Sigma bonding electrons

A similar situation holds for a molecule containing a tetrahedral carbon is shown in (Figure 16). The reaction converting one enantiomer to another, is formally equivalent to the exchange of two sigma-bond electron pairs, and... 

Simple indices, which encode information on sigma bonded electrons that can be observed directly from bonding patterns in structural formulae of PAHs. 

The sigma-bonding electron pairs in the following examples are indicated by before the ligand formulae. 

J. W. Raymonda and W. T. Simpson, J. Chem. Phys., 47, 430 (1967). Experimental and Theoretical Study of Sigma-Bond Electronic Transitions in Alkanes. 

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

Rule 1 Both sigma bonding electrons and lone pairs can occupy hybrid orbitals. The number of hybrid orbitals on an atom is computed by adding the number of sigma bonds and the number of lone pairs of electrons on that atom. 

Anisotropic elfects occur in addition to the ever present molecular field, induced by sigma-bond electrons. 

In a long flexible chain molecule there are various segmental motions. Eventually at one point there will be such a concentration of energy that the chain breaks. In the simplest case, that of polyethylene (PE) with only C-C and C-H bonds, the disassociation energy for these bonds is about 80 and kcal/mol, respectively. So when the energy exceeds the amount, the chain breaks, the two sigma bonding electrons are separated and two lone electrons (free radicals) are formed. 

The molecule on the left has a lone pair that resides in a/ orbital despite the fact that in ap orbital the lone pair resides closer (90° vs. 109.5°) to N-H and N-C sigma-bonding electrons. Construct an explanation for why this lone pair resides in ap orbital. 

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