Atomic orbitals: 6f 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 6f 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 6f 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.

6fz3, 6fx3, and 6fy3 electron "dot-density"

The 6fz3, 6fx3, and 6fy3 orbitals are all in the cubic set of 6f. Additionally, the 6fz3 orbital appears in the general set.

Electron dot-density plot of the 6f_zzz orbital.
The first image shows a two-dimensional electron dot-density plot of the 6fz3 orbital (z-axis is vertical). The 6fx3, and 6fy3 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.

6fxz2 and 6fyz2 electron "dot-density"

The 6fxz2, 6fx3, and 6fy3 orbitals are both in the general set of 6f but neither is in the cubic set.

Electron dot-density plot of the 6f_xzz orbital.
The first image shows a two-dimensional electron dot-density plot of the 6fxz2 orbital (across the x=0 plane). The 6fyz2is 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.

6fxyz and 6fz(x2-y2) electron "dot-density"

The 6fxyz and 6fz(x2-y2) orbitals are both in the general set of 6f and both in the cubic set. The cubic set also contains 6fx(z2-y2) and 6fy(z2-x2) orbitals which are the same in appearance, differing only in direction.

Electron dot-density plot of the 6f_xyz orbital.
The first image shows a two-dimensional electron dot-density plot of the 6fxyz orbital (across the x=y plane). The 6fxyz and 6fz(x2-y2) 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 second image is an interactive (see below for instructions) represention of electron density in three-dimensions for the same orbitals.

6fy(3x2-y2) and 6fx(x2-3y2) electron "dot-density"

The 6fy(3x2-y2) and 6fx(x2-3y2) orbitals are both in the general set of 6f but neither is in the cubic set.

Electron dot-density plot of the 6f_xxx_3xyy orbital.
The first image shows a two-dimensional electron dot-density plot of the 6fx(x2-3y2) orbital (across the z=0 plane, x axis pointing right). The 6fy(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

The OrbitronTM, a gallery of orbitals on the WWW: https://winter.group.shef.ac.uk/orbitron/
Copyright 2002-2021 Prof. Mark Winter [The University of Sheffield]. All rights reserved.