Questions: Molecular Orbital Diagrams and Bond Order

Question 1

O₂ is drawn with a double bond in Lewis notation. What does the MO diagram for O₂ reveal that the Lewis structure cannot predict?

• A. O₂ has a bond order of 3 due to σ-π mixing at this atomic number
• B. O₂ is paramagnetic because two electrons occupy degenerate π* antibonding orbitals unpaired
• C. O₂ has no antibonding electrons, which explains its atmospheric stability
• D. MO theory confirms the Lewis double bond but adds no additional information

Answer: (B)

The π* antibonding orbitals of O₂ are degenerate (equal energy), so by Hund's rule the last two electrons enter them one each — unpaired. Unpaired electrons produce paramagnetism. Lewis structures pair all electrons into bonds and lone pairs and cannot represent this situation; they predict a diamagnetic molecule, which experiment refutes. Liquid O₂ visibly clings between magnet poles. This is one of MO theory's definitive victories over Lewis structures.

Question 2

He₂ would place 2 electrons in σ1s (bonding) and 2 electrons in σ*1s (antibonding). What bond order does this give, and what does MO theory predict for He₂?

• A. Bond order = 1; He₂ forms a stable single bond
• B. Bond order = 2; He₂ is doubly bonded because both bonding and antibonding orbitals are full
• C. Bond order = 0; He₂ is predicted not to exist as a stable molecule
• D. Bond order = −1; He₂ is anti-bonded and strongly repulsive

Answer: (C)

Bond order = (bonding electrons − antibonding electrons) / 2 = (2 − 2) / 2 = 0. A bond order of zero means no net bonding: the stabilization from filling σ1s is exactly cancelled by the destabilization from filling σ*1s. He₂ does not exist under normal conditions, consistent with this prediction. This is why noble gases are monatomic — filling both bonding and antibonding MOs gives zero net stabilization regardless of how many electrons are involved.

Question 3

Electrons in antibonding molecular orbitals actively destabilize the molecule — they do not merely fail to contribute to bonding.

• T. True
• F. False

Answer: True

This is a critical distinction. A bonding MO lowers the molecular energy relative to separated atoms; an antibonding MO raises it. Each antibonding electron partially cancels the stabilization of a bonding electron — this is why bond order subtracts antibonding occupancy. A molecule like He₂ with equal bonding and antibonding occupancy has zero net bond precisely because the antibonding electrons undo all the stabilization of the bonding ones.

Question 4

A molecule with a higher MO bond order will generally have a shorter and stronger bond than a molecule with a lower bond order.

• T. True
• F. False

Answer: False

Bond order correlates with bond strength and length within closely related species (e.g., comparing N₂ bond order 3 with O₂ bond order 2), but is not a universal rule across different molecular frameworks. Atomic size, nonbonding electron repulsion, and the specific orbital types involved all affect bond parameters. The misconception is treating bond order as the sole determinant, when it is a rough guide meaningful primarily within comparable families of molecules.

Question 5

Why does MO theory predict O₂ is paramagnetic while a Lewis structure predicts it is diamagnetic, and what does this reveal about Lewis structures?

Model answer: MO theory fills electrons into molecular orbitals by energy, applying Aufbau and Hund's rules. O₂'s last two electrons enter two degenerate π* orbitals one each — unpaired — producing paramagnetism. Lewis structures assign electrons to bonds and lone pairs without access to orbital degeneracy; they cannot represent a state where electrons in equivalent orbitals remain unpaired. This reveals that Lewis structures capture electron counting but miss the quantum mechanical orbital structure governing magnetic and spectroscopic properties.

The experimental paramagnetism of O₂ was known before MO theory provided its explanation. Lewis and valence bond approaches both predicted a paired, diamagnetic structure. MO theory's correct prediction established it as the more complete model of electronic structure, particularly for properties that depend on orbital occupancy and symmetry rather than simple electron-pair counting.