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General Chemistry I · Chemical Bonding & Molecular Geometry

Molecular Orbital Theory

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On this page 7 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Key takeaway
  6. Study tools
  7. Sources & references

In 30 seconds

Molecular orbital theory describes bonds differently from valence bond theory: instead of localized electron pairs between two atoms, atomic orbitals combine to form molecular orbitals that spread over the entire molecule. Each pair of atomic orbitals produces a lower-energy bonding MO and a higher-energy antibonding MO. Electrons fill these MOs (lowest energy first, obeying Hund's rule), and the bond order — ½(bonding electrons − antibonding electrons) — measures bond strength. MO theory uniquely explains magnetism: it predicts that O₂ has two unpaired electrons and is therefore paramagnetic.

Why this matters

MO theory succeeds where simpler models fail. Lewis and valence bond theory draw O₂ with a double bond and all electrons paired — yet liquid oxygen is visibly attracted to a magnet. MO theory explains this paramagnetism with two unpaired π* electrons. The bond-order formula also predicts trends the simple models miss: removing an electron from O₂ (to O₂⁺) strengthens the bond (order 2 → 2.5), and adding one (O₂⁻) weakens it. MO theory underlies our understanding of spectroscopy, conductivity, and the electronic structure of materials.

The college version

Key Ideas

  • Molecular orbitals (MOs): combinations of atomic orbitals; each is delocalized over the whole molecule.
  • Bonding MO (σ, π): lower in energy; electron density concentrated between the nuclei (stabilizes the bond).
  • *Antibonding MO (σ, π):* higher in energy; a node between the nuclei (destabilizes the bond).
  • Bond order = ½(N_bonding − N_antibonding). Higher bond order = stronger, shorter bond; bond order 0 = no bond.
  • Paramagnetic: has unpaired electrons → attracted to a magnetic field. Diamagnetic: all electrons paired → weakly repelled.
  • Hund's rule in MOs: degenerate orbitals (e.g., π*2p) fill singly before pairing.
  • s–p mixing: for N₂ and lighter diatomics, σ2p lies above π2p; for O₂ and F₂, σ2p lies below π2p.

Equations and Variables

  • Bond order = ½(N_bonding − N_antibonding)
    • N_bonding = number of electrons in bonding MOs
    • N_antibonding = number of electrons in antibonding MOs

How It Works

  1. Two atoms each contribute valence atomic orbitals; these combine in pairs into bonding + antibonding MOs.
  2. Fill the MOs with the total valence electrons, lowest energy first, pairing only when necessary (Hund's rule).
  3. Count bonding vs. antibonding electrons and compute the bond order.
  4. Unpaired electrons in the filled diagram indicate paramagnetism.
  5. For O₂ (16 electrons): σ2s² σ2s² σ2p² π2p⁴ π2p² → bonding = 8, antibonding = 4 → bond order 2, with two unpaired electrons in π*2p (paramagnetic).

Worked Example

Calculate the bond order and magnetism of O₂, O₂⁺, O₂⁻, and N₂.

Using the O₂/F₂ MO order (σ2s < σ2s < σ2p < π2p < π2p < σ*2p):

  1. O₂ (16 e⁻): (σ2s)² (σ2s)² (σ2p)² (π2p)⁴ (π2p)². Bonding = 2+2+4 = 8, antibonding = 2+2 = 4. Bond order = ½(8 − 4) = 2. Two unpaired electrons → paramagnetic.
  1. O₂⁺ (15 e⁻): remove one π2p electron → π2p¹. Bond order = ½(8 − 3) = 2.5 (stronger, shorter bond than O₂).
  1. O₂⁻ (17 e⁻): add one π2p electron → π2p³. Bond order = ½(8 − 5) = 1.5.
  1. N₂ (14 e⁻): with s–p mixing, order is σ2s < σ2s < π2p < σ2p < π2p < σ2p: (σ2s)² (σ2s)² (π2p)⁴ (σ2p)². Bonding = 2+4+2 = 8, antibonding = 2. Bond order = ½(8 − 2) = 3 (a triple bond), all electrons paired → diamagnetic.

Common Confusions

  • "Antibonding orbitals don't get filled." — Wrong: they fill after the bonding orbitals; O₂ has two π*2p electrons, which is why it's paramagnetic.
  • "O₂ is diamagnetic because all its electrons are paired." — Wrong: O₂ is paramagnetic (two unpaired π*2p electrons), a key experimental fact that only MO theory explains.
  • "Bond order is just the number of bonds." — It equals the number of bonds for simple cases, but the formula (½(bonding − antibonding)) is general and can give fractional orders (O₂⁺ = 2.5).
  • "Adding an electron always strengthens a bond." — Not always: adding an electron to O₂ (→ O₂⁻) lowers the bond order from 2 to 1.5.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Think of MO theory as two singers harmonizing. One note (a bonding orbital) is where their voices reinforce each other — loud and pleasant (lower energy, holds the molecule together). Another note (an antibonding orbital) is where their voices cancel out — quiet and jarring (higher energy, works against bonding). The molecule "sings" by filling the notes low-to-high. Count the harmony notes minus the canceling notes, halve it, and you get the bond order — how strongly the two are stuck together. Oxygen's last two electrons are forced to sit in two separate canceling notes with nobody to pair with, which is what makes oxygen magnetic. (The analogy captures constructive/destructive combination; the real "harmony" is wave interference of electron orbitals.)

Key takeaways

  • AOs combine into bonding (lower) and antibonding (higher) MOs.
  • Bond order = ½(bonding e⁻ − antibonding e⁻).
  • Bond order 0 = no bond; higher order = stronger, shorter bond.
  • O₂ bond order 2, paramagnetic (two unpaired π*2p electrons).
  • N₂ bond order 3, diamagnetic (all paired).
  • O₂⁺ bond order 2.5; O₂⁻ bond order 1.5.
  • Paramagnetic = unpaired electrons (attracted to a magnet); diamagnetic = all paired.
  • For O₂/F₂, σ2p < π2p; for N₂ and lighter, s–p mixing raises σ2p above π2p.
  • MOs = bonding (lower) + antibonding (higher) combinations of atomic orbitals.
  • Fill MOs lowest-first, Hund's rule for degenerate orbitals.
  • Bond order = ½(bonding e⁻ − antibonding e⁻).
  • O₂: bond order 2, paramagnetic (2 unpaired π*2p electrons).
  • N₂: bond order 3, diamagnetic.
  • O₂⁺ (2.5) and O₂⁻ (1.5) show how adding/removing electrons changes bond strength.
  • Paramagnetism = unpaired electrons; diamagnetism = all paired.

Keep learning

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Practice General Chemistry I

This lesson has no separate scored set. Practice draws from the subject’s question bank.

Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • Explain how molecular orbital (MO) theory differs from valence bond theory.
  • Construct a simple MO diagram for homonuclear diatomic molecules (O₂, N₂).
  • Calculate bond order from the formula ½(bonding − antibonding) electrons.
  • Use MO theory to explain why O₂ is paramagnetic while N₂ is diamagnetic.

Sources & references

  1. OpenStax, *Chemistry 2e*, "8.4 Molecular Orbital Theory."
  2. OpenStax, *Chemistry 2e*, "8.3 Multiple Bonds."
  3. PubChem, "Oxygen (Element)."

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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