Molecules are reactive when they have groupings of atoms that give rise to unusually high-energy HOMOs or unusually low-energy LUMOs. Understanding the causes of such unusual orbitals allows one to recognize "functional" groups and to predict which functional groups should react with which other functional groups. SOMOs react with SOMOs, such that a molecule with a SOMO can react with an identical molecule. However, high HOMOs react not with other high HOMOs, but with low LUMOs, and vice versa.

So to understand reactivity we need to be able to recognize unusually high HOMOs and unusually low LUMOs. Every molecule has a HOMO and a LUMO, the key word is "unusual."

Something is unusual only in comparison to what is usual. We have to decide what "usual" is. Our benchmarks for usual HOMO and LUMO energies are those of the garden-variety unreactive molecules of organic chemistry, the alkanes. These are the occupied σ orbital and the unoccupied σ* orbital of single bonds like H-C and C-C, the kind of bonds that occur in alkanes.

This recalls an old vaudeville routine, which we might update as follows: Two friends meet at the health club and begin chatting. Marilyn asks Pauline, "How's your husband?" Pauline replies, "Compared to what?" "Compared to what?" is the second most important question we address this year. The most important is "How do you know?"

[One might worry that individual H-C and C-C molecular orbitals within the same alkane molecule might mix with one another to give composite higher- energy HOMOs and lower-energy LUMOs. But the overlap between adjacent H-C and C-C MOs is very small, typically less than 10% as large as the overlap that generated these sigma bonds and antibonds in the first place. Thus even it they do mix, there is no substantial influence on the orbital energies. There are appreciable effects for the π (and π*) MOs of double bonds. We'll worry about this later on when we talk about "conjugation".]

In C-H and C-C there is good overlap and good energy match of the atomic orbitals, which results in substantial splitting between the σ HOMO and σ* LUMO in this "normal" case.

There are a number of cases where species are acids (or bases) because the LUMO (or HOMO) is an atomic orbital that has not been mixed with another atomic orbital to form a bond and still has its unshifted atomic energy. [The energy levels in the diagram to the right are schematic. Don't try to interpret them quantitatively.] Two examples of surviving atomic orbitals are the 1s LUMO of H+ and the sp~3 HOMO of CH3-. [Note that the + charge makes the H+ LUMO even lower in energy (a better home for electrons), and the negative change makes the CH3- HOMO even higher in energy. Here we are taking electron repulsion into account in a way.] Because of the higher nuclear charge, an atomic orbital on N is lower in energy than a corresponding orbital on C. But the unshared pair orbital on NH3 is still an unusually high HOMO, because our standard is not a C atomic orbital, but the σC-H bonding orbital. The N pair has not been stabilized by overlap with another AO. Because of the lower nuclear charge, an atomic orbital on B is higher in energy than a corresponding orbital on C. But the vacant atomic orbital on BH3 is still an unusually low LUMO, because our standard is not a C atomic orbital, but the σC-H antibonding orbital. The p-orbital on B has not been destabilized by overlap with another AO.

Unshared pairs on oxygen make H₂O basic for the same reason that NH₃ is. But H₂O is a much weaker base (lower energy HOMO), because oxygen's greater nuclear charge make its AOs lower in energy than those on nitrogen. On the other hand OH^- is a stronger base than NH₃, because the negative charge raises the energy of its unshared pairs. Of course OH^- is not as strong a base as CH₃^-, because of the difference in nuclear charge.

So the first source of unusual orbitals is the survival of valence-shell atomic orbitals as vacant orbitals or unshared pairs. The energy of these orbitals is influenced by nuclear and molecular charge.

A second source of unusual HOMO/LUMO energies is molecular orbitals that result from poor overlap between atomic orbitals (the orbitals in the previous examples had no overlap at all). As we saw previously, the side-to-side overlap of atomic p orbitals is only about half as effective as the end-to-end overlap of atomic hybrid orbitals. Thus the energies of the unusual π and π* MOs are not "split" by as much as those of "usual" σ and σ* MOs. In the case of the C=C double bond, p AOs are used to form these MOs. This high-energy start makes the π MO particularly unusual, so that the C=C group is basic and normally attacked by acids. In the case of the C=O double bond, p AO of oxygen is much lower in energy than the AOs used to form the C-C bond, this low-energy start makes the π* MO particularly unusual, so that the C=O group is acidic and normally attacked by nucleophiles (Bases are called "nucleophiles" when they attack atoms other than hydrogen). There can be other reasons for poor overlap - for example when the atomic hybrids of carbon do not point directly toward one another to achieve maximal overlap. This gives three-membered-ring hydrocarbons high HOMOs and makes them reactive with acids (remember the x-ray evidence for bent bonds?).

The third source of unusual HOMO/LUMO energies (and the last) is that one or more of the AOs used in making the MOs is higher or lower in energy than the valence orbitals of carbon and hydrogen. In fact this factor was already invoked above in deciding that the HOMO of C=C and the LUMO of C=O were particularly unusual. As shown schematically on the right, the low energy of the F valence orbital (high nuclear charge) makes σ*C-F an unusually low LUMO. Carbon-halogen bonds are subject to attack by bases (high HOMOs). By similar reasoning the high energy of the Li valence orbital (low nuclear charge) makes σC-Li an unusually high HOMO, susceptible to attack by acids (low LUMOs). Most such "organometallic" compounds are reactive with acids. Note that since boron has a lower nuclear charge than carbon, the sp2B orbital is higher than the 1s orbital of hydrogen. This makes σB-H an unusually high HOMO and makes BH3 a base. Above we saw that because of the vacant p orbital on B, BH3 is also an acid. This means that two BH3 molecules should react with one another, and indeed they do react to generate B2H6.

You should be able to use these three considerations (presence of valence-shell AOs, poor overlap, unusual AO components) to identify what kind of reactivity (as acids or bases) the functional groups in Table 3.1 should exhibit.