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.[1]
Roughly, the HOMO level is to organic semiconductors what the valence band is to inorganic semiconductors and quantum dots. The same analogy exists between the LUMO level and the conduction band.
A SOMO is a singly occupied molecular orbital such as half-filled HOMO of a radical.[2]