Core electrons bonding pairs

As these compact orbitals are usually concentrated in the regions where core electrons, bonds, non-bonding electron pairs are expected, the introduction of localized MOs has played an important role in understanding the above classical chemical concepts and valence. Most of the localized orbitals, on the other hand, are also well displaced in space from each other. This property makes them an excellent tool for separating local and long-range electron interaction effects. 

I lc. Ci ond reason why the ZDO approximation is not applied to all pairs of orbitals is that the major contributors to bond formation are the electron-core interactions between pairs of orbila l.s and the nuclear cores (i.e. These interachons are therefore not subjected to the ZDO approximation (and so do not suffer from any transformation problems). 

Molecular orbitals are not unique. The same exact wave function could be expressed an infinite number of ways with different, but equivalent orbitals. Two commonly used sets of orbitals are localized orbitals and symmetry-adapted orbitals (also called canonical orbitals). Localized orbitals are sometimes used because they look very much like a chemist s qualitative models of molecular bonds, lone-pair electrons, core electrons, and the like. Symmetry-adapted orbitals are more commonly used because they allow the calculation to be executed much more quickly for high-symmetry molecules. Localized orbitals can give the fastest calculations for very large molecules without symmetry due to many long-distance interactions becoming negligible. 

It is important to point out that recent results on density based overlap integrals [16] confirm the interest of the formulation of Erep as a sum of bond-bond, bond-lone pair and lone pair-lone pair repulsion indeed, core electrons do not contribute to the value of the overlap integrals. 

Core electrons and electrons engaged in bonding are relatively tightly bound to the molecular nuclear framework. Lone-pair electrons or electrons in a (previously) virtual orbital, are relatively loosely held, and are on the average at a larger distance from the nuclei than core or bonding electrons. These expanded electron clouds... 

It is a small step from van der Waals, electron-domain models of the C—H bonds of, e.g., biphenyl, cyclohexane, or methane (Figs. 1—3), to molecular models in which to a first, and useful, approximation each valence-shell electron-pair is represented by a spherical, van der Waals-like domain 7h (Non-spherical domains may be useful for describing, e.g., lone pairs about atoms with large atomic cores, -electrons, and the electron-pairs of multiple bonds vide infra.)... 

A drawing of a two-dimensional, electron-domain model of a conventional Lewis lone pair is shown in Fig. 23. The lone pair and bonding pairs are structurally equivalent they have identical van der Waals envelopes. Such seems to be nearly the case for lone pairs in the valence-shells of small-core, non-octet-expanding atoms (carbon, nitrogen, oxygen and fluorine). 

Consider only one 2pz AO per aromatic atom. (Ignore all hydrogens, core electrons, "sigma bond" electrons, lone pairs, etc.)... 

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