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Atomic orbitals: 4f wave functions

This page addresses the 4fxyz, 4fx(z2-y2), 4fy(z2-x2), and 4fz(x2-y2) wave functions. See below for links to images of the wave functions of the other 4f wave functions.

Schematic plot of the 4f wave function ψ4fxyz.

The line graph on the left is a plot of values along along the x = y = z line. The surface plot is on the x = y plane, so the line plot is along the diagonal from bottom left to top right of the surface plot.

The 4fxyz, 4fx(z2-y2), 4fy(z2-x2), and 4fz(x2-y2) are identical in appearance and differ only is direction. The 4fx(z2-y2), 4fy(z2-x2), and 4fz(x2-y2) orbitals can be generated from the 4fxyz orbital by 45° rotations about the x-, y-, and z-axes respectively. This is best seen when viewing all four together.

Links to 4f wave functions

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Document served: Monday 28th September, 2020