MOLECULAR ORBITALS

Molecular orbitals 

In molecules, as In isolated atoms, electrons occupy orbitals, and in accordance with much the same "rules". These molecular orbitals are considered to be centered about many nuclei, perhaps covering the entire molecule; the distribution of nuclei and electrons is simply the one that results in the most stable molecule. 

To make the enormously complicated mathematics more workable, two simplifying assumptions are commonly made: (a) that each pair of electrons 1s essentially localized near just two nuclei, and (b) that the shapes of these localized molecular orbitals and their disposition with respect to each other are related in a simple way to the shapes and disposition of atomic orbitals in the component atoms. 

The idea of localized molecular orbitals-or what we might call bond orbitals is evidently not a bad one, since mathematically this method of approximation is successful with most (although not all) molecules. Furthermore, this idea closely parallels the chemist's classical concept of a bond as a force acting between two atoms and pretty much independent of the rest of the molecule; it can hardly be accidental that this concept has worked amazingly well for a hundred years. Significantly, the exceptional molecules for which classical formulas do not work are just those for which the localized molecular orbital approach does not work either. (Even these cases, we shall find, can be handled by a rather simple adaptation of classical formulas, an adaptation which again parallels a method of mathematical approximation.) 

The second assumption, of a relationship between atomic and molecular orbitals, is a highly reasonable one, as discussed in the following section. It has proven so useful that, when necessary, atomic orbitals of certain kinds have been Invented just so that the assumption can be retained.