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Atomic orbitals: 4f (cubic set)

For any atom, there are seven 4f orbitals. The f-orbitals are unusual in that there are two sets of orbitals in common use. Those shown here are the cubic set and these are appropriate to use if the atom is in a cubic environment, for instance. The other set is known as the general set. Three of the orbitals are common to both sets. These are are the 4fxyz, 4fz3, and 4fz(x2-y2) orbitals.

Follow the links towards the base of the page for information about individual orbitals.

The shape of the seven 4f orbitals (cubic set). From left to right: (top row) 4fy3, 4fx3, 4fz3, (middle row) 4fx(z2-y2), 4fy(z2-x2), 4fz(x2-y2), and (bottom row) 4fxyz. For each, the copper zones are where the wave functions have negative values and the gold zones denote positive values.

In the cubic set of 4f orbitals, there are two distinct shapes, each of which possess a number of planar and conical nodes. None of the 4f orbitals possess radial nodes.

The 4fxyz, 4fx(z2-y2), 4fy(z2-x2), and 4fz(x2-y2) (bottom two rows in the image above) each have eight lobes. The 4fx(z2-y2), 4fy(z2-x2), and 4fz(x2-y2) orbitals are related to each other by 45° rotations about the x, y, and z-axis respectively. Each orbital has three nodal planes, which for the 4fxyz are the xy, xz, and yz planes.

The 4fx3, 4fy3, and 4fz3 orbitals (top row in the image above) has a planar node in the xy plane and two conical nodes orientated along the z-axis. The other two orbitals are related through 90° rotations.

Links to 4f wave functions

Links to 4f electron density functions

Links to 4f electron "dot-density" functions

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Document served: Wednesday 21st October, 2020