since the results of the population analyses are often strongly dependent on an inclusion of diffuse orbitals into the basis (useful for the electronic-structure calculations) and on the scheme chosen for the population analysis. 

It is sometimes assumed that the long range of the Coulomb potential makes it impossible to define a localized bond in the ionic model, but in fact the ionic model is the only model that provides a useful and unambiguous definition of a bond. Since the electrostatic flux that links two ions is equal to the valence of the bond that links them, a bond only exists between ions if they are linked by flux. A simple picture of the electrostatic field in the ionic model is provided by the lines of field that connect a cation to its first shell of anion neighbors as shown in Fig. 5. 

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