For any atom, there are seven 4*f* 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 4*f**xyz*, 4*f**z*3, and 4*f**z*(*x*2-*y*2) orbitals.

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The higher *f*-orbitals (5*f*, 6*f*, and 7*f*) are more complex since they have one or more spherical nodes.

## 4*f* atomic orbitals general set

**The shape of the seven 4 f orbitals (general set).** From left to right: (top row) 4

*f*

*z*3, (next to top row) 4

*f*

*y*

*z*2, 4

*f*

*x*

*z*2, (next to bottom row) 4

*f*

*xyz*, and 4

*f*

*z*(

*x*2-

*y*2), (bottom row) 4

*f*

*y*(3

*x*2-

*y*2), 4

*f*

*x*(

*x*2-3

*y*2). For each, the green zones are where the wave functions have positive values and the white zones denote negative values.

The seven 4*f* orbitals. Use the previous and next icons to see other views

The seven 4*f* orbitals including orbital nodes. Use the previous and next icons to see other views

Nodes of the seven 4*f* orbitals. Use the previous and next icons to see other views

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In the general set of 4*f* orbitals, there are four distinct shapes, each of which possess a number of planar and conical nodes. The 4*f* orbitals do not possess any radial nodes.

The 4*f**z*3 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 4*f**y**z*2 and 4*f**x**z*2 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 4*f**y*(3*x*2-*y*2) and 4*f**x*(*x*2-3*y*2) 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 4*f**xyz* and 4*f**z*(*x*2-*y*2) (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 4*f**xyz* are the *xy*, *xz*, and *yz* planes.

The 4*f**y*(3*x*2-*y*2) and 4*f**x*(*x*2-3*y*2) 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.

## 4*f* atomic orbitals cubic set

**The shape of the seven 4 f orbitals (cubic set).** From left to right: (top row) 4

*f*

*y*3, 4

*f*

*z*3, 4

*f*

*x*3, (middle row) 4

*f*

*y*(

*z*2-

*x*2), 4

*f*

*z*(

*x*2-

*y*2), and 4

*f*

*x*(

*z*2-

*y*2)(bottom row) 4

*f*

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

The 4*f**xyz*, 4*f**x*(*z*2-*y*2), 4*f**y*(*z*2-*x*2), and 4*f**z*(*x*2-*y*2) (bottom two rows in the image above) each have eight lobes. The 4*f**x*(*z*2-*y*2), 4*f**y*(*z*2-*x*2), and 4*f**z*(*x*2-*y*2) 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 4*f**xyz* are the *xy*, *xz*, and *yz* planes.

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The 4*f**x*3, 4*f**y*3, and 4*f**z*3 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.