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Atomic orbitals: 5f (cubic set)

For any atom, there are seven 5f 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 5fxyz, 5fz3, and 5fz(x2-y2) orbitals.

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

The shape of the seven 5f orbitals (cubic set). From left to right: (top row) 5fy3, 5fx3, 5fz3, (middle row) 5fx(z2-y2), 5fy(z2-x2), 5fz(x2-y2), and (bottom row) 5fxyz. For each, the blue zones are where the wave functions have negative values and the silver zones denote positive values.

In the cubic set of 5f orbitals, there are two distinct shapes, each of which possess a number of planar and conical nodes. Each of the 5f orbitals possess one radial node.

The 5fxyz, 5fx(z2-y2), 5fy(z2-x2), and 5fz(x2-y2) (bottom two rows in the image above) each have eight lobes. The 5fx(z2-y2), 5fy(z2-x2), and 5fz(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 5fxyz are the xy, xz, and yz planes.

The 5fx3, 5fy3, and 5fz3 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 5f wave functions

Links to 5f electron density functions

Links to 5f electron "dot-density" functions

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Document served: Wednesday 21st October, 2020