HOMO AND LUMO

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

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

• They involve either proton transfer (Bronsted), or unshared pair/empty orbital interactions (Lewis).
• When the interacting atomic orbitals are considered, the Bronsted reactions can be seen as simply a special case of the Lewis, in which the empty orbital is the antibonding orbital of the H-X bond.

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.

• One of the new orbitals is higher in energy than the original ones (the antibonding orbital), and one is lower (the bonding orbital).
• When one of the initial orbitals is filled with a pair of electrons (a Lewis base), and the other is empty (a Lewis acid), we can place the two electrons into the lower energy of the two new orbitals.
• The "filled-empty" interaction therefore is stabilizing.

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

• The highest energy occupied molecular orbital (HOMO) of one molecule,
• The lowest energy unoccupied molecular orbital (LUMO) of the other molecule.
• These orbitals are the pair that lie closest in energy of any pair of orbitals in the two molecules, which allows them to interact most strongly.
• These orbitals are sometimes called the frontier orbitals, because they lie at the outermost boundaries of the electrons of the molecules.

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.

• Water is both a Bronsted base (capable of accepting a proton) and a Lewis base, with one of its unshared pairs (the HOMO).
• H-Cl is a Bronsted acid, capable of donating a proton, but it also is a Lewis acid, using the s* orbital of the H-Cl bond (the LUMO).
• Here are pictures of the relevant HOMO and LUMO, again from AM1 semi-empirical molecular orbital calculations:

H2O HOMO	HCl LUMO

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

Another example is the S_N2 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.