Pauling's rules

Pauling's rules are five practical guidelines, published by Linus Pauling in 1929, for predicting and rationalising the structures of ionic crystals. Before computers could calculate crystal energies, these rules let chemists reason about why an oxide or silicate looks the way it does, using little more than ion sizes and charges. They remain a superb intuition-builder.

The five, in plain terms. First, each cation sits in a polyhedron of anions whose type (tetrahedron, octahedron, cube) is set by the radius ratio. Second, the electrostatic valence rule: an anion's charge is balanced locally by the sum of bond strengths reaching it from its cation neighbours, so charges cancel neighbourhood by neighbourhood, not just overall. Third, sharing edges and especially faces between coordination polyhedra lowers stability, because it pushes the positive cations closer together. Fourth, this sharing-avoidance is strongest for small, highly charged cations. Fifth, the rule of parsimony: a structure tends to use only a few chemically distinct kinds of site.

These rules are qualitative and have exceptions, especially where bonding is covalent rather than ionic, but they are remarkably effective for oxides and silicates and explain real facts, for instance why silicate tetrahedra share corners rather than edges. The second rule, local charge balance, is generally the sharpest and most reliable of the five, and a modern refinement of it (the bond-valence method) is still used today.