Homo and Lumo for acid and base lewis

In 1923, G. N. Lewis (yes, the Lewis structure guy) suggested a way of describing a number of reactions that did not fit the Bronsted definition of acid-base reactions, yet seemed to have some unifying structural features.

He suggested:

• A base is any species with an unshared pair of electrons; examples are:

  

• An acid is any species lacking an octet; examples are:

  

This definition allows us to write acid-base reactions like these:

• 

Several things about these reactions:

• They are charge balanced - that is the total charge of all species is the same on both sides of the equations

• The red arrows are used to show how the bond between acid and base is formed
  • The tail of the arrow rests on a pair of electrons

  • The arrow points to where those electrons will be in the product

• The product is sometimes described as a Lewis "complex"

Giles Klopman points out that:

• The acid-base nomenclature is easy to confuse with Bronsted nomenclature

• Reactions like

  

  are a little confusing viewed as the acid (FeCl₃) being a species lacking an octet - Fe³⁺ is 4s², 3d⁴; and three Cl^- add six electrons to give a neutral species.

He suggested that all of these reactions be viewed as involving the interaction of a filled atomic or molecular orbital on the base, and an empty atomic or molecular orbital on the acid, regardless of the octet rule.

• The filled orbital would be the highest energy occupied molecular orbital, the HOMO

• The empty orbital will be the lowest energy unoccupied molecular orbital, the LUMO

• Then we refer to the reaction simply as a "filled-empty" interaction, or a HOMO-LUMO interaction

Here is this idea pictured in orbital terms:

Look at the formation of a molecule of hydrogen. Here are two H atoms, each with an electron, forming a molecule:

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Each atom brings an electron.

• The interaction of their 1s orbitals creates two molecular orbitals (MOs)

• Put the two electrons in the lower energy orbital, just like building up atomic electron configurations in GenChem.

This is absolutely general:

• When any two orbitals combine, two new orbitals are produced, one higher in energy than either of the originals, and one lower

• These new orbitals are filled with the available electrons, starting with the lowest energy one (just like the aufbau principle from GenChem)

• This is why the reaction occurs! A pair of electrons moves to lower energy.

• If both species had a pair of electrons, the higher energy new orbital would have to be filled also; this is why He₂ doesn't exist

Now suppose we bring together a proton, H⁺, with no electrons, and a hydride ion, H^-, with two electrons. The proton is a Lewis acid, and the hydride ion is a Lewis base!

Again, the process occurs because the energy of a pair of electrons is lowered.

In general, the HOMO and the LUMO will not move up or down by the same amount, and the energy diagram will look more like this:

Every step of every reaction we write can be described as a filled-empty orbital interaction! Each step proceeds because a pair of electrons moves to lower energy.

Finally, let's demonstrate that all acid base reactions are really Lewis acid-base reactions.

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, from AM1 semi-empirical molecular orbital calculations:

H2O HOMO	HCl LUMO (antibonding)

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