Molecular Orbital Theory: Why O2 Is Magnetic and He2 Isn't Real

Two atomic orbitals in, two molecular orbitals out

Molecular orbital (MO) theory builds bonds by combining atomic orbitals mathematically — the Linear Combination of Atomic Orbitals (LCAO) approach. Whenever two atomic orbitals overlap, they combine in two ways: constructively, reinforcing electron density between the nuclei (a bonding orbital, lower in energy), and destructively, creating a node of zero electron density between the nuclei (an antibonding orbital, marked with an asterisk and higher in energy).

1s + 1s  (same phase, constructive)      →  σ1s     bonding, lower energy
1s - 1s  (opposite phase, destructive)   →  σ1s*    antibonding, higher energy

Bond order = (electrons in bonding MOs - electrons in antibonding MOs) / 2

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Why He2 is a footnote and H2 is a real molecule

H₂ has 2 electrons total, both going into σ1s: bond order = (2-0)/2 = 1, a genuine, stable single bond. He₂ would have 4 electrons — 2 fill σ1s, and the remaining 2 are forced into the higher-energy σ1s* antibonding orbital: bond order = (2-2)/2 = 0. A bond order of zero means the bonding and antibonding contributions exactly cancel, so there's no net stabilization from forming the molecule — which is exactly why helium exists only as single atoms, never as He₂.

Filling second-row diatomics: N2 through Ne2

For second-row elements, the 2s and 2p atomic orbitals each combine into their own bonding/antibonding pairs, and the 2p orbitals split further: one σ2p (from the p-orbitals pointing directly at each other) and two degenerate π2p (from the perpendicular p-orbitals overlapping side-on):

Filling order for O2, F2, Ne2 (no s-p mixing):
σ2s  <  σ2s*  <  σ2p  <  π2p(×2)  <  π2p*(×2)  <  σ2p*

Filling order for Li2 through N2 (with s-p mixing):
σ2s  <  σ2s*  <  π2p(×2)  <  σ2p  <  π2p*(×2)  <  σ2p*
      (σ2p and π2p swap places — see below)

O2's paramagnetism: the prediction Lewis structures miss

O₂ has 12 valence electrons to place. Filling the levels in order eventually leaves exactly 2 electrons for the two degenerate π2p* orbitals. Hund's rule says degenerate orbitals fill singly, with parallel spins, before any pairing happens — so those last two electrons go into separate π2p* orbitals, unpaired. This gives O₂ a bond order of 2 (matching the familiar O=O double bond) and two unpaired electrons, which is exactly why liquid oxygen is measurably paramagnetic — it's visibly attracted into the gap of a strong magnet, a fact the simple Lewis dot structure, with all electrons neatly paired, cannot explain at all. This was one of MO theory's earliest and most convincing experimental confirmations.

The s-p mixing swap: why N2's order looks different

For Li₂ through N₂, the 2s and 2p atomic orbitals sit close enough in energy that the σ2s and σ2p molecular orbitals interact with each other (s-p mixing), pushing σ2p up above the π2p pair. From O₂ onward, the increasing nuclear charge pulls the 2s orbital down further away from 2p, weakening the mixing enough that σ2p drops back below π2p — the ordering you'd naively expect. This single crossover explains a real, measurable quirk: N₂ (bond order 3, no unpaired electrons) is diamagnetic and exceptionally strong, while its neighbor O₂ is both weaker (bond order 2) and magnetic — a difference in orbital filling order, not just electron count.

Frequently asked questions

Why doesn't He2 exist, but H2 does?

H2 has 2 electrons, both filling the bonding σ1s orbital, giving bond order 1 — a stable single bond. He2 would have 4 electrons, filling both σ1s and σ1s*, giving bond order (2-2)/2 = 0. Zero bond order means no net attraction stronger than the natural repulsion, so He2 simply doesn't form as a stable molecule.

Why is O2 magnetic when its Lewis structure shows all electrons paired?

The simple Lewis dot structure for O2 (O=O with lone pairs) is a useful shortcut but doesn't capture the true orbital picture. Molecular orbital theory shows O2's last two electrons occupy two separate, degenerate π* antibonding orbitals, and Hund's rule keeps them unpaired with parallel spins — that's what makes liquid oxygen visibly cling to a strong magnet.

Why do N2, O2 and F2 fill their orbitals in a different order?

For Li2 through N2, the 2s and 2p atomic orbitals are close enough in energy to mix (s-p mixing), which pushes the σ2p orbital above the two π2p orbitals. From O2 onward, the growing nuclear charge separates 2s and 2p energies enough that mixing becomes negligible, and σ2p drops back below π2p, its expected position from simple energy ordering.

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