Molecular Geometry & Bonding
what the shape decides
Figure

Every set of point groups here that shares a table

Found by comparing character matrices rather than named: five sets among the tabulated groups, at orders 2, 4, 6, 8, 20. The smallest is the most startling — a mirror plane, a centre of inversion and a twofold axis all have the two-row table with entries 1, 1 and 1, −1, and one of the three describes a chiral molecule. The largest is the eclipsed and staggered conformers of ferrocene, which are one molecule at two temperatures.
Every set of point groups here that shares a table. Found by comparing character matrices rather than named: five sets among the tabulated groups, at orders 2, 4, 6, 8, 20. The smallest is the most startling — a mirror plane, a centre of inversion and a twofold axis all have the two-row table with entries 1, 1 and 1, −1, and one of the three describes a chiral molecule. The largest is the eclipsed and staggered conformers of ferrocene, which are one molecule at two temperatures.

One of the figures on representations: Character tables generated from a molecule's own operations, bases reduced in them, and what a descent in symmetry does to a level.

One essay draws this figure, each at the values its own argument needs rather than at the setting shown above. What each one uses it to show is below, in the words of its own caption.

In the essays

One table, three groups

Every set of point groups here sharing a character table, found by comparing matrices rather than by being named. Four sets, at orders 2, 4, 8 and 20.

The character table of C₂ᵥ, C₂ₕ and D₂ — all three of them. The rows are printed once because there is only one set of rows. The class sizes agree, the characters agree, and only the class labels differ.

The three groups and four questions a chemist asks of a group. Not one of the answers can be read off the numbers.

Every figure · Every orbital, by what it encloses · All essays