Recent calculations
Formula used
Bond order: BO = (Nb − Na) ÷ 2
Linear Hückel levels: Ek = α + 2β cos(kπ/(n + 1))
Cyclic Hückel levels: Ek = α + 2β cos(2πk/n)
How to use this calculator
- Select automatic, manual, or Hückel calculation mode.
- Choose a preset molecule or enter custom electron information.
- Select the orbital ordering model when automatic selection is unsuitable.
- Add electronegativity values for heteronuclear polarity estimates.
- Choose whether detailed calculation steps should appear.
- Press the calculate button and review the diagram, bond order, and magnetic prediction.
- Copy, print, share, or export the completed result.
Example molecular orbital results
| Species | Valence electrons | Bond order | Unpaired electrons | Prediction |
|---|---|---|---|---|
| H₂ | 2 | 1 | 0 | Diamagnetic and bonded |
| B₂ | 6 | 1 | 2 | Paramagnetic |
| N₂ | 10 | 3 | 0 | Strong triple bond |
| O₂ | 12 | 2 | 2 | Paramagnetic |
| F₂ | 14 | 1 | 0 | Diamagnetic |
| Ne₂ | 16 | 0 | 0 | No net bond predicted |
Understanding molecular orbital results
Molecular orbital theory combines atomic orbitals across an entire molecule. Constructive combinations create bonding orbitals, while destructive combinations create antibonding orbitals. Electrons occupy the available levels under standard filling rules.
The bond order compares bonding electrons with antibonding electrons. A larger positive value usually indicates a stronger and shorter bond. A zero value suggests that the simplified model predicts no stable bond.
Magnetic behavior depends on electron pairing. One or more unpaired electrons produce paramagnetism, while fully paired electrons produce diamagnetism. Oxygen is a classic example because its two π-star electrons remain unpaired.
HOMO means the highest occupied molecular orbital. LUMO means the lowest unoccupied molecular orbital. Their separation helps describe excitation and chemical reactivity in simplified models.
Heteronuclear molecules require unequal atomic-orbital energies. Bonding orbitals often contain more contribution from the more electronegative atom. Antibonding orbitals may show the opposite weighting pattern.
The Hückel mode treats conjugated π systems using alpha and beta parameters. It is useful for trends, orbital energies, electron filling, and simple aromaticity checks. It does not replace a full quantum-chemistry calculation.
Frequently asked questions
What does the asterisk mean in an orbital label?
An asterisk identifies an antibonding molecular orbital, such as σ* or π*.
How is bond order calculated?
Subtract antibonding electrons from bonding electrons, then divide the difference by two.
Why are B₂ and O₂ orbital orders different?
The relative σ2p and π2p energies change across the second period because orbital mixing becomes weaker.
How does the calculator identify paramagnetism?
It applies Hund’s rule and counts singly occupied orbitals after filling each energy level.
Can this calculator handle ions?
Yes. Several ionic presets are included, and custom electron counts can represent additional cations or anions.
What is the HOMO–LUMO gap?
It is the energy difference between the highest occupied and lowest unoccupied molecular orbitals.
What does a bond order of zero mean?
It means bonding and antibonding effects cancel within the selected simplified orbital model.
Is the polarity result quantitative?
No. The displayed polarity is an estimate based mainly on electronegativity difference and user input.
Does this replace quantum chemistry software?
No. Accurate geometries, coefficients, densities, and energies require methods such as Hartree–Fock or density functional theory.