# Atomic orbitals: 6*f* 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 6*f* 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 6*f* 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.

## 6*f*_{z3}, 6*f*_{x3}, and 6*f*_{y3} electron "dot-density"

The 6*f*_{z3}, 6*f*_{x3}, and 6*f*_{y3} orbitals are all in the cubic set of 6*f*. Additionally, the 6*f*_{z3} orbital appears in the general set.

*f*

_{z3}orbital (

*z*-axis is vertical). The 6

*f*

_{x3}, and 6

*f*

_{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.

## 6*f*_{xz2} and 6*f*_{yz2} electron "dot-density"

The 6*f*_{xz2}, 6*f*_{x3}, and 6*f*_{y3} orbitals are both in the general set of 6*f* but neither is in the cubic set.

*f*

_{xz2}orbital (across the

*x*=0 plane). The 6

*f*

_{yz2}is 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.

## 6*f*_{xyz} and 6*f*_{z(x2-y2)} electron "dot-density"

The 6*f*_{xyz} and 6*f*_{z(x2-y2)} orbitals are both in the general set of 6*f* and both in the cubic set. The cubic set also contains 6*f*_{x(z2-y2)} and 6*f*_{y(z2-x2)} orbitals which are the same in appearance, differing only in direction.

*f*

_{xyz}orbital (across the

*x*=y plane). The 6

*f*

_{xyz}and 6

*f*

_{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 6

*f*

_{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.

## 6*f*_{y(3x2-y2)} and 6*f*_{x(x2-3y2)} electron "dot-density"

The 6*f*_{y(3x2-y2)} and 6*f*_{x(x2-3y2)} orbitals are both in the general set of 6*f* but neither is in the cubic set.

*f*

_{x(x2-3y2)}orbital (across the

*z*=0 plane,

*x*axis pointing right). The 6

*f*

_{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

The Orbitron

^{TM}, 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.