Valence Bond Theory vs Molecular Orbital Theory

Chemists have two main quantum-mechanical pictures of the covalent bond. Valence bond (VB) theory sees a bond as two atoms sharing a pair of electrons in overlapping orbitals — the language of Lewis structures, hybridisation and resonance. Molecular orbital (MO) theory sees electrons as occupying orbitals that spread over the whole molecule. Both are approximations to the same underlying physics, and both are used every day. This comparison sets out how they differ, where each succeeds and fails, and when to reach for which.

The two ideas in one sentence each

• Valence bond theory: a covalent bond forms when an orbital on one atom overlaps with an orbital on another, and the two electrons in that region pair up. Bonds are localised between pairs of atoms.
• Molecular orbital theory: atomic orbitals combine into molecular orbitals that belong to the whole molecule; electrons fill these MOs in order of energy. Bonding is delocalised by default.

Origins

VB theory grew from the 1927 work of Walter Heitler and Fritz London on the hydrogen molecule, and was developed by Linus Pauling, who added hybridisation and resonance in the early 1930s. MO theory was developed at the same time by Robert Mulliken and Friedrich Hund. Mulliken received the 1966 Nobel Prize in Chemistry for it; Pauling received the 1954 prize for his work on the nature of the chemical bond.

Side by side

Feature	Valence bond theory	Molecular orbital theory
Where electrons are	In bonds between two atoms, or lone pairs on one atom	In MOs spread over the molecule
Basic unit	The electron-pair bond	The molecular orbital
Explains shapes via	Hybridisation (sp³, sp², sp) + VSEPR	Orbital symmetry; less direct for shapes
Multiple bonds	σ + π bonds from hybrids and p orbitals	σ and π MOs, bonding and antibonding
Delocalisation	Needs resonance (several structures)	Built in naturally
Antibonding orbitals	Not part of the basic model	Central
Magnetism of O₂	Predicts diamagnetic ✗	Predicts paramagnetic ✓
Fractional bond orders	Only via resonance averages	Natural (H₂⁺ = ½, O₂⁺ = 2½)
Excited states and spectra	Awkward	Natural (electrons promoted between MOs)
Ease of use by hand	Easy; matches drawn structures	Harder for large molecules
Main use	Organic chemistry, shapes, reaction mechanisms	Spectroscopy, magnetism, colour, computational chemistry

Example 1: H₂

VB: each H has one electron in a 1s orbital. The orbitals overlap and the electrons pair with opposite spins, forming a σ bond. Simple and correct.

MO: the two 1s orbitals combine into a bonding σ1s and an antibonding σ*1s. Both electrons go into σ1s. Bond order = 1.

Both give a single bond. The difference only becomes important for harder cases.

Example 2: methane, CH₄

VB: carbon’s 2s and three 2p orbitals mix into four sp³ hybrids, pointing to the corners of a tetrahedron. Each overlaps with a hydrogen 1s orbital to form a localised C–H σ bond. This matches the tetrahedral shape and four identical bonds (see hybridisation explained).

MO: the eight valence electrons occupy four bonding MOs spread over the whole molecule — one of lower energy and three of equal, higher energy. This predicts that methane should have two different ionisation energies for its valence electrons. Photoelectron spectroscopy shows exactly that: two bands, at about 14 eV and 23 eV. The simple VB picture of four identical localised bonds doesn’t predict this.

So VB gives the most intuitive picture of shape; MO better matches the measured electron energies. (Mathematically, the two descriptions can be transformed into each other — the total electron distribution is the same.)

Example 3: oxygen, O₂

VB: the Lewis structure O=O has all electrons paired, predicting a diamagnetic molecule.

MO: the last two electrons occupy two equal-energy π*2p orbitals singly, so O₂ has two unpaired electrons and is paramagnetic, while still having a bond order of 2.

Experiment: liquid oxygen is attracted to a magnet. MO wins (see why is oxygen paramagnetic?).

Example 4: benzene

VB: no single Lewis structure works. Benzene is described as a resonance hybrid of two Kekulé structures, plus sometimes minor contributors. It works, but it needs several drawings to describe one molecule (see resonance structures).

MO: the six p orbitals on the ring carbons combine into six π MOs: three bonding (filled with benzene’s six π electrons) and three antibonding (empty). The π electrons are delocalised around the ring in a single description. The theory also explains why rings with 6 π electrons (more generally, 4n + 2) are especially stable — the basis of Hückel’s rule for aromaticity.

MO gives the more natural and more predictive description here, though chemists still draw Kekulé structures to track electrons in mechanisms.

Example 5: He₂ and He₂⁺

VB: helium’s 1s² orbital is full, with no unpaired electron to share, so no bond forms. It can explain why He₂ doesn’t exist, but has no simple way to describe He₂⁺.

MO: He₂ has bond order ½(2 − 2) = 0, so no bond. He₂⁺ has bond order ½(2 − 1) = ½, so a weak bond — and the ion is observed experimentally (see bond order calculations).

Where VB theory shines

• Molecular shapes: hybridisation plus VSEPR predicts geometry quickly (see VSEPR and molecular geometry).
• Organic chemistry: reaction mechanisms with curly arrows are drawn with localised bonds and lone pairs.
• Intuition: the idea of a bond “between A and B” matches how chemists think and draw.
• Bond breaking: VB correctly describes H₂ splitting into two neutral H atoms at large distances; simple MO theory incorrectly mixes in ionic H⁺ + H⁻ character, a known flaw that more advanced MO methods correct.

Where MO theory shines

• Magnetism (O₂, B₂, radicals such as NO).
• Fractional bond orders and ions (O₂⁺, O₂⁻, He₂⁺).
• Spectroscopy and colour: electrons jump between MOs; the HOMO–LUMO gap sets which light is absorbed (see sigma and pi bonds).
• Delocalisation and aromaticity without resonance.
• Computational chemistry: most modern quantum chemistry software is built on MO methods.
• Metals and semiconductors: extending MO theory to huge numbers of atoms gives band theory, which explains why metals conduct and how semiconductors work (see metallic bonding).

Which is “right”?

Neither is the complete truth; both are approximations. When each is improved — VB with more resonance structures, MO with methods that mix in more electron configurations — they converge on the same answers. Modern valence bond methods are also used in research. The practical rule is: choose the model that makes the problem simplest while still giving the right answer.

A quick decision guide

Question	Use
What shape is this molecule?	VB (hybridisation, VSEPR)
How does this reaction mechanism work?	VB (curly arrows)
Is this species paramagnetic?	MO
What’s the bond order of an ion like O₂⁻?	MO
Why is this compound coloured?	MO
Why is benzene unusually stable?	MO (or VB with resonance)
Why do metals conduct?	MO / band theory

Common misconceptions

• “MO theory replaced VB theory.” Both remain in daily use for different purposes.
• “Hybrid orbitals are physically real.” They’re a mathematical description, as are MOs.
• “VB theory can’t handle delocalisation.” It can, through resonance — just less compactly.
• “The two theories disagree about electron density.” Properly done, they describe the same total electron distribution.

Key takeaways

• VB theory: localised electron-pair bonds from overlapping (often hybrid) orbitals; great for shapes and mechanisms.
• MO theory: delocalised molecular orbitals, including antibonding ones; great for magnetism, bond order, spectra and delocalisation.
• O₂’s paramagnetism and methane’s photoelectron spectrum are key evidence that MO captures things simple VB misses.
• Both are approximations that converge when refined; chemists pick the one that fits the question.

For the MO basics, see molecular orbital theory for beginners.