Molecular Geometry & Bonding
what the shape decides
Concept

Octet — where it appears

Eight valence electrons round a second-row atom, which is what four valence orbitals hold. The count follows from the orbitals available and fails where more than four centres share them.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

sulfur hexafluoride — Oh. The molecule with the point group found from its coordinates rather than looked up: every candidate operation was applied and kept when it permuted the atoms among themselves.

Hypervalency without d orbitals

Sulfur hexafluoride is not d²sp³ hybridised. The d orbitals are far too high in energy to contribute meaningfully, the bonding is three-centre four-electron, and the textbook account has been known to be wrong for fifty years.

beyond · Hypervalency Hückel levels of three-centre four-electron. The orbital energies of the pi system, computed as the eigenvalues of the molecule's adjacency matrix. Degenerate levels share a line. The electrons are placed by aufbau with Hund's rule, so a half-filled degenerate shell shows as two unpaired spins.

Three-centre bonding, computed

Three orbitals in a line and four electrons: a bonding level, a level with exactly zero amplitude on the central atom, and an empty antibonding one. The middle atom never exceeds an octet, and the ligands carry the charge — which is why every molecule that needs this arrangement has electronegative ligands.

beyond · Hypervalency Where the orphan pair actually sits. A σ-only Hückel model of each molecule, built from its own coordinates: the central atom's four valence orbitals, one σ orbital on each ligand, and the coupling between them the direction cosine of that ligand. Lone pairs need no special handling — they come out of the diagonalisation as the central orbitals no ligand combination transforms like. The charge is measured rather than assigned, and PF₅ comes out with two kinds of fluorine at 3 at -0.13 and 2 at -0.3, the more charged pair being the axial one that carries the orphan.

The count is the population

The census counted how many ligand combinations have no partner on the central atom and called the count n + L − 4. A σ-only model built from each molecule's own coordinates says what that count is worth: with no electronegativity difference anywhere, the mean charge on a ligand is minus the orphan count divided by the ligand count, exactly, in all ten cases. And the prediction the census made — that the charge grows with the orphan count — is refused by the divisor.

beyond · Hypervalency

Named alongside it

The objects these essays reach for when they reach for this one.

ElectronegativityHypervalencyNon-bonding orbitalsThree-centre bondingAxialCharge densityd orbitalsEigenvectorElectron-deficient bondingEquatorialIrreducible representationsLone pair

All concepts