LUMO Energy in eV
Orbital energies are computed in Hartree, quoted in electronvolts and compared with thermochemistry in kJ/mol. This guide gives the exact conversion factors, works through examples and lists the sign and unit slips that cause most mistakes.
Key takeaways
- 1 Hartree (Eh) = 27.211386245988 eV, and 1 eV = 96.485332 kJ/mol (CODATA 2018).
- Conversions never change the sign: a negative LUMO energy stays negative in every unit.
- Keep full precision until the final step, then round for display.
Why electronvolts
An electronvolt is the energy an electron gains when it moves through a potential difference of one volt. Orbital energies of molecules fall in a convenient range in this unit, typically from about −20 eV to a few eV, and experimental quantities such as ionization energies and electron affinities are usually quoted in eV. That is why most chemists report LUMO energies in eV even though quantum chemistry programs work internally in atomic units.
The atomic unit of energy is the Hartree (symbol Eh, sometimes written au or Ha). It equals twice the ionization energy of a hydrogen atom in the simplest model. Thermochemists prefer kJ/mol or kcal/mol, which express energy per mole of molecules rather than per molecule.
Conversion factors
| From | To | Multiply by |
|---|---|---|
| Hartree (Eh) | eV | 27.211386245988 |
| eV | Hartree | 0.036749322175655 |
| eV | kJ/mol | 96.485332 |
| kJ/mol | eV | 0.010364269 |
| Hartree | kJ/mol | 2625.4996 |
| eV | kcal/mol | 23.060548 |
| eV | cm−1 | 8065.5439 |
The Hartree to eV factor and the eV to kJ/mol factor are the CODATA 2018 recommended values published by NIST. The kcal/mol factor uses the thermochemical calorie, 1 kcal = 4.184 kJ.
Worked conversions
Hartree to eV and kJ/mol
This site's calculator gives a benzene LUMO of −8.307 eV (Extended Hückel, standard formula). Suppose you had instead read −0.30528 Eh from an output file.
eV to Hartree
Notice how many decimals each unit needs for the same precision. Three decimals in eV correspond to roughly five in Hartree and one in kJ/mol. The calculator uses exactly those display precisions and keeps full double precision in its JSON download.
Sign conventions and common slips
- Orbital energy versus electron affinity: a LUMO energy of −1.2 eV corresponds, under Koopmans' approximation, to an electron affinity of +1.2 eV. The two have opposite signs by definition. Do not report the LUMO energy as the electron affinity without changing the sign.
- Per molecule versus per mole: eV and Hartree are per-molecule energies. kJ/mol multiplies by Avogadro's number. A value of −801.5 kJ/mol is not a reaction enthalpy, it is an orbital energy expressed per mole.
- Rydberg units: some solid-state codes use Rydberg (1 Ry = 0.5 Eh = 13.605693 eV). Check the unit before converting.
- Rounding too early: converting a rounded value back and forth accumulates error. Convert from the most precise number you have.
- Old constants: older texts use 27.2114 or 27.21 eV per Hartree. Differences appear only in the fourth or fifth significant figure, but they matter if you compare to many digits.
Energy and wavelength
For photons, energy and wavelength are linked by E = hc / λ. In practical units:
This is a correct conversion for photon energies. It does not turn a ground-state HOMO-LUMO gap into an absorption wavelength, because the orbital gap is not an excitation energy. See the HOMO-LUMO gap guide for why.
References and further reading
- 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.
- NIST. The NIST Reference on Constants, Units, and Uncertainty. physics.nist.gov/cuu/Constants
- Cohen, E. R. et al. Quantities, Units and Symbols in Physical Chemistry (IUPAC Green Book), 3rd ed. RSC Publishing, 2007.