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Atomic orbitals: 6f (general set)

For any atom, there are seven 6f orbitals. The f-orbitals are unusual in that there are two sets of orbitals in common use. Those shown here are the general set. The other set is known as the cubic set and might be more appropriate to use if the atom is in a cubic environment. Three of the orbitals are common to both sets. These are are the 6fxyz, 6fz3, and 6fz(x2-y2) orbitals.

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

The shape of the seven 6f orbitals (general set). From left to right: (top row) 6fz3, (next to top row) 6fxz2, 6fyz2, (next to bottom row) 6fy(3x2-y2), 6fx(x2-3y2), (bottom row) 6fxyz, and 6fz(x2-y2). For each, the copper zones are where the wave functions have negative values and the blue zones denote positive values.

In the general set of 6f orbitals, there are four distinct shapes, each of which possess a number of planar and conical nodes. Each of the 6f orbitals possess two radial nodes.

The 6fxyz and 6fz(x2-y2) (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 6fxyz are the xy, xz, and yz planes.

The 6fy(3x2-y2) and 6fx(x2-3y2) orbitals (next to 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.

The 6fxz2 and 6fyz2 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 6fy(3x2-y2) and 6fx(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". Look closely! In the case of the 6fxz2 orbital these two bean-shaped lobes lie on the x-axis while in the 6fyz2 case they lie along the y-axis. These differences may be appreciated better by examining the electron density plots for the 6fxz2 and 6fx(x2-3y2) orbitals.

The 6fz3 orbital (top row in the image above) has a planar node in the xy plane and two conical nodes orientated along the z-axis.

Links to 6f wave functions

Links to 6f electron density functions

Links to 6f electron "dot-density" functions

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Document served: Monday 20th August, 2018