HOMO/LUMO

As MO for larger molecules tend to be more complicated (the electrons are spread out all over the big molecule). At this point we generally no longer focus on a comparison between the MOs and the AOs but instead just take the MOs as a set of orbitals for the whole molecule. There are many such orbitals (an infinite number), but we will always focus simply on the electrons that are most important for the chemistry. These are: the highest occupied molecule orbital or HOMO and the lowest un-occupied molecular orbital or LUMO. The HOMO is the highest energy MO that has any electrons in it. The LUMO is the next highest energy orbital (it will be empty). The LUMO is the lowest energy place to put or excite an electron.

The energy difference between the HOMO and LUMO or HOMO-LUMO gap is generally the lowest energy electronic excitation that is possible in a molecule. The energy of the HOMO-LUMO gap can tell us about what wavelengths the compound can absorb. Or alternatively, measuring the wavelengths a compound absorbs in the lab can be used as a measure of the HOMO-LUMO gap.

Finally, for most molecules (that are not extremely symmetric) there are no degenerate molecular orbitals (MOs with the same energy). Thus the MOs are a series of single orbitals of increasing energy. Since most stable molecules have an even number of electrons (closed shell), nearly all molecules will have all their electrons paired in molecular orbitals.