Resonance & molecular-orbital theory

The honest picture under every cartoon. Lewis structures, hybrids, and resonance arrows all speak a localized language — bonds that live between two atoms — and they patch over delocalization by drawing several structures and averaging. MO theory drops the patch: atomic orbitals combine into molecular orbitals that span the whole molecule (N orbitals in, N orbitals out), filled lowest-first. Each combination is either bonding (in-phase, density between nuclei) or antibonding (out-of-phase, a node between), and the count of filled bonding minus antibonding is the bond order. This is what predicts the things the cartoons get wrong — that O₂ is magnetic, why benzene's magic number is 4n+2, why methane shows two ionization energies, not four.

Bridge-Burners LLC · Fiddler · LCAO · bonding/antibonding · the truth under resonance · anchor: AKASHA

State

viewO₂ — LCAO
bond order2
verdictparamagnetic

Resonance vs MO

Resonance is the localized model confessing: when one Lewis structure won't do, draw several and call the molecule their average. The arrow ↔ is not the molecule flipping — it means neither drawing is real.

MO theory never localizes in the first place. The resonance hybrid ≈ the filled bonding MOs; both describe one electron density, but MO handles delocalization, magnetism, and spectra directly.

What MO explains that Lewis can't

O₂ magnetic2 e⁻ in degenerate π* → unpaired → paramagnetic (Lewis says paired)
He₂, bond 0σ + σ* both full → cancels
4n+2closed bonding shell at 2,6,10 (Frost circle)
colourHOMO→LUMO gap = light absorbed

Status discipline

LiteralN AOs → N MOs, filled aufbau; bond order = ½(bonding−antibonding); O₂ paramagnetic (2 unpaired π*); benzene's 6 π e⁻ fill 3 bonding MOs → closed shell → aromatic; 4n+2 = closed shell.
BridgeThe honest frame under hybridization, Kekulé, and resonance; H₂'s σ/σ* generalized; benzene's torus resolved into 6 MOs with nodes.
SpeculativeMO theory is still the orbital (mean-field) approximation — real electrons correlate. The simple Hückel π-only model ignores σ; both are excellent, not exact.