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13:00in productionCh. 1 · A bond that belongs to the whole molecule/ 13:00 · ceiling 15 min
Chemistry · Physics

Molecular orbital theory

Ordinary oxygen is attracted to a magnet, a fact the older theory of chemical bonds simply could not explain. Molecular orbital theory got it right by giving up on the idea that a bond belongs to two atoms alone.

Molecular orbital theory, developed mainly by Friedrich Hund, Robert Mulliken and John Lennard-Jones from the late 1920s, treats a molecule's electrons as spread across the whole structure rather than tied to individual bonds between pairs of atoms. Built on the quantum mechanics worked out earlier that decade by Schrödinger, Heisenberg and Born, it correctly predicts oxygen's attraction to a magnetic field, a property the older valence bond picture cannot account for, and gives a bond-order arithmetic that explains why some simple molecules, such as a bound helium pair, do not exist as stable species at all.

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Chapters & takeaways6
  1. 0:08
    A bond that belongs to the whole molecule

    Molecular orbital theory treats electrons as moving under the influence of every nucleus in a molecule, not just the two atoms in a given bond.

  2. 2:10
    Built on a decade of new physics

    The theory rests directly on the quantum mechanics of the mid-1920s, including the Schrödinger equation and Born's probability interpretation.

  3. 4:20
    The test valence bond theory failed

    Molecular orbital theory correctly predicts that ordinary oxygen gas is attracted to a magnet, a property the older bonding picture cannot explain.

  4. 6:30
    Arithmetic that predicts whether a molecule exists

    A simple bond-order calculation from bonding and antibonding electrons correctly distinguishes stable molecules from ones that never form.

  5. 8:40
    From benzene's equal bonds to graphite's conductivity

    The same delocalised-electron picture explains benzene's identical carbon-carbon bonds, methane's shared electrons, and why graphite conducts electricity.

  6. 10:50
    A framework worth the effort it asks for

    The theory is more abstract than drawing lines between atoms, but it earns that abstraction by predicting things the simpler picture gets wrong.

Worth your time?

Selectively. Start with the brief, then study the parts we point at.

4/ 5
What works
  • names the specific failure, oxygen's magnetism, that separates molecular orbital theory from its predecessor
  • gives the bond-order arithmetic plainly enough to see why helium does not form a stable two-atom molecule
  • traces the theory to named contributors and dated milestones rather than presenting it as arriving fully formed
What does not
  • does not walk through the underlying mathematics of the Schrödinger equation itself
  • leaves the later refinements, such as Hartree-Fock and density functional theory, only briefly mentioned
Study it if
  • readers who want to know why a chemistry textbook sometimes draws bonds as shared lines and sometimes as clouds
  • anyone curious what quantum mechanics actually buys chemistry beyond abstract physics
  • people who like a theory that is judged by a specific, checkable prediction rather than general plausibility
Skip it if
  • readers who want the Schrödinger equation explained from first principles
  • anyone looking for a simple, single mental picture of a chemical bond rather than two competing frameworks
The written brief3 min read

A bond that belongs to the whole molecule

The core claim is a shift in what a chemical bond is taken to be. Rather than assigning a shared pair of electrons to a specific bond between two named atoms, as the older valence bond picture does, molecular orbital theory treats a molecule’s electrons as moving under the combined influence of every atomic nucleus present, distributed across orbitals that can span the entire structure rather than sitting between just one pair of atoms. Molecular orbitals are typically built from the Linear Combination of Atomic Orbitals method, which combines existing atomic orbitals into new ones, provided those atomic orbitals share compatible symmetry, meaningful spatial overlap, and reasonably similar energy levels.

Built on a decade of new physics

This picture only became possible once quantum mechanics itself had been worked out. Quantum theory developed through the mid-1920s, building on Max Planck’s 1900 treatment of black-body radiation and Einstein’s 1905 explanation of the photoelectric effect, into the fuller framework established by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born and Paul Dirac. Central to this framework is the Schrödinger equation, whose solutions are wave functions, and the Born rule, which interprets the square of a wave function as a probability density rather than a certainty about where a particle actually is — a foundation molecular orbital theory applies directly to electrons distributed across a molecule.

The test valence bond theory failed

The theory’s clearest advantage over valence bond theory is a specific, checkable prediction rather than a general claim of superiority. Molecular orbital theory correctly explains why ordinary molecular oxygen is paramagnetic, meaning it is weakly attracted into a magnetic field, a property that follows naturally from how electrons fill oxygen’s molecular orbitals but that the valence bond picture, built around paired electrons in fixed bonds, cannot account for. Friedrich Hund, Robert Mulliken and John Lennard-Jones developed the framework mainly through the late 1920s and 1930s, with Lennard-Jones’s 1929 work providing the first quantitative application, and Mulliken introducing the term orbital itself in 1932.

Arithmetic that predicts whether a molecule exists

The theory also comes with working arithmetic that predicts molecular stability directly. Bond order is calculated as half the difference between the number of electrons in bonding orbitals and the number in antibonding orbitals, and this simple figure tracks real chemical behaviour: hydrogen, with a bond order of one, has a bond energy of 436 kilojoules per mole, while the more weakly bound hydrogen cation, with a bond order of one half, holds together with roughly 171 kilojoules per mole. A hypothetical two-atom helium molecule comes out with a bond order of zero, correctly predicting that no such stable molecule exists under ordinary conditions, since its bonding and antibonding electrons cancel out entirely.

From benzene’s equal bonds to graphite’s conductivity

The same delocalised picture extends naturally to more complex molecules. In benzene, six electrons spread evenly around the ring explain why all six carbon-carbon bonds are chemically identical rather than alternating between two different bond types, and in graphite, electrons delocalised across entire sheets of carbon atoms account for the material’s unusually high electrical conductivity. Extended systems of this kind, found in molecules such as beta-carotene and chlorophyll, are also what allow those molecules to absorb specific wavelengths of visible light, connecting the same underlying orbital picture to something as directly observable as a pigment’s colour.

A framework worth the effort it asks for

This is worth the effort selectively rather than universally: the payoff is real, but it asks a reader to give up the intuitive picture of a bond as a simple line between two atoms in exchange for a more accurate, more abstract one. That trade is worth making for anyone who wants an explanation that actually predicts oxygen’s magnetism, distinguishes real molecules from impossible ones through a short calculation, and extends cleanly from simple diatomic gases to the electronic structure of pigments and conductive materials. Readers content with the simpler valence bond picture for everyday purposes will find rather less urgency here, since molecular orbital theory earns its keep specifically in the cases where the simpler picture breaks down.

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