Calculator Inputs
Example Data Table
| Molecule | HOMO (eV) | LUMO (eV) | Gap (eV) | Hardness (eV) | Electrophilicity (eV) |
|---|---|---|---|---|---|
| Ethene | -10.51 | 1.12 | 11.63 | 5.82 | 0.37 |
| Formaldehyde | -9.42 | -0.56 | 8.86 | 4.43 | 1.40 |
| Aniline | -5.48 | -0.76 | 4.72 | 2.36 | 2.08 |
| Nitrobenzene | -7.35 | -2.46 | 4.89 | 2.45 | 4.90 |
Formula Used
The calculator applies common conceptual DFT descriptors derived from HOMO and LUMO energies. Energies are internally converted to eV for consistent reporting.
I ≈ -E_HOMO
A ≈ -E_LUMO
ΔE = E_LUMO - E_HOMO
μ = (E_HOMO + E_LUMO) / 2
χ = -μ
η = (E_LUMO - E_HOMO) / 2
S = 1 / (2η)
ω = μ² / (2η)
ΔNmax = -μ / η
N = E_HOMO - E_HOMO(reference)
Optional donor–acceptor interaction gaps:
ΔE(primary→partner) = E_LUMO(partner) - E_HOMO(primary)
ΔE(partner→primary) = E_LUMO(primary) - E_HOMO(partner)
These formulas are approximation-based descriptors. They are useful for trend analysis, screening, and interpretation, but they do not replace full excited-state or reaction-path calculations.
How to Use This Calculator
- Enter the primary molecule name for easier reporting.
- Select the orbital energy unit used in your source data.
- Provide HOMO and LUMO energies for the primary molecule.
- Keep the default reference HOMO or enter your own benchmark.
- Add partner HOMO and LUMO values only when comparing donor–acceptor behavior.
- Click the analyze button to generate descriptors and the orbital plot.
- Review gap, hardness, electrophilicity, and charge-transfer indicators together.
- Use the CSV or PDF buttons to export the calculated report.
Frequently Asked Questions
1. What does a smaller HOMO–LUMO gap usually mean?
A smaller gap often suggests easier electronic excitation, higher polarizability, and stronger chemical responsiveness. It can indicate greater reactivity, though steric effects and solvent behavior still matter.
2. Why is the HOMO linked to donor strength?
The HOMO contains the most weakly held valence electrons. When its energy is relatively high, electron donation often becomes easier during intermolecular or intramolecular interactions.
3. Why is the LUMO linked to acceptor strength?
The LUMO is the lowest accessible orbital for incoming electron density. A lower LUMO energy usually means the molecule can accept electrons more readily.
4. Is this calculator suitable for reaction prediction?
It is useful for screening trends and comparing candidates. Detailed reaction prediction still needs steric analysis, solvent effects, transition states, and sometimes excited-state modeling.
5. What is electrophilicity in this context?
Electrophilicity combines chemical potential and hardness into one descriptor. Higher values often indicate a stronger tendency to accept electron density under favorable conditions.
6. Why does the calculator use Koopmans-style relations?
They provide a fast approximation connecting orbital energies to ionization potential and electron affinity. The approach is practical for trend analysis, even though exact values may differ.
7. What does ΔNmax tell me?
ΔNmax estimates the maximum amount of charge a species could accept before reaching electronic equilibrium under the conceptual DFT model. It is best used comparatively.
8. Should I input Hartree or eV values?
Use whichever unit matches your computational output. The calculator converts Hartree values to eV internally so all reported descriptors remain consistent and comparable.