An illustration of the shape of the 4f orbitals

The lanthanide series is defined by the progressive filling of the 4f orbitals. These seven orbitals have the following ml values:

ml=0, ±1, ±2, ±3

ml=0 are real, all the others are complex and so linear combinations must be taken to obtain real orbitals.

General set

These are produced by simply taking linear combinations of ml=±1, ±2, ±3






xz2 yz2


xyz z(x2-y2)


x(x2-3y2) y(3x2-y2)

Explore other atomic orbitals

s-orbitals |2p-orbitals |3p-orbitals | 3d-orbitals | 4f-orbitals

Comparison of 1s, 2s and 2p-orbitals