Molecular Geometry & Bonding
what the shape decides
Concept

Valence — where it appears

The electrons of an atom's outermost shell and the orbitals holding them, which for a main-group atom is one s and three p. The count of four is what limits how many ligand combinations can find a partner, and everything beyond it has to be accommodated without a central orbital.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

benzene — D6h. 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.

Counting electrons in an extended structure

The octet rule, Hückel's 4n + 2 and the 8 − N rule that predicts the structures of the main-group elements are one rule counted three ways. Each says the same thing — close the shell — and each stops being reliable at exactly the point where closing it becomes impossible.

solids · Metal Four, however many ligands there are. For each molecule, the number of ligand σ combinations that find a partner among the central atom's four s and p orbitals, against the number of ligands and lone pairs it has. The matched count rises along the diagonal and then stops at four, because there are four orbitals; everything above the ceiling is a pair with nowhere on the central atom to go, and that is what the word hypervalent names.

Four is all that s and p can match

Reduce the ligand σ set of ten molecules in each one's own point group and ask how many of its components transform as one of the central atom's four valence orbitals. The answer is never more than four — not by arrangement, in every geometry from linear to octahedral — and what is left over is n + L − 4, with exactly twice that many electrons in excess of an octet.

beyond · Hypervalency

Named alongside it

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

Electron countOctet ruleBands in a solidClosed-shell configurationsCoordination numberFillingHOMO–LUMO gapHypervalencyInsulatorIrreducible representationsLone pairMetal

All concepts