Atomic orbitals: 7f 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 7f 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 7f 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.

7fz3, 7fx3, and 7fy3 electron "dot-density"

The 7fz3, 7fx3, and 7fy3 orbitals are all in the cubic set of 7f. Additionally, the 7fz3 orbital appears in the general set.

Electron dot-density plot of the 7f_zzz orbital.
The first image shows a two-dimensional electron dot-density plot of the 7fz3 orbital (z-axis is vertical). The 7fx3, and 7fy3 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.

7fxz2 and 7fyz2 electron "dot-density"

The 7fxz2, 7fx3, and 7fy3 orbitals are both in the general set of 7f but neither is in the cubic set.

Electron dot-density plot of the 7f_xzz orbital.
The first image shows a two-dimensional electron dot-density plot of the 7fxz2 orbital (across the x=0 plane). The 7fyz2is 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.

7fxyz and 7fz(x2-y2) electron "dot-density"

The 7fxyz and 7fz(x2-y2) orbitals are both in the general set of 7f and both in the cubic set. The cubic set also contains 7fx(z2-y2) and 7fy(z2-x2) orbitals which are the same in appearance, differing only in direction.

Electron dot-density plot of the 7f_xyz orbital.
The first image shows a two-dimensional electron dot-density plot of the 7fxyz orbital (across the x=y plane). The 7fxyz and 7fz(x2-y2) are related to each other by a 45° rotation about the z-axis. Each orbital has three nodal planes, which for the 7fxyz 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.

7fy(3x2-y2) and 7fx(x2-3y2) electron "dot-density"

The 7fy(3x2-y2) and 7fx(x2-3y2) orbitals are both in the general set of 7f but neither is in the cubic set.

Electron dot-density plot of the 7f_xxx_3xyy orbital.
The first image shows a two-dimensional electron dot-density plot of the 7fx(x2-3y2) orbital (across the z=0 plane, x axis pointing right). The 7fy(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 2002-2023 Prof. Mark Winter [The University of Sheffield]. All rights reserved.