HOMO vs. LUMO
The HOMO and LUMO sit on either side of the boundary between a molecule's filled and empty orbitals. This guide compares them property by property and shows how their interaction drives chemical reactions.
Key takeaways
- The HOMO is the highest orbital that holds electrons; the LUMO is the lowest one that is empty.
- The HOMO describes electron donation (oxidation, nucleophilicity); the LUMO describes electron acceptance (reduction, electrophilicity).
- Many reactions are governed by the interaction between one molecule's HOMO and another's LUMO.
Two orbitals, one boundary
A molecule in its ground state fills its molecular orbitals from the lowest energy upward. The filled orbitals end at the HOMO, the highest occupied molecular orbital. The empty orbitals begin at the LUMO, the lowest unoccupied molecular orbital. The HOMO and LUMO sit on either side of the boundary between occupied and empty levels, which is why they are called the frontier orbitals.
Because they sit at the edge, the frontier orbitals are the ones most easily disturbed. Taking an electron away removes it from the HOMO. Adding an electron puts it into the LUMO. Mixing with another molecule during a reaction mostly involves these two orbitals as well.
Side-by-side comparison
| Property | HOMO | LUMO |
|---|---|---|
| Occupation | Holds the highest-energy electrons | Empty in the ground state |
| Related experimental quantity | Ionization energy (IE ≈ −EHOMO) | Electron affinity (EA ≈ −ELUMO, much less reliable) |
| Redox process | Oxidation removes an electron from it | Reduction adds an electron to it |
| Reactivity role | Nucleophile, electron donor, Lewis base | Electrophile, electron acceptor, Lewis acid |
| Effect of electron-donating groups | Raised (easier to oxidize) | Raised (harder to reduce) |
| Effect of electron-withdrawing groups | Lowered (harder to oxidize) | Lowered (easier to reduce) |
| Typical sign of the computed energy | Negative | Negative or small positive, depending on method |
How each relates to measurable energies
Koopmans' theorem links Hartree-Fock orbital energies to experiment. Minus the HOMO energy approximates the first ionization energy, and the agreement is often within about 1 eV for organic molecules, partly because two errors (missing orbital relaxation and missing electron correlation) tend to cancel.
The corresponding estimate for the LUMO, EA ≈ −ELUMO, is much weaker. The same two errors add instead of cancel, so Hartree-Fock LUMO energies often sit too high and can even be positive for molecules that clearly bind an extra electron. With density functional theory, orbital energies have a different meaning again: the HOMO energy of an exact functional equals minus the ionization energy, but practical functionals place both frontier orbitals too high, and the LUMO in particular should not be read as an electron affinity.
Frontier orbital interactions
When two molecules approach, their orbitals mix. The interaction that lowers the energy most is usually between the HOMO of one partner and the LUMO of the other, because an occupied orbital mixing with an empty one stabilizes the electrons without the penalty of putting four electrons into a bonding and antibonding pair. The smaller the energy difference between that HOMO and that LUMO, and the larger their overlap, the stronger the interaction.
- Nucleophilic addition: the nucleophile's HOMO (a lone pair or a C-C π bond) donates into the electrophile's LUMO, for example the C=O π* orbital of a ketone.
- Normal electron-demand Diels-Alder: the diene HOMO interacts with the dienophile LUMO. Electron-rich dienes and electron-poor dienophiles react fastest because their frontier orbitals are closest in energy.
- Charge transfer complexes: a donor with a high HOMO and an acceptor with a low LUMO can form a complex in which partial charge moves from donor to acceptor.
A worked example
The values below were calculated with this site's calculator (Extended Hückel, standard formula, MMFF94s geometry).
| Molecule | HOMO (eV) | LUMO (eV) | Gap (eV) |
|---|---|---|---|
| Ethylene | −13.227 | −8.208 | 5.019 |
| Benzene | −12.804 | −8.307 | 4.497 |
| Naphthalene | −12.079 | −9.341 | 2.738 |
Going from ethylene to benzene to naphthalene, conjugation spreads over more atoms. The HOMO rises and the LUMO falls, so the gap shrinks. This is the same trend that makes larger aromatic molecules absorb at longer wavelengths and react more readily. The absolute numbers are specific to Extended Hückel theory; the trend is the useful part.
Common mistakes
- Comparing a HOMO from one method with a LUMO from another, then quoting the difference as a gap.
- Reading a positive LUMO energy as proof that a molecule cannot accept an electron. In many methods, especially those with diffuse basis functions, the LUMO energy is positive for ordinary molecules.
- Assuming the orbital with the largest coefficient on an atom always predicts the reaction site. Sterics, charge and solvent matter too.
References and further reading
- Fukui, K. Role of Frontier Orbitals in Chemical Reactions. Science 1982, 218, 747-754.
- Koopmans, T. Physica 1934, 1, 104-113.
- Fleming, I. Molecular Orbitals and Organic Chemical Reactions. Wiley, 2010.
- Zhan, C.-G.; Nichols, J. A.; Dixon, D. A. Ionization Potential, Electron Affinity, Electronegativity, Hardness, and Electron Excitation Energy: Molecular Properties from Density Functional Theory Orbital Energies. J. Phys. Chem. A 2003, 107, 4184-4195.
- Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry. Dover, 1996.