HOMO and LUMO are acronyms used in orbital interaction theory of organic chemistry. HOMO stands for highest occupied molecular orbital and LUMO for 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.
Using molecular orbital theory, a molecular orbital diagram can be constructed that features the individual atomic basis orbitals and the molecular orbitals resulting from atomic interactions to form molecules. Through qualitative molecular orbital analysis through a molecular orbital diagram, the chemist is able to display the resulting molecular orbitals stemming from atomic interaction based on their relative energies and assign bonding, nonbonding and/or antibonding character to each molecular orbital. After these assignments are made, the chemist is able to identify the Highest Occupied Molecular Orbital (HOMO) that contains electrons and the Lowest Unoccupied Molecular Orbital (LUMO) that does not contain electrons. The difference in energy between these two frontier orbitals can be used to predict the strength and stability of transition metal complexes, as well as the colors they produce in solution.