# 5f atomic orbitals

For any atom, there are seven 5f orbitals. The f-orbitals are unusual in that there are two sets of orbitals in common use. The first set is known as the general set, this page. The second set is the cubic set, this page and these might be appropriate to use if the atom is in a cubic environment, for instance. Three of the orbitals are common to both sets. These are are the 5fxyz, 5fz3, and 5fz(x2-y2) orbitals.

The higher f-orbitals ( 6f and 7f) are more complex since they have more spherical nodes while the lower orbitals (5f) have none.

## 5f atomic orbitals general set

The shape of the seven 5f orbitals (general set). From left to right: (top row) 5fz3, (next to top row) 5fyz2, 5fxz2, (next to bottom row) 5fxyz, and 5fz(x2-y2), (bottom row) 5fy(3x2-y2), 5fx(x2-3y2). For each, the green zones are where the wave functions have positive values and the white zones denote negative values.

In the general set of 5f orbitals, there are four distinct shapes, each of which possess a number of planar and conical nodes. The 5f orbitals do not possess any radial nodes.

The 5fz3 orbital (top row in the image above) has a planar node in the xy plane and two conical nodes with their exes along the z-axis.

The 5fyz2 and 5fxz2 orbitals (next to top row in the image above) are related to each other by a 90° rotation about the z-axis. At first sight, they are similar in shape to the 5fy(3x2-y2) and 5fx(x2-3y2) orbitals but they are not. While these orbitals contain six lobes, the nodal planes are not at 60° to each other and two of the six lobes are "bean-shaped".

The 5fxyz and 5fz(x2-y2) (next to bottom row in the image above) each have eight lobes and are related to each other by a 45° rotation about the z-axis. Each orbital has three nodal planes, which for the 5fxyz are the xy, xz, and yz planes.

The 5fy(3x2-y2) and 5fx(x2-3y2) orbitals (bottom row in the image above) are related to each other by a 90° rotation about the z-axis. Each orbital has six lobes separated by three nodal planes lying at 60° to each other.

## 5f atomic orbitals cubic set

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

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

The OrbitronTM, a gallery of orbitals on the WWW: https://winter.group.shef.ac.uk/orbitron/