HOMO LUMO Gap Calculator

Analyze frontier orbitals with clarity and confidence. Convert energies into gap, hardness, softness, and wavelengths. Explore molecular behavior using precise orbital energy comparisons today.

Calculator Inputs

Enter one sample per line using this format: name, HOMO, LUMO. Valid rows will populate the comparison graph.

Plotly Graph

The chart compares calculated HOMO–LUMO gaps for each valid sample line you entered.

Example Data Table

Molecule HOMO (eV) LUMO (eV) Gap (eV) Approx. Wavelength (nm)
Benzene -6.72 -1.15 5.57 222.62
Ethylene -10.51 0.48 10.99 112.83
Aniline -5.82 -0.72 5.10 243.14
Naphthalene -5.97 -1.02 4.95 250.51
Anthracene -5.38 -1.86 3.52 352.27

Formula Used

Primary equation: Egap = ELUMO - EHOMO

Chemical hardness: η = Egap / 2

Chemical softness: S = 1 / Egap

Mulliken electronegativity: χ = -(EHOMO + ELUMO) / 2

Chemical potential: μ = -χ

Electrophilicity index: ω = χ² / (2η)

Optical wavelength estimate: λ (nm) = 1240 / Egap

These relations are common conceptual descriptors in computational chemistry, molecular electronics, and frontier orbital analysis.

How to Use This Calculator

  1. Enter a molecule name for easier result tracking.
  2. Type HOMO and LUMO energy values in electron volts.
  3. Add temperature if you want the thermal comparison ratio.
  4. Optionally paste several samples in the textarea for graphing.
  5. Click Calculate Gap to show results above the form.
  6. Review the derived descriptors, sample table, and Plotly chart.
  7. Use the CSV or PDF buttons to export your output.

Frequently Asked Questions

1. What does the HOMO–LUMO gap indicate?

It estimates how easily electrons can be promoted from an occupied orbital to an unoccupied orbital. Smaller gaps often suggest higher reactivity, easier excitation, and stronger charge-transfer behavior.

2. Why must the LUMO value be greater than the HOMO value?

A positive gap requires the unoccupied orbital energy to lie above the occupied orbital energy. If not, the entered values are inconsistent with the expected frontier orbital ordering.

3. Are the results only valid for DFT calculations?

No. The calculator works with any HOMO and LUMO energies expressed in electron volts. Interpretation still depends on the computational method, basis set, and the quality of the underlying model.

4. What does the wavelength estimate represent?

It gives an approximate optical wavelength corresponding to the energy gap using a simple photon-energy relation. Real spectra may differ because transitions can involve selection rules and solvent effects.

5. Why does chemical hardness equal half the gap here?

This follows a common conceptual chemistry approximation derived from frontier orbital theory. It is a practical descriptor rather than a full experimental measurement.

6. Can I compare several molecules at once?

Yes. Add multiple lines in the sample list area using the name, HOMO, and LUMO format. The calculator will build a comparison table and a gap graph.

7. What units should I use for orbital energies?

Use electron volts. If your source data is in another unit, convert it first. Keeping consistent units is essential because every derived quantity here depends directly on the gap value.

8. Does a smaller gap always mean better conductivity?

Not always. A smaller gap often supports easier excitation or charge transport, but actual conductivity also depends on packing, morphology, defects, interfaces, and measurement conditions.