HOMO and LUMO are acronyms for highest occupied molecular orbital and lowest unoccupied molecular orbital, respectively. The energy difference between the HOMO and LUMO is termed the HOMO–LUMO gap. HOMO and LUMO are sometimes referred to as frontier orbitals.
Roughly, the HOMO level is to organic semiconductors what the valence band maximum is to inorganic semiconductors and quantum dots. The same analogy exists between the LUMO level and the conduction band minimum.
In organometallic chemistry the size of the LUMO lobe can help predict where addition to pi ligands will occur.
See also 
- Frontier molecular orbital theory
- Diels–Alder reaction
- Electron configuration
- Koopmans' theorem
- Organic semiconductor
- OrbiMol Molecular orbital database