HOMO-LUMO ("filled-empty") Orbital Interactions

A fundamental principle: all steps of all heterolytic reaction mechanisms are either Bronsted or Lewis acid-base reactions

In short, all heterolytic reactions are just examples of interactions between filled atomic or molecular orbitals and empty atomic or molecular orbitals - that is, Lewis acid-base reactions. Here is a diagram to explain this point:

The interaction of any two atomic or molecular orbitals, as you learned in general chemistry, produces two new orbitals.

When we are dealing with interacting molecular orbitals, the two that interact are generally

Here is the filled-empty interaction redrawn as a HOMO-LUMO interaction.

Let's look at some examples. First, a reaction that you would have categorized as a Lewis acid-base reaction when you were studying general chemistry:

NH3 has an unshared pair on nitrogen, occupying the HOMO (it is generally true that unshared pairs occupy HOMOs). BH3 has an empty valence orbital on B, since B is a Group II element. This is the LUMO.

Here are pictures of the two orbitals from AM1 semi-empirical molecular orbital calculations:

NH3 HOMO BH3 LUMO

The HOMO-LUMO energy diagram above describes the formation of a bond between N and B.

Now let's try a slightly more complex case. Here's a typical Bronsted acid-base reaction:

The curly arrows track which bonds are made, and which are broken, but they do not indicate what orbitals are involved.

Another example is the SN2 reaction, which involves the HOMO of the nucleophile and the s* orbital of the R-X bond:

Here are the relevant orbitals:

OH- HOMO CH3-Cl LUMO

The interaction stabilizes the unshared pair of the oxygen, while simultaneously breaking the CH3-Cl bond because the interaction is with the antibonding orbital.

Other examples include the reaction of alkenes with H-X, where the HOMO is the p MO of the alkene and the LUMO is the H-X s* orbital:

and the capture of the carobcation in an SN1 reaction by nucleophile:

You should need no reminder that the carbocation is stabilized by a filled-empty interaction between the empty p orbital of the positive carbon and the s orbital of an adjacent C-H or C-C bond

In short, all heterolytic reactions proceed because the energy of a pair of electrons is lowered by the interaction of a filled atomic or molecular orbital with an empty one.

The same reasoning can be appllied to bimolecular pericyclic reactions like the Diels-Alder cycloaddition.


This page last modified 3:24 PM on Thursday September 30th, 2010.
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