Absolutely localized molecular orbital

Khahulhn RZ, Cobar EA, Lochan RC, Bell AT, Head-Gordon M (2007) Unravelling the origin of intermolecular interactions using absolutely localized molecular orbitals. J Phys Chem A 111 8753... 

In a molecule such as ethane H C-CH, each carbon atom has four sp hybrids. Between the two carbon nuclei, there is a localized molecular orbital built up from two hybrids, one for each carbon atom, and pointing at one another. The alignment of the hybrid axes gives the most stable system. Indeed the orbital overlap is maximum and therefore the interaction between atomic orbitals is the strongest The corresponding energy is the highest in absolute... 

The molecular orbital treatment of can be applied to organic molecules such as CH4 or CH2=CH2 in two different ways First, molecular orbitals can be setup as linear combinations of all of the atomic orbitals of the molecule, their energies can be calculated, and the appropriate number of electrons can be put,in. This is necessarily a complicated procedure and not of great interest to organic chemists because "absolute" numbers for CH4 and CH2=CH2 are less useful than comparisons relative to other molecules of the same general type. The second and simpler approach is to make the approximation that electrons in some, or most, of the bonds are "localized". Localized electrons are assumed not to contribute importantly to the electronic character of the bonds in the rest of the molecule. 

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