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Atomic orbitals: 4f electron density

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

Schematic plot of the 4fxyz electron density function ψ4fxyz. Blue represents negative values for the wave function and red represents positive values. Each of the eight lobes is identical as regards shape but each is orientated in a different direction.

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 "surface" of the orbital represents points for which the electron density for that orbital is the same - an isosurface. By choosing different values of electron density, denoted by the bar moving up and down on the line plot or by the moving plane on the surface plot, then the size of the three-dimensional plot changes.

All values are of necessity not negative since the square of any real number cannot be less than zero.

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 electron density functions

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Document served: Monday 28th September, 2020