CHEM 121 glossary

HOMO (highest occupied molecular orbital)

The highest-energy molecular orbital that contains electrons. For a conjugated polyene with $N$ π electrons in the particle-in-a-box model, each level holds 2, so the HOMO is $n = N/2$ ; the lowest-energy absorption moves an electron from the HOMO to the LUMO.

$\psi_2$ , the HOMO of 1,3-butadiene: one node in the middle of the box.

Example

1,3-Butadiene has 4 π electrons filling $n = 1$ and $n = 2$ , so its HOMO is $n = 2$ . In $\ce{N2}$ the HOMO is $\sigma_{2p}$ , which lies above the $\pi_{2p}$ pair because of s–p mixing.