Atomic orbitals: 4f electron "dot-density"

This page shows representations of electron density in two ways. The first is two-dimensional electron "dot-density" diagrams - plots across an appropriate plane of each 4f orbital. These were created using a Monte Carlo computational method. The second page allows you interact (zoom, rotate) with three-dimensional electron "dot-density" models representing electron density of the various 4f atomic orbitals created by the same Monte Carlo computational method. Green represents regions for which the wave functions are positive and white represents where values are negative.

4f_z³, 4f_x³, and 4f_y³ electron "dot-density"

The 4f_z³, 4f_x³, and 4f_y³ orbitals are all in the cubic set of 4f. Additionally, the 4f_z³ orbital appears in the general set.

The first image shows a two-dimensional electron dot-density plot of the 4f_z³ orbital (z-axis is vertical). The 4f_x³, and 4f_y³ plots are identical in appearance but respectively with x-axis vertical and y-axis vertical. The second image is an interactive (see below for instructions) represention of electron density in three-dimensions for the same orbitals.

4f_xz² and 4f_yz² electron "dot-density"

The 4f_xz², 4f_x³, and 4f_y³ orbitals are both in the general set of 4f but neither is in the cubic set.

The first image shows a two-dimensional electron dot-density plot of the 4f_xz² orbital (across the x=0 plane). The 4f_yz²is identical in appearance but rotated by 90° about the y-axis. The second image is an interactive (see below for instructions) represention of electron density in three-dimensions for the same orbitals.

4f_xyz and 4f_z(x²-y²) electron "dot-density"

The 4f_xyz and 4f_z(x²-y²) orbitals are both in the general set of 4f and both in the cubic set. The cubic set also contains 4f_x(z²-y²) and 4f_y(z²-x²) orbitals which are the same in appearance, differing only in direction.

The first image shows a two-dimensional electron dot-density plot of the 4f_xyz orbital (across the x=y plane). The 4f_xyz and 4f_z(x²-y²) are related to each other by a 45° rotation about the z-axis. Each orbital has three nodal planes, which for the 4f_xyz are the xy, xz, and yz planes. The second image is an interactive (see below for instructions) represention of electron density in three-dimensions for the same orbitals.

4f_y(3x²-y²) and 4f_x(x²-3y²) electron "dot-density"

The 4f_y(3x²-y²) and 4f_x(x²-3y²) orbitals are both in the general set of 4f but neither is in the cubic set.

The first image shows a two-dimensional electron dot-density plot of the 4f_x(x²-3y²) orbital (across the z=0 plane, x axis pointing right). The 4f_y(3x²-y²) orbital is identical in appearance but rotated by 90° about the z-axis. The second image is an interactive (see below for instructions) represention of electron density in three-dimensions for the same orbitals.

Using JSmol

You can use your mouse to manipulate the "orbital" in the "JSmol" image above. How you do this depends upon how you are viewing this page.

• On a computer, to rotate about the x and y directions, drag mouse around the image
• On a computer, to rotate about the z direction (which comes out of the screen towards you), hold shift and drag mouse horizontally
• To zoom, hold shift key down and drag mouse vertically
• To reset the image, hold down shift key and double click ony part of the image not containing dots
• On a mobile device experiment using one or two fingers to rotate and zoom