Point-group determination

Genuine symmetry-element detection from 3D coordinates (rotation axes, mirror planes, an inversion center), combined into a point-group classification, and the corresponding character tables.

Schoenflies point-group symbols for water, ammonia, methane, and carbon dioxide

Schoenflies point-group symbols for water, ammonia, methane, and carbon dioxide

Werner’s coordination theory: counting isomers to prove the octahedron

Werner's coordination theory: counting isomers to prove the octahedron

Mulliken symbols: reading the labels of irreducible representations

Mulliken symbols: reading the labels of irreducible representations

Bethe’s crystal-field splitting: d orbitals in an octahedral field

Bethe's crystal-field splitting: d orbitals in an octahedral field