What Molecular Orbital Theory actually claims
Valence Bond Theory treats a bond as two atoms sharing a patch of overlapping electron cloud while keeping their own orbital identities. MOT rejects that picture entirely. The moment two atoms approach, their atomic orbitals (AOs) stop existing as separate entities — they combine, mathematically and physically, into brand-new orbitals called molecular orbitals (MOs) that belong to the whole molecule, not to either nucleus alone.
This combination is called the Linear Combination of Atomic Orbitals (LCAO): ψMO = c₁ψA ± c₂ψB. The + combination is in-phase addition — the two wavefunctions reinforce between the nuclei, electron density piles up there, and the resulting orbital sits lower in energy than either parent AO. That is a bonding MO. The − combination is out-of-phase — the waves cancel between the nuclei, a node (zero probability plane) appears right where the bond should be, and the orbital sits higher in energy. That is an antibonding MO, marked with a star (σ*, π*).
Same energy
Only AOs of comparable energy combine effectively — 1s only really combines with 1s, 2s with 2s, and so on.
Same symmetry about the bond axis
The orbitals must have matching symmetry — a 2pz pointed along the bond axis combines head-on; a 2px lying sideways cannot combine with it.
Maximum overlap
The greater the overlap between the two AOs, the lower the bonding MO drops and the stronger the resulting bond.
Phase, not distance, decides bond vs antibond
Whether the result is bonding or antibonding is decided purely by the relative sign (phase) of the two wavefunctions where they meet — this is the single idea the whole lab is built to make visible.
Four overlap geometries, four orbital types
| Combining AOs | Orientation | Resultant (bonding) | Resultant (antibonding) | Nodal planes containing the axis |
|---|---|---|---|---|
| 1s + 1s, 2s + 2s | Head-on, spherical | σ (sigma) | σ* | 0 |
| 2pz + 2pz | Head-on, along bond axis | σ2p | σ*2p | 0 |
| 2px + 2px (or 2py+2py) | Sideways, parallel lobes | π2p | π*2p | 1 |
σ orbitals are symmetric about the bond axis — rotate them around the axis and nothing changes. π orbitals are not: they always carry one nodal plane that contains the internuclear axis itself, which is exactly why every diatomic molecule has at most one σ bond but can have up to two π bonds (from the two perpendicular p-orbital pairs).
Orbital Combination Lab
Two 1s orbitals approach in-phase. Amplitude reinforces between the nuclei — electron density builds up right where it can attract both nuclei at once.
Reading the shapes
σ bonding: one continuous, cigar-shaped cloud wrapped around both nuclei along the bond axis. No node between them — this is the strongest possible bond for a given pair of AOs because the overlap is head-on and maximal.
σ* antibonding: the cloud is pinched to zero exactly at the midpoint. Electron density is thrown to the outside of each atom instead of the region between them, so instead of holding the nuclei together it lets them fly apart.
π bonding: two lobes — one above, one below the bond axis — each spanning both nuclei as one continuous piece. The plane containing the two nuclei is always a node; that's the defining feature of every π orbital, bonding or not.
π* antibonding: the merge breaks — each atom keeps its own separate lobes now, with a second node opening up between the nuclei in addition to the permanent one along the axis. Two nodal planes total.
Phase matching, in the wave language
Top: the two atomic wavefunctions ψA and ψB. Middle: their sum, ψMO. Bottom: electron probability density |ψMO|² — this is the curve that becomes the 3D orbital cloud.
MO Energy Level Diagram Builder
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Energy ordering — and why it flips after N₂
For Li₂, Be₂, B₂, C₂, N₂ (low nuclear charge, noticeable 2s–2p mixing):
σ1s < σ*1s < σ2s < σ*2s < π2px=π2py < σ2pz < π*2px=π*2py < σ*2pz
For O₂, F₂, Ne₂ (higher nuclear charge, 2s–2p mixing negligible):
σ1s < σ*1s < σ2s < σ*2s < σ2pz < π2px=π2py < π*2px=π*2py < σ*2pz
Quick reference table — all second-period homonuclear diatomics
| Species | Electrons | Bond order | Exists? | Magnetic nature |
|---|---|---|---|---|
| H₂ | 2 | 1 | Yes | Diamagnetic |
| He₂ | 4 | 0 | No | — |
| Li₂ | 6 | 1 | Yes | Diamagnetic |
| Be₂ | 8 | 0 | No (MOT prediction) | — |
| B₂ | 10 | 1 | Yes | Paramagnetic |
| C₂ | 12 | 2 | Yes | Diamagnetic |
| N₂ | 14 | 3 | Yes | Diamagnetic |
| O₂ | 16 | 2 | Yes | Paramagnetic |
| F₂ | 18 | 1 | Yes | Diamagnetic |
| Ne₂ | 20 | 0 | No | — |
Bond order 0 means bonding and antibonding electrons cancel exactly — the "molecule" has no net attraction and does not form. Higher bond order → shorter, stronger bond and higher bond dissociation energy.
Definitions worth memorising verbatim
| Term | Meaning |
|---|---|
| Bonding MO | Lower energy than parent AOs; formed by in-phase (constructive) combination; increases electron density between nuclei. |
| Antibonding MO (*) | Higher energy than parent AOs; formed by out-of-phase (destructive) combination; has a node between the nuclei. |
| Nonbonding MO | Energy essentially unchanged from the AO; occurs when symmetry mismatch prevents effective overlap. |
| Bond order | ½ (electrons in bonding MOs − electrons in antibonding MOs). Predicts bond existence, strength, and length. |
| Paramagnetic | Contains one or more unpaired electrons in the MO configuration; weakly attracted into a magnetic field. |
| Diamagnetic | All electrons paired; weakly repelled by a magnetic field. |