What Is LUMO in Chemistry?
The lowest unoccupied molecular orbital is the first empty level above a molecule's filled electrons. This guide explains where it comes from, how its energy is measured and computed, and why it is one of the most useful single numbers in reactivity and materials chemistry.
Key takeaways
- The LUMO is the lowest-energy molecular orbital that contains no electrons.
- A lower (more negative) LUMO energy usually means a better electron acceptor.
- Calculated LUMO energies depend on method and basis set, so compare like with like.
A working definition
In molecular orbital theory, atomic orbitals combine into molecular orbitals that spread over the whole molecule. Each molecular orbital has an energy, and electrons fill them from the bottom up, two per orbital with opposite spins. The highest one that holds electrons is the HOMO (highest occupied molecular orbital). The next one up, the first that is empty, is the LUMO (lowest unoccupied molecular orbital).
Together the HOMO and LUMO are called the frontier orbitals, a term introduced by Kenichi Fukui, because most chemical reactions involve electrons moving out of the HOMO of one species or into the LUMO of another. Fukui shared the 1981 Nobel Prize in Chemistry with Roald Hoffmann for work on how orbital symmetry and frontier orbitals control reactions.
The LUMO is not a place where electrons already are. It is a description of where an electron would go if one were added, and of how much energy that electron would have in the model being used.
Where the LUMO sits
Picture the orbitals as rungs on a ladder, with energy increasing upward. In an ordinary closed-shell molecule, every rung up to the HOMO holds a pair of electrons. Above the HOMO there is a gap, and then the empty rungs start, beginning with the LUMO, then LUMO+1, LUMO+2 and so on.
Because the LUMO is the lowest empty level, it is where an added electron goes first. Its energy therefore tells you, in the language of the model, how strongly the molecule would hold on to an extra electron. A deep (strongly negative) LUMO means the molecule is hungry for electrons. A high LUMO means it is not.
What the LUMO looks like
Every orbital has a shape as well as an energy. In a carbonyl compound such as formaldehyde, the LUMO is the C=O π* orbital, with a large lobe on carbon and a node between carbon and oxygen. That is why nucleophiles attack the carbonyl carbon: they push electron density into the LUMO where it is largest. In benzene, the LUMO is a pair of degenerate π* orbitals spread around the ring. In pyridine, the electronegative nitrogen pulls the π* orbitals down in energy, which is one reason pyridine is easier to reduce than benzene.
The key relationships
The first relationship defines the HOMO-LUMO gap, the energy spacing between the two frontier orbitals. The second is Koopmans' approximation: in Hartree-Fock theory, minus the LUMO energy is a rough estimate of the electron affinity (EA). It is only rough, because it ignores how the other electrons relax when an electron is added. The third is the conversion from the atomic unit of energy, the Hartree, to electronvolts.
Worked example (hypothetical values)
Suppose a calculation reports EHOMO = −6.50 eV and ELUMO = −1.20 eV. The orbital gap is −1.20 − (−6.50) = 5.30 eV. In Hartree, the LUMO energy is −1.20 / 27.211386 = −0.0441 Eh. In kJ/mol it is −1.20 × 96.485332 = −115.8 kJ/mol.
Why the LUMO matters
- Reactivity: nucleophiles donate electrons into the LUMO of an electrophile, so a low LUMO often signals a reactive electrophile.
- Reduction: LUMO energies often correlate with reduction potentials within a related series, because reduction places an electron in the LUMO.
- Cycloadditions: in a normal electron-demand Diels-Alder reaction, the key interaction is between the HOMO of the diene and the LUMO of the dienophile. Lowering the dienophile LUMO with an electron-withdrawing group speeds the reaction.
- Materials: electron-transport and acceptor materials in organic electronics are screened partly by LUMO level.
| If the LUMO is | The molecule tends to be |
|---|---|
| Lower (more negative) | A stronger electron acceptor, easier to reduce |
| Higher | A weaker electron acceptor, harder to reduce |
An example series from this calculator
The values below were calculated with this site's calculator (Extended Hückel, standard formula, MMFF94s geometry). The absolute numbers belong to that model, but the ordering matches chemical experience: adding nitrogen to the ring or attaching carbonyl groups lowers the LUMO.
| Molecule | SMILES | LUMO (eV) |
|---|---|---|
| Benzene | c1ccccc1 | −8.307 |
| Pyridine | c1ccncc1 | −9.235 |
| 1,4-Benzoquinone | O=C1C=CC(=O)C=C1 | −11.389 |
Limitations to keep in mind
Orbital energies are not directly observable. Their values shift with the method, basis set, geometry and solvent model, and density functional methods in particular are known to place LUMO energies differently from Hartree-Fock. Extended Hückel theory, the method used by this calculator, gives LUMO energies that are several electronvolts lower than either. Use orbital energies to compare molecules treated the same way, not as absolute physical constants. Read more in Accuracy and Limitations.
References and further reading
- Fukui, K.; Yonezawa, T.; Shingu, H. A Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons. J. Chem. Phys. 1952, 20, 722.
- Koopmans, T. Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms. Physica 1934, 1, 104-113.
- Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry. Dover, 1996.
- Fleming, I. Molecular Orbitals and Organic Chemical Reactions. Wiley, 2010.
- Tiesinga, E.; Mohr, P. J.; Newell, D. B.; Taylor, B. N. CODATA Recommended Values of the Fundamental Physical Constants: 2018. Rev. Mod. Phys. 2021, 93, 025010.